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A MODEL INDEPENDENT SEARCH FOR NEW PHYSICS IN

FINAL STATES CONTAINING LEPTONS AT THE DZ
EXPERIMENT

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Joel M. Piper

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A MODEL INDEPENDENT SEARCH FOR NEW PHYSICS IN FINAL STATES
CONTAINING LEPTONS AT THE DO EXPERIMENT

By
Joel M. Piper

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Physics and Astronomy

2010

ABSTRACT

A MODEL INDEPENDENT SEARCH FOR NEW PHYSICS IN FINAL STATES
CONTAINING LEPTONS AT THE DO EXPERIMENT

By
Joel M. Piper

The standard model is known to be the low energy limit of a more general theory. Sev-
eral consequences of the standard model point to a strong probability of new physics
becoming experimentally visible in high energy collisions of a few TeV, resulting in
high momentum objects. The speciﬁc signatures of these collisions are tepics of much
debate. Rather than choosing a specific signature, this analysis broadly searches the
data, preferring breadth over sensitivity.

In searching for new physics, several different approaches are used. These include
the comparison of data with standard model background expectation in overall num-
ber of events, comparisons of distributions of many kinematic variables, and ﬁnally
comparisons on the tails of distributions that sum the momenta of the objects in an
event.

With 1.07 fb—1 at the DO experiment, we ﬁnd no evidence of physics beyond the
standard model. Several discrepancies from the standard model were found, but none

of these provide a compelling case for new physics.

For Kirsten

iii

Acknowledgements

First, I would like to thank my thesis adviser, J irn Linnemann. As I was struggling
to ﬁnd a research position upon my return from France, Jim was willing to take a
chance on me. He provided me speciﬁc guidance when I needed it and at the same
time gave me the independence and responsibility I needed to mature as a scientist.
Throughout all of the ups and downs of this analysis, I never had any question that
Jim was behind me, supporting me every step of the way.

I would like to thank Jim Kraus, who took as long as I needed to answer all of my
daily questions about physics and research methods, while at the same time providing
a steady stream of obscure historical facts and cultural minutiae.

I would like to thank Chip Brock, who introduced me to the world of high energy
physics. It was intimidating at ﬁrst, but I got the hang of it.

I would like to thank the other current and former members of my guidance
committee: Sekhar Chivukula, C.P. Yuan, Gary Westfall, and Carlo Piermarocchi. I
never failed to leave a committee meeting without a clear idea of how much more I
had to learn.

I would like to thank all current and former members of the L2 team. Linnematm,
Bob, Kraus, Miroslav, Abaz, Roger, and Reinhard all helped change my response to a
2 A.M. page from sheer panic into mild annoyance. Thanks also to Mandy, Shannon,
Ernest, Mikolaj, Ike, James, Weigang, Emmanuel, and Enrique.

I would like to thank all of the current and former members of the MIS group:
Litmemann, Kraus, Nayeem, Peter, Prolay, Anatoly, Oleksiy, and especially Serban,
who taught me how to work through each step of a high energy physics analysis.
I would also like to thank the members of the editorial board, the NP conveners,
physics coordinators and DO spokespeople, who always took an active interest in the
analysis, particularly Todd, Arnaud, Horst, Aurelio, and Jean-Francois. Also, thanks

to Bruce for building the foundations for this search with his Run I work and for his

iv

early technical advice in this analysis.

I would like to thank eVeryone at MSU, especially Brenda and Debbie for all of
their hard work in making the group and the department function. Everything would
fall apart without you. Also, thank you Reinhard and Reiner, for your help in my
transition to DO.

I would like to thank Betta, Jorge, and Monica for making the hour-long commute
from Chicago bearable, sometimes even fun. Also, to my roommates, Gorge and
Mango, thanks for dragging me out of the house every now and then.

I would like to thank my in—laws for inviting me into their family and for their
generosity while Kirsten and I ﬁgure out our next steps.

I would like to thank the rest of my family, especially Mom, Dad, and Mary. When
immediately upon receiving my undergraduate degree in Environmental Engineering,
I had the crazy idea of getting a Ph.D. in particle physics, they didn’t blink. Knowing
that I always have their love and support has given me the courage to live life on my
own terms, making decisions based on hope rather than fear.

Finally, I would like to thank Kirsten. To get this degree, we spent years in
Lansing and years in Chicago with months of separation. My research often required
long hours and intense stress, but I was able to enjoy even the most difﬁcult times
because I knew that every night when I came home, the stress of the day would melt
away, and I’d be happy again. I really couldn’t have done this without you. Thank
you for going through this with tne. Thank you for your love and support. Thank

you for making my life so much happier. I love you.

Table of Contents

List of Tables ........... , ...................... x
List of Figures ................................ xii
Introduction . . . . . . ......... . . . . . ....... 1
Symmetry, the Standard Model and Beyond . . . . ....... 4
2.1 Symmetry ................................. 6
2.1.1 Symmetry and Conservation Laws ................ 6
2.1.2 Syrmnetry and Particle Interactions ............... 9
2.1.3 Symmetry and the Standard Model ............... 10
2.1.4 Symmetry, Broken ........................ 10

2.2 The Standard Model ........................... 14
2.2.1 Particles and Interactions .................... 15
2.2.2 Experimental Conﬁrmation ................... 18
2.2.3 Difﬁculties with the Standard Model .............. 19
2.2.3.1 Theoretical Difﬁculties ................. 19

2.2.3.2 Experimental Difﬁculties ................ 21

2.3 Beyond ................................... 23
2 .3. 1 Supersymmetry .......................... 23

2.3.2 Extra Dimensions ......................... 24
2.3.3 Technicolor ............................ 25
2.3.4 Experimental Signatures ..................... 26

2.4 Analysis Strategy ............ , ................. 27
2.4.1 DO MIS Analysis Packages ................... 27
2.4.2 VISTA ............................... 28
2.4.3 SLEUTH .............................. 28

The DC Experiment at the Fermilab Tevatron Collider ..... 30
3.1 The Fermilab Tevatron Collider ..................... 31
3.1.1 Creation and Acceleration of H _ ................ 31
3.1.1.1 Preaccelerator ...................... 31

3.1.1.2 Linac .......................... 33

3.1.2 Creation and Acceleration of the Proton Beam ......... 35
3.1.2.1 Booster ......................... 36

3.1.2.2 Main Injector ...................... 37

3.1.3 Antiproton Production and Storage ............... 40
3.1.3.1 Target .......................... 40

vi

3.1.3.2 Debuncher ....................... 41

3.1.3.3 Accumulator ...................... 43

3.1.3.4 Recycler ......................... 43

3.1.4 The Tevatron ........................... 45

3.2 The DO Experiment ........................... 46
3.2.1 Central Tracking, Solenoidal Magnet, and Preshower ..... 51
3.2.1.1 Silicon Microstrip Tracker ............... 53

3.2.1.2 Central Fiber Tracker ................. 56

3.2.1.3 Solenoidal Magnet ................... 58

3.2.1.4 Preshower Detectors .................. 59

3.2.2 Calorimeters and Intercryostat Detectors ............ 62
3.2.2.1 Calorimeters ...................... 64

3.2.2.2 Intercryostat Detectors and Massless Gaps ...... 66

3.2.3 The Muon System ........................ 67
3.2.3.1 Toroidal Magnets .................... 68

3.2.3.2 Central Muon ...................... 69

3.2.3.3 Forward Muon ..................... 71

3.3 The Trigger System, Data Acquisition, and Luminosity Measurement 74
3.3.1 'IYigger System .......................... 74
3.3.1.1 The Level 1 Trigger .................. 75

3.3.1.2 The Level 2 Trigger .................. 79

3.3.1.3 The Level 3 Trigger .................. 83

3.3.2 Data Acquisition ......................... 84
3.3.3 Luminosity ............................ 85
Event Reconstruction and Object Identiﬁcation ......... 88
4.1 Tracks and Vertices ............................ 89
4.1.1 Tracks ............................... 89
4.1.1.1 Alternate Algorithm (AA) ............... 90

4.1.1.2 Histogramming Track Finder ............. 92

4.1.1.3 Kalman Filter and Fit ................. 92

4.1.2 Primary Vertices ......................... 93
4.1.3 Secondary Vertices ........................ 96

4.2 Electromagnetic Objects ......................... 97
4.2.1 Electrons ............................. 100
4.2.2 Photons .............................. 102

4.3 Muons ................................... 103
4.4 Hadronic Objects ............................. 105
4.4.1 Taus ................................ 105
4.4.2 Jets ................................ 110
4.4.2.1 Jet Reconstruction ................... 110

4.4.2.2 Jet Energy Scale .................... 113

4.4.2.3 Jets from Bottom Quarks ............... 116

4.5 Missing Transverse Energy (ET) .................... 119

Vii

5 Data and Monte Carlo Samples . . . .............. 120
5.1 Data Sample ................................ 120
5.2 Monte Carlo Samples ........................... 121

5.2.1 Monte Carlo Production Process ................ 124
5.2.1.1 PYTHIA ......................... 124

5.2.1.2 ALPGEN ......................... 124

5.2.1.3 Additional MC Corrections .............. 126

5.2.2 Monte Carlo Samples ....................... 126
5.2.2.1 W boson + Jets .................... 127

5.2.2.2 Drell-Yan + Jets .................... 129

5.2.2.3 tf ............................. 132

5.2.2.4 Diboson ......................... 133

5.3 Multijets Background from Data .................... 133
5.3.1 Multijets Background Using Loose Electrons .......... 134
5.3.2 Multijets Background Using Non-isolated Muons ........ 136
5.3.3 Multijets Background Using Loose Taus ............ , 136

6 Corrections to Monte Carlo ............ . . . . . . . 139

6.1 Lepton Smearing and Efﬁciency ..................... 139
6.1.1 Muon Smearing .......................... 139
6.1.2 Electron Smearing ........................ 140
6.1.3 Muon Efﬁciency .......................... 141
6.1.4 Electron Efﬁciency ........................ 144

6.2 Jet Weights ................................ 145
6.2.1 JSSR ................................ 146
6.2.2 b—tagging Rate Correction .................... 149
6.2.3 'Itack Jet Finding (Taggability) Scale Factors ......... 150

6.3 Common Analysis Reweighting ..................... 152
6.3.1 Weak Gauge Boson PT Reweighting ............... 153
6.3.2 Luminosity and z Vertex Reweighting .............. 155

6.4 Analysis-speciﬁc Weights ......................... 155
6.4.1 Same Sign Reweighting ...................... 155
6.4.2 A¢ Correction ........................... 159

7 MIS Analysis Packages ....... . . . . .......... 162

7.1 Inclusive Final States ........................... 162
7.1.1 [1, + jets .............................. 164
7.1.2 6 + jets .............................. 164
7J”3 pp ................................. 165
7JH4 ee ................................. 165
7JH5 p7 ................................. 165
7JH6 eT ................................. 165
7JH7 pe ................................. 166

7.2 The MIS Fit ................................ 166

7.3 Text File Production ........................... 185

viii

8 VISTA and SLEUTH . . . ..................... 187

8.1 VISTA ................................... 187
8.1.1 Exclusive Final States ...................... 188
8.1.2 Final State Populations ..................... 196
8.1.3 Histogram Shapes ......................... 198
8.2 SLEUTH .................................. 198
8.2.1 SLEUTH Final States ....................... 208
8.2.2 SLEUTH Algorithm ........................ 209
8.2.3 tf Sensitivity Test .......................... 210
9 Results ............. . . . . ........... . 217
9.1 Model Independent Search Normalization Fits ............. 218
9.2 VISTA ................................... 218
9.3 SLEUTH ........................... . ....... 230
10 Conclusions . . . . . . . . . . ................. 239
A Level 2 Global . ........................ . 242
A.1 Data Flow ................................. 243
A2 TIigger Conﬁguration ........................... 246
A21 Quick Overview of Relation Among Components of Level 2
Trigger Decision .......................... 248
A3 Triggerbits, Superscripts, and Scripts .................. 252
A4 Filters and Tools ............................. 253
A5 L2 Global Packages ............................ 269
A6 Monitoring and Common Problems ................... 270
A7 Main Projects ............................... 283
A71 Triggering 011 Events with b—Jets ................. 283
A.7.2 Implementation of Electron Likelihood, Tau Objects, Spheric-
ity, and Acoplanarity ....................... 284
A73 L2 ﬁeta Multiple Processing Boards Study ........... 285
B The High-pT Data Format . . . . ................ 287
C Calculation of 75 . . . . . . . . . . . . . . . . . ....... 291
Bibliography . . . . . . . . . . . . ............. . 292

ix

2.1

2.2

2.3

3.1

5.1

5.2

01
w

5.4

6.1

7.1

7.2

7.3

List of Tables

The four fundamental forces with their approximate interaction dis—
tances and strengths [1]. .........................

The fundamental particles with their force-related quantum numbers
and masses [2]. ..............................

Fundamental particles, revised. This is an example of the full particle
content of the standard model. Each particle listed has a corresponding
antiparticle with opposite electromagnetic charge. Furthermore, each
particle has left-handed and right-handed members to determine if they
interact through the weak force. Additionally, quarks come in three
types of colors. The gluons carry color combinations and total eight
separate particles ..............................

Amount of material in each of the calorimeter layers measured in ra-
diation lengths, X0, and nuclear interaction lengths, AA. The outer
hadronic is ~ 6.0 A A thick ........................
W + jets samples ............ . ................
Drell—Yan Monte Carlo samples .....................
tf samples .................................
Diboson samples .............................
The width of the peaks using a best ﬁt to a double Gaussian. In both
the Z boson and J / ‘11 peaks, the Monte Carlo has a better energy

resolution than the data. This table was taken from [3] .........

Table of ﬁnal state object cuts: The seven inclusive ﬁnal states that
are being considered, along with their basic object cuts .........

Table of object cuts required for inclusion as additional objects (X) in
one of the seven ﬁnal states listed in Table 7 .1 ..............

Table of input processes for which the normalization is determined
from inclusive ﬁnal state ﬁts along with the ﬁnal states that are used
in determining its value. .........................

15

16

18

66

128

129

133

134

140

163

164

8.1

9.1

9.2

9.3

A.1

A2

A3

A4

A5

31

B2

The 180 VISTA ﬁnal states ......................... 188

The results of the MIS inclusive ﬁts for all inclusive ﬁnal states. Ignor-
ing k-factors and trigger efﬁciencies, all Monte Carlo samples should
ﬁt to 1.0 for 1.0 fb-1 of data. The dominant standard model process
is listed ﬁrst for each ﬁnal state ...................... 219

The full list of VISTA shape discrepant histograms listed by VISTA ﬁnal
state ..................................... 229

The top ﬁve SLEUTH states with only leptons and jets. The value ’P
represents the probability that the standard model background for an
individual ﬁnal state would have a ﬂuctuation at any cut that would be
more Signiﬁcant than what is seen in data. The variable P calculates
the probability that one would observe a ﬁnal state with ’P less than
or equal to the one observed in data based on a statistical ﬂuctuation. 233

The contents of the VME crate that houses the L2 Global processor.
Each card is listed by the VME slot. in which it resides. ........ 248

L2 Global data sources ........................... 250
Full list of tools available to L2 Global with the conﬁgurable parameters.257
Full list of ﬁlters available to L2 Global with the conﬁgurable parameters.262
The translation of MBT channels to global objects sent to Level 3.
Here the channel of interest is 256 which is translated as global track.
The MBT channel overﬂow message is triggered when more than 100
of these objects are found. ........................ 280
Additional parameters stored for each object in the high-pT format. . 289
Storage comparison for some of the datasets used in this analysis com-

paring the standard DO CAF tree format and the reduced high-pT
format after the high-pT skim ....................... 290

xi

2.1

2.2

2.3

2.4

3.1

3.2

3.3

3.4

3.6

List of Figures

Images in this dissertation are presented in color.

Longitudinal W boson scattering. This is one of the processes that
would have a divergent cross section without additional diagrams. In
this thesis, the time axes in Feynman diagrams run left to right. . . . 12

Additional diagrams involving the Higgs boson that cancel divergences
of longitudinal W boson scattering in the standard model. ...... 13

The Mexican hat potential shown as an analogue of the Spontaneous
symmetry breaking of the standard model. The overall potential is
completely symmetric, but nature must choose a speciﬁc minimum
within the potential for the vacuum expectation value [4] ........ 14

Many experiments measure values that are interconnected by the stan—
dard model. This ﬁgure shows how much each measurement pulls on
the overall ﬁt. Most of the measurements show excellent agreement.

The value of 130118534772 Z) is taken from low energy experiments; the
next ﬁve are LEP I line shape and lepton asymmetries; Ag(PT) is from
LEP I tau polarization; the next six are from LEP I and SLD heavy-

ﬂavor measurements; sin26i?t(be) is from LEP I q? asymmetry; the
two W boson measurements are from both the Tevatron and LEP II,

and the top mass is only from the Tevatron [5]. ............ 20
The Fermilab accelerator chain [6]. ................... 32
The Magnetron: Creating H _ [7] ..................... 33
The Drift Tube Linac [8] ......................... 34
The energy of particles as they travel through the DTL [8] ....... 35

The H _ ion is stripped of its electrons and merged with an existing
beam of protons using a carbon foil and dogleg magnet [7] ....... 38

Loading the Tevatron from the coalesced protons and antiprotons in
the Main Injector [9] ............................ 39

3.7

3.8

3.9

3.10

3.11

3.12

3.13

3.14

3.15

3.16

3.17

3.18

3.19

A ﬁgure showing the 1’) target and the lithium lens used to select an—
tiprotons at 8 GeV [7]. ..........................

This Shows the process of bunch rotation. The phase of individual

particles is sacriﬁced to get a more consistent momentum in the beam
[10]. ....................................

The ﬁgure shows the path of the antiprotons within the Accumulator
as a function of energy. As the particle begins to lose energy, it slowly
moves into the center of the orbit [7]. ..................

The process of electron cooling. A stream of electrons is pushed over
the antiproton beam, absorbing energy until the antiprotons are at
thermal equilibrium with the cool electron beam [11]. .........

The Tevatron bunch structure. Collisions happen every 396 us within
a superbunch. There are three “Trains” of twelve bunches with an
abort gap between “Trains” of 2.617 ,us [12]. ..............

The Bethe equation showing the stopping power for a muon traveling
through copper. The solid line represents the total energy loss [2]. . .

High-energy electrons and positrons lose most of their energy from
bremsstrahlung. The relative energy loss for an electron or positron
in lead per radiation length is plotted against the electron or positron
energy [2]. .................................

The DO Detector— The z—axis is in the direction of the proton beam, the
y—axis is straight up, and the :c-axis points out, away from the center
of the Tevatron. The central tracking system is within the calorimeter
[13]. ....................................

The inner tracking system showing the SMT, CFT, the solenoidal mag-
net and preshower detectors [13]. ....................

The layout of the silicon microstrip detector [13]. ...........

The pT resolution expectation with respect to 77 for different particle
momenta [13] ................................

The impact parameter resolution expectation from the SMT technical
design report [14] ..............................

The central ﬁber tracker with supports within the solenoid [15].

xiii

41

44

45

47

48

49

52

54

CI!
C51

56

57

3.20

3.21

3.22

3.23

3.24

3.26

3.27

3.28

3.29

3.30

3.31

3.32

3.33

4.1

4.2

The process used to create the electron avalanche from the incoming
scintillated ﬁght in the VLPC. A photon enters the intrinsic region of
undoped silicon creating an electron-hole pair. The hole moves to the
drift region where it removes an electron from an atom. The electron
accelerates through the gain region freeing more electrons from atoms.
The current from these freed electrons is then collected to record the
presence of the initial photon [15] .....................

The magnetic ﬁeld seen by particle traveling through the DO experi-
ment in kG [13] ...............................

The general scintillator geometry for the central and forward preshower
system [13]. ................................

The arrangement of scintillation tiles in the central preshower [13]. . .
The arrangement of scintillation tiles in the forward preshower [13]. .
The three DO calorimeters showing the division into layers [13]. . . .

A calorimeter cell Showing absorber plates, liquid argon and Signal

boards [13]. ................................
The layout of the wire chambers used in the DO muon system [13].

The layout of the scintillators used in the DO muon system [13]. . . .
A diagram of the individual MDT cells [13]. ..............
The DO trigger system and basic communication layout [13] ......
Data ﬂow in L2STT [13] ..........................

Data path from the L3 farm nodes to tape storage and the online
examines [13]. ...............................

The placement of the luminosity detector as seen in the rz plane [16].

The Alternative Algorithm looks for at least three hits in the SMT and
extrapolates outward to the OFT [17]. .................

The Histogramming Method looks for at peaks in 2—D histograms plot-
ting p and d). Histograms with the most hits deﬁne tracks [17] .....

xiv

60

62

63

63

64

65

70

71

73

76

82

86

91

93

4.3

4.4

4.6

4.7
4.8

5.1

5.2

5.3

01
.43

C31
01

6.1

6.2

Values for the weighting function of a given track to its contribution
to a particular primary vertex given a ﬁxed X2 and various impact
parameter resolutions of the track-vertex system [18]. .........

The isolation of EM objects is determined by looking at the fraction
of total energy in a cone of ’R < 0.4 minus the amount of energy in the
EM calorimeter in a cone of R < 0.2 normalized to the EM energy.
The CPS is the central preshower detector [19]. ............

The muon isolation cone for calm'imeter isolation is a hollow cone of
0.1 < R < 0.4 [20]. ............................

Hadronic tau objects at DO are deﬁned by three types of decays. This
analysis identiﬁes taus that undergo any of these decays. .......

The partons of the initial physics processes decay and hadronize to
particle jets which then leave tracks in the inner tracking system and
energy in the calorimeters .........................

Efﬁciency versus fake rate for various operating using the neural net
and jet lifetime probability tagger .....................

Trigger efﬁciencies for single muon triggers in single [.L ﬁnal state. The
p 7} distribution is shown to not be completely ﬂat. This, along with
a multiplicity dependence led us to incorporate trigger eﬂ‘iciencies di-
rectly in later analysis runs. .......................

Trigger efﬁciencies for single electron triggers in single e ﬁnal states. .
A comparison of the multijets background to the data minus MC for
the electron PT in (5.3(a)) and the likelihood for electrons from the Z
peak vs. those from back-to—back electron-jet in (5.3(b)). .......
A comparison of the multijets background to the data minus MC for
the muon pp in (5.4(a)) and the calorimeter halo for muons from the
Z peak VS. those from back-to—back muon-jet in (5.4(b)). .......
A comparison of the multijets background to the data minus MC for
the tau pp in (5.5(a)) and the neural network output value for Monte
Carlo taus vs. Monte Carlo jets reconstructed as taus (5.5(b)) .....

The J / a") peak before applying muon smearing [3] ............

p. smearing effects in the Z and J / zit peaks. Figures taken from [3].

XV

99

105

107

114

117

122

123

135

137

138

141

142

6.3

6.4

6.6

6.7

6.8

6.9

6.10

6.11

6.12

6.13

6.14

6.15

6.16

7.1

Electron smearing effects in the Z peak. Figure taken from [21]. . . . 143

Combination p efﬁciency for local muon system, cosmic veto, and track
match. The hole is due to supports for the calorimeter preventing
placement of muon chambers. Figure taken from [22] .......... 144

p efﬁciency for tight track reconstruction. Figure taken from [22]. . . 145

,u isolation efﬁciency for N PTight isolation requirement. Figure taken
from [22]. ................................. 146

Electron efﬁciencies for preselection and top tight. Figures taken from
[23] .................................... 147

The difference in the energy measurements between the photon and a
jet in back-to-back events. The distribution can be approximated by
convolving a Gaussian distribution with an error function [24]. . . . . 149

The efﬁciency and scale factor necessary to apply to the Monte Carlo
for the “Tight” operating point using the N N b—tagger [25] ....... 151

The fake tag rate for the “Tight” operating point using the N N b—tagger
[25] .................................... 152

The taggability used in this analysis for W and Drell-Yan heavy-ﬂavor
processes that are binned as single muon plus jets ﬁnal states. . . . . 153

The generator-level reweighting function extracted from the cross—section
ratio of W boson to Z boson production [26]. ............. 154

The dielectron invariant mass for oppositely charged data (black), op-
positely charged MC (red), same Sign data (blue), and same sign MC
(green). The plot integrals are all normalized to 1.0. These plots are
for electrons with 77 < 2.5 [27] ....................... 157

Same Sign 6.14(a) and opposite Sign 6.14(b) scale factors VS. "det- The
black line shows the scale factors that are incorporated into the analysis. 158

Ratio of Aqﬁ distributions between data and Monte Carlo in inclusive
single lepton ﬁnal states .......................... 160
Ratio of Ad) distributions between data and Monte Carlo in inclusive
dilepton ﬁnal states. ........................... 161
,u + jets ﬁnal state ﬁtting histograms: ,u. PT» ET. ........... 170

xvi

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

7.10

7.11

7.12

7.13

7.14

7.15

M + jets ﬁnal state checking histograms: transverse mass (II, ET), num-
ber of jets ..................................

e + jets ﬁnal state ﬁtting histograms: 8 PT, 6 77 .............

e + jets ﬁnal state checking histograms: transverse mass (6, ET), in-
variant mass of leading jet with other jets in the event. ........

[up ﬁnal state ﬁtting histograms: leading ,u pT, second [I r). ......

up ﬁnal state checking histograms: invariant mass (11, [1), Z boson PT-

66 ﬁnal state ﬁtting histograms: leading 6 pp, leading jet PT ......

66 ﬁnal state checking histograms: invariant mass (6,8), Z boson 77.
Several distributions, such as the Z 77 Show some several bin discrepan-
cies. When the trials-corrected probabilities are determined for these
discrepancies, the signiﬁcance is Shown to be at the level of one sigma.
We work to generally improve the standard model background model-
ing, but the focus is on statistically signiﬁcant discrepancies. .....

[.rr ﬁnal state ﬁtting histograms: II pp, T pT ...............

[17' ﬁnal state checking histograms: T type, invariant mass (,u, 7'). Low
values of invariant tnass Show single-bin discrepancies in the three ﬁnal
states that are dominated by the Drell-Yan TT process. These are
related to pT threshold issues with the taus, and when accounting for
trials are not statistically signiﬁcant. ..................

61' ﬁnal state ﬁtting histograms: e pT, ET ......... . .......

er ﬁnal state checking histograms: transverse mass (e,ET), invariant
mass (e,7') ..................................

,ue ﬁnal state ﬁtting histograms: p 77, e pT ................

Ire ﬁnal state checking histograms: transverse mass (alt-IT), invariant.
mass (an) ..................................

One ﬁnal ﬁt is performed after ﬁxing the ratios of light-parton to no-
parton and heavy—ﬂavor to light-parton. This ﬁgure shows the dimuon

ﬁnal state after these ratios are averaged with the dielectron and then
ﬁxed .....................................

xvii

171

172

173

174

175

176

177

178

179

180

181

182

183

184

7.16

7.17

8.1

8.2

8.3

8.4

8.6

8.7

8.8

8.9

8.10

The scalar sum of the transverse energy of jets in ,u + jets events with
at least 4 jets. This ﬁnal state shows the necessity of ti Monte Carlo
to properly describe the data. ......................

The ﬁgure shows one line of a pT text ﬁle used as input into the
VISTA algorithm. Only the run and event numbers, the vertex po—
sition, weight, and the object pT, 77, cf) information are kept for each
event. In the ﬁgure, each object is Shown in a different color ......

All of the histograms plotted for the VISTA state with one muon and
one tau. The 77 PT and p 77 distributions .................

All of the histograms plotted for the VISTA state with one muon and
one tau. The p 45 and a detector 77 distributions .............

All of the histograms plotted for the VISTA state with one muon and
one tau. The T pp and the T 77 distributions ...............

All of the histograms plotted for the VISTA state with one muon and
one tau. The T a and the T detector 77 distributions ...........

All of the histograms plotted for the VISTA state with one muon and
one tau. The ET and minimum pT of the ,u and T. ..........

All of the histograms plotted for the VISTA state with one muon and
one tau. The maximum 77 of the 77 and T .................

All of the histograms plotted for the VISTA state with one muon and
one tau. The AR between the p and T. The clustered object recoil is
the vector sum of the ET and unclustered energy. ...........

All of the histograms plotted for the VISTA state with one muon and
one tau. A thrust axis is deﬁned as the vector sum of the two objects
in the event. The clustered object recoil is then determined for the

185

186

199

200

201

202

203

204

205

transverse and longitudinal components with respect to the thrust axis. 206

All of the histograms plotted for the VISTA state with one muon and
one tau. The plot cos(6*) shows the cosine of the angle between the
positively-charged lepton and the reconstructed Z boson in the frame
of the Z boson. Also, the invariant mass of the ,u and T. .......

All of the histograms plotted for the VISTA state with one muon and

one tau. The scalar sum of the transverse momenta of all of the objects
in the event plus the missing transverse energy. ............

xviii

8.11

8.12

8.13

8.14

8.15

9.1

9.2

9.3

9.4

An example SLEUTH plot for the opposite-sign light dilepton (dimuon
or dielectron) ﬁnal state with two or three additional jets (not b-
tagged). In this ﬁgure, the 2 PT cut that maximizes the discrepancy
is at 109 GeV, which encompasses almost the entire distribution. This
region is enlarged in the plot in the upper right, showing 580 data
events compared 550 predicted from the standard model background
providing a probability of a statistical ﬂuctuation of 0.62 ........

Sensitivity test for tf. In this ﬁgure the tf Monte Carlo is included,
and there are only minor differences between data and standard model
background. ................................

Sensitivity test for tf. The ﬁgure shows the results of pushing through
the entire analysis procedure without the tf Monte Carlo. In this case,
SLEUTH easily passes the criterion of interest at 0.001 for this common
tf ﬁnal state. ...............................

Sensitivity test for It? in 100 pb“1. This ﬁgure includes the tf Monte
Carlo, and the differences between data and standard model back—
ground are again minor. .........................

Sensitivity test for tf in 100 pb‘l. This ﬁgure Shows the results of
running the full analysis procedure using 10% of the Run IIa dataset
when the tf Monte Carlo is removed. Even with this smaller sample,
the SLEUTH algorithm still crosses the threshold .............

VISTA ﬁnal state a distribution for Run IIa sample before accounting
for the trials factors. The curve represents a Gaussian distribution
centered at zero to guide the eye. The event count distributions are
expected to obey Poisson statistics, which is why the distribution is
narrower than the curve. .........................

Figure 9.2(a) shows the excess of data in ,u. + 2 jets + E T to be focused
on events with muons that have 77 values > 1.0. Figure 9.2(b) shows the
A45 distribution between a muon and the ET, with the ET pointing
opposite to a muon .............................

Two ﬁgures showing the pp distributions of the photon .........

VISTA histogram a distribution for 100% sample before accounting for
the trials factor. Each curve is a Gaussian distribution. The curve
that is shifted to lower values is centered at zero while the second
curve is centered at the mean. The difference between the two curves
approximates the average systematic uncertainty found in the plots. .

xix

211

212

213

215

216

221

222

223

224

9.5

9.6

9.7

9.8

9.9

9.10

9.11

9.12

9.13

9.14

9.15

The plot 9.5(a) shows the AR difference between the p and trailing
pT jet. Figure 9.5(b) shows the A77 distribution between the two jets
in the e + 2 jets + ET ﬁnal state .....................

Figure 9.6(a) shows the invariant mass of the ,u and the jet in a ,u +
jet + ET ﬁnal state. Finally, 9.6(b) shows the cf distribution for the
jet in the e + jet + ET ﬁnal state. Each of these is tied to difﬁculties
in spatial jet modeling ...........................

Plots 9.7(a) and 9.7(b) Show the ET distribution in the opposite sign
dielectron and dimuon ﬁnal states. Both of these point to E T modeling
issues in dilepton states. .........................

Figure 9.8(a) shows the (75 distribution of the ET in the dimuon state
with large ET, which also points to dilepton ET modeling issues. Fi-
nally, Figure 9.8(b) shows the minimum PT of the ,u and the T for the
same—sign 7n + ET ﬁnal state which shows the diﬂiculty in modeling
the jet to T misidentiﬁed background using loosened data cuts .....

7
SLEUTH plot for opposite sign 66 + ET. The ”P value at the top right
corner of the plot is the probability before ﬁnal state trials factor.

SLEUTH plot for E + ET. The ’P value at the top right corner of the
plot is the probability before ﬁnal state trials factor. This plot shows
the same issue in the tails of the distribution as Figure 9.9 .......

Distribution of ﬁnal state SLEUTH probabilities converted into units of
a before inclusion of the ﬁnal state trials factor. ............

Electron-only distribution of ﬁnal state SLEUTH probabilities converted
into units of a before inclusion of the ﬁnal state trials factor. The two
points in the tails Show issues with jets misidentiﬁed as T’s. . . . . . .

Check of most discrepant CDF plots from [28], same sign (SS) 66’. The
’P values at the top right corner of the plots are the probabilities before
ﬁnal state trials factors. .........................

I

Check of most discrepant CDF plots from [28], same Sign 66 + ET-
The ”P values at the top right corner of the plots are the probabilities
before ﬁnal state trials factors .......................

7
Check of most discrepant CDF plots from [28], €i€T€ + ET. The P
values at the top right corner of the plot is the probability before ﬁnal
state trials factors. ............................

226

227

228

231

232

233

234

236

9.16 Since there are no data events in the for DO in the descrepant CDF

A.1

A2

A3

A4

A5

A6

A7

A8

A9

state, [it at + 2 jets + ET, the distribution for pi ezF + 2 jets +
ET is shown. The lack of data in 1 fb‘1 shows that we do not see the
same data excess in that ﬁnal state ....................

Data ﬂows from the front end detectors through the Level 1 and Level
2 trigger systems. The solid lines show the path of the detector data
while the dotted lines show the path of the Level 1 and Level 2 triggers.
The ﬁnal Level 1 decision is determined by the trigger framework. The
Level 2 system also sends the trigger decisions to the framework, but
the Level 2 Global processor makes the ﬁnal decisions on Level 2 event
acceptance. ................................

Data ﬂow within the L2 Global VME crate. ..............
Physical setup of the L2 Global cards within its VME crate. .....

The Level 2 Global crate, front A.4(a) and back A.4(b) On the front,
the Visisble cards from left to right are the Bit 3 card, SBC, FIC, Beta,
2 SFOs and 2 MBTs. On the back, 2 MBUS terminators and the VTM
for the L1 trigger framework input. The white jumpers shown in the
photo of the back of the crate are needed for proper functioning of the
readout SBCS. In order to run the L2 event loop at the teststand, the
L3 handshaking must be faked. .....................

One of the triggers used in this analysis (“MUH5_LM15”). This is a
screen shot taken from the trigger database for trigger list global_CMT-
14.92 [29]. .................................

The Level 1 trigger term associated with MUH5_LMI5. ........

The Level 2 superscript associated with MUH5_LMI5. In the trigger
database, the superscripts are known as L2 Groups. ..........

The single Level 2 script associated with MUH5_LMI5. Since this
trigger was used for Run IIa, there is only one script associated with
the superscript. In Run IIb, more than one script are allowed for each
superscript. ................................

The Level 2 muon tool associated with MUH5_LMl5. This is actually
the only L2 muon tool used in this particular trigger list .........

A.10 The main Level 2 ﬁlter associated with MUH5_LM15. There is also a

PASSlOO ﬁlter used as placeholder for a possible track requirement as
seen in the muon tool. ..........................

xxi

238

247

249

254

255

256

261

A.11 Monitoring the global information from the trigger framework. This
includes overall L2 accept rate and L2 rejection fraction. .......

A.12 More monitoring from l2mon program. This looks at each individual
trigger and monitors the input, output and rejection information. This
can be useful to isolate problems with trigger rates ...........

A.13 The L2 monitoring program trigstripmon. Each trigger can be indi—
vidually monitored with this program. .................

AM The most common tool used in L2 monitoring. Shown are the parts of
the GUI relevant to L2 Global. .....................

A.15 The object overlow error shown as a function of luminosity in the top
ﬁgure. The bottom shows the normalized number of occurances with
respect to the overall luminosity proﬁle. All data is from September
2008 - June 2009. The spike in the errors near [I = 100- 1030 cm"2

s‘l, is due to an error in the luminosity fetching program. ......

A.16 The object overlow error shown as a function of lumi in the top ﬁgure.
The bottom shows the normalized number of occurances with respect
to the overall luminosity proﬁle. All data is from September 2008 -
June 2009 ..................................

A17 The path of the L2 trigger decision through the online system. Thick
lines correspond to full 128-bit triggers. The thin lines represent a
single bit accept / reject decision. The blue lines are L1 trigger bits, red

lines are L2 bits, and the green line is the AND of the L1 and L2 bits.

B.1 The information stored in a high-pT object is Shown. Basic information
is the same for all object types but four parameters are dependent upon
the object type ...............................

xxii

271

272

273

274

277

281

284

288

Chapter 1

Introduction

AS the Fermilab Tevatron Collider heads into its ﬁnal years, the two major high energy
experiments there, DO and CDF, will ﬁnish collecting data. The energy frontier in
high energy physics is now beginning its transition to the Large Hadron Collider
outside of Geneva, Switzerland and the major high energy physics experiments there,
ATLAS and CMS. As these experiments begin, it is fair to ask one central question
from the Tevatron. Are the results of the DO and CDF experiments consistent with
the standard model? The standard model is the single theoretical framework that
has successfully predicted all new fundamental particles discovered after its inception,
with the exception of the Higgs boson, a particle still within the reach of the Tevatron.

While many analyses check the precision of the standard model using measure-
ments of known particles and others check for well-motivated extensions, the focus
of this analysis is to determine if the standard model is well—described as broadly as
possible given the constraints of our detector and limitations in modeling the stan-
dard model. Most searches for new physics at the Tevatron have focused on a speciﬁc
model, often molding the search to be sensitive to a particular signal. However, the
proposed extensions to the standard model include so many possible signals, there
are too many areas of phase space to conduct dedicated searches. We ﬁnd that. the

major constraints in these searches is the sensitivity of the detector to a particular

area of phase space and the ability of our Monte Carlo and detector simulation to
properly model it.

While this analysis strives for model independence, several assmnptions about
physics beyond the standard model are necessary to provide some sensitivity. We
assume that the new physics will manifest itself by containing objects with reasonably
high transverse momentum. And, we check ﬁnal states containing leptons because
this is where our detector has been most heavily tested and where we believe we can
have enough sensitivity to detect deviations.

Our focus is on three methods to test agreement between data and the standard
model background. We divide our data and background into ﬁnal states based on
object content, then check event counts in data against our expectation. We plot
many different event distributions to see if there are any large disagreements. Then,
we focus speciﬁcally on one distribution, the sum of object momenta and the missing
transverse momentum in each event, and search for large data excesses in the tails of
these distributions.

Many other quantities could also be checked for disagreement, but we believe these
three tests should provide us with a good sense of whether there is new physics for
which our experiment and current background simulation could be sensitive.

The focus of this dissertation is to describe such a search, a process that leads
from opening a container of hydrogen gas to probing the edges of scientiﬁc under—
standing. The description of this process is divided into four basic parts. The ﬁrst
part contains three chapters which describe background material that is not speciﬁc
to this particular analysis. This includes an explanation of the standard model (the
gmup of theories that we are testing) with a brief overview of the current landscape
0f potential extensions. Then, the chain of events that turns hydrogen gas into 1.96
TeV proton-antiproton collisions is brieﬂy discussed, followed by a description of the

pr Ocedure DO uses to identify the remnants of collisions and turns into a comprehen-

sive understanding of the underlying physics processes. The last part of this section
discusses the selection and storage of those collisions (events) which are considered
the most useful for scientiﬁc understanding. The second part involves a description of
the selected events speciﬁc to this analysis, the simulation of events representing the
standard model expectation needed as background for this analysis, and the necessary
additional corrections needed to modify the simulation to account for known defects
and oversimpliﬁcations. The third part will discuss the specific analysis strategy and
the details of the procedure in comparing the selected data with the expectations of
the standard model. Finally, the last two chapters present the results of the compar-

ison along with their interpretation.

Chapter 2

Symmetry, the Standard Model

and Beyond

Physics is a science of symmetries. In classical, relativistic, and quantum theory,
symmetries provide profound insights into the laws of nature. Many of the symmetries
used in classical physics are intuitive, but deeper symmetries in quantum ﬁeld theory
helped to produce the current theory of all interactions observed at the quantum scale,
known as the standard model. While the gauge syrmnetries of quantum ﬁeld theory
are fundamentally different than the space-time symmetries of classical physics, they
share a basic commonality. The space-time symmetries involve the invariance of
physical laws to translations, rotations, etc. The internal phase symmetries of the
standard model are invariant to “rotations” within the space of the interactions. The
SU(3)C invariance of the strong force, for instance, simply means that the strong
force is invariant with respect to the color of the quarks or gluons that it. is acting
on. If one “rotates” the quarks in this nonphysical space, the strong force will act
in exactly the satne way. While these symmetries are no longer in a physical space
a11d simply represent a redundancy in the theory, they still obey the dictates of
Noether’s theorem, discussed in Section 2.1.1, and possess a conserved current. The

unClerstanding of the redundancies that describe the spaces of the three interactions,

led to the creation of the standard model, whose interactions are determined by the
gauge group, SU(3)C ® SU(2) L <8) U(1)y. It has been extensively tested and has
often shown remarkable agreement with nature.

Despite its success, the standard model has a limited reach. This leads to the
idea that new physics lies beyond the currently accepted theory. Searches for physics
beyond the standard model, such as the one described in this thesis, are now common
at the major collider experiments. These searches look for extensions to the standard
model that encapsulate it within a more general theory which can maintain its validity
to higher energy scales. Currently, there are theoretical and experimental hints that
we are currently at the energetic limit of the standard model and we will be able to
measure properties of new physics at the LHC and possibly even at the Tevatron. The
form of this new physics is not a settled topic. Theorists have proposed many different
strategies to extend the standard model. These theories are not only consistent with
all of the current data, but they are also typically analogues of current processes and
build on their observed properties. The most well-accepted extensions tend not to
predict one speciﬁc signature in a particle detector. They are more general with many
different signatures and provide little reason for one signature to be expected over
another. (The choice of which possibility to search for is often made based on the
acceptance and sensitivity of the detector.)

The approach in this dissertation is to look across many ﬁnal states to check for any
disagreements with the standard model, rather than focus on any of these extensions
Speciﬁcally. This is done in three stages. First, events with high momenta are selected
and some small corrections are applied. Then, the data are searched broadly for
large discrepancies. Finally, the tails of the transverse momentum distributions are
Compared against expectation in speciﬁc ﬁnal states.

The symmetry discussion in this chapter follows discussions in [30] and [31]. The

rest, borrows heavily from the books [1], [32], and a series of lectures given at the

01

Hadron Collider Summer School of 2008 [33].

2. 1 Symmetry

Using the Lagrangian form of particle motion, basic: conservation laws can be derived
by ﬁnding symmetries in nature. This is true in Newtonian and relativistic classical
physics in properties such as conservation of energy and momentum. In quantum
ﬁeld theory, besides the spatial quantities, additional phase symmetries suggest new
conserved quantities that lead to the basic interactions of particle physics.

The formulation of the standard model can be found by modifying basic free
particle Lagrangians to be invariant under certain phase transformations in a space
that is not physically observable. The presence of massive particles, however, prevents
these symmetries from being complete explanations of the model. To account for
particle masses, a form of symmetry breaking is introduced to preserve the symmetric

structure while matching the observed experimental results.

2.1.1 Symmetry and Conservation Laws

The content of an introductory physics course can be surmnarizml from a handful of
observations about nature. These are typically given in the form of Newton’s three
laws, but particle motion can also be described by the principle of least action, where
a particle chooses a path such that the action integral S is minimized in S 2 It? Ldt.
The function E is called the Lagrangian density and leads to the equations of nrotion

given in Equation 2.1.

d (913 8£

— — ——=0 i=1,2,....s 2.1
C“ (342') 542' ( ) ( )
The list of qi’s are the position coordinates and the (ifs are the velocities associated

with the qi’s. There is one equation for each degree of freedom in the system. Fi'om

these basic equations, assumptions about symmetries of space and time can lead
to conserved quantities. For example, assuming the homogeneity of time leads to
the conservation of energy. The homogeneity of space leads to the conservation of
momentum, and the isotropy of space leads to the conservation of angular momentum.

When particles are considered relativistically, the same arguments can be used
to account for the possible symmetries in the four dimensional space—time of special
relativity (Minkowski space): translations, time displacements, rotations and Lorentz
transformations.

Irr quantum theory, we abandon speciﬁc kinematic predictions for a probabilistic
wave function using statistics to determine particle properties. The nonrelativistic
Schréidinger wave equation is shown in Equation 2.2.

a 712

mad/(r, t) = —%V2\r(r, t) + V(r)\IJ(r, t) (2.2)

where h is the reduced Planck constant, \II is the wavefunction, a probability ampli—
tude for a particle to have a position r at a time t, m is the mass of the particle, and
V is the timeindependent potential energy of the particle at r.

The simple deterministic equations of motion have been replaced by the proba-
bilistic interpretation of quantum theory. The Schrr'idinger equation describes how a
particle moves when in the presence of a force described by the potential V.

The Schriidinger equation does not, however, satisfy the requirements of special
relativity. To incorporate special relativity, the relativistic Dirac equation is used,
Equation 2.3. This version of the Dirac equation is not the simplest notationally, but
it shows the direct predictions of antimatter partners (q5+ , ¢_), and the relation to
spin in the Pauli matrices, a. The ¢+,_ are two component. spinors representing the
wave functions of a particle and its antiparticle. The Dirac equation does not include
the potential in the Schriidinger equation. Interactions in quantum ﬁeld theory are

determined by the interaction of separate ﬁeld equations rather than the simpliﬁcation

of a separate potential.

mc2 ca ~p (25+ _
= zh

2 4+
2 4L at

d)-

(2.3)
ca ~p —-mc

The Euler-Langrange equations are still effective ﬁeld theory descriptions of prob-

abilistic particle motion, and in this context take the form of Equation 2.4.

 

Bi: 6‘ 8E
53 _ 8ch [3 (87,40] 2 0 (2'4)

Noether’s theorem relates a symmetry in a physical law to a conserved quantity,
called a charge [34]. The theorem is typically cast in the language of classical electro-
magnetism, but it can be used to classify any of the syrmnetries that will be discussed
in this chapter. In any system, the quantity that is conserved must ﬂow continuously
across the system. In the case of momentum, this means that the momentum of one
particle must be transferred to that of another, or to some other part of the sys-
tem. A particle that loses momentum in one part of the system, while a completely
unrelated particle gains momentum in another part of the system would satisfy an
overall conservation of the momentum “charge”, but it could not be described as a
continuous momentum ﬂow and would fail the requirements of N oether’s theorem.
The ﬂow of this quantity is termed generally, as a current, J, and the quantity itself
is generally called a charge Q. Noether’s theorem is shown in Equation 2.5.

d

@

dt = 0 (2.5)

This equation can describe the energy, momentum, angular momentum, as well as all

of the quantities that will be introduced later in the chapter.

2.1.2 Symmetry and Particle Interactions

Any measurable property of the free particle depends 011 [Er/'41 rather than on the
wave function (In) itself. Therefore, there is a freedom in picking an absolute phase
of the wave. While the phase choice has no effect on predictions about the properties
of the wave itself, it determines the interference effects when the. wave interacts with
another ﬁeld. In order for the Dirac equation to properly describe the interaction, the
phase of the second wave must be chosen to be consistent with the ﬁrst. This is true
even if the waves are not causally connected. In order to preserve causality, it was
suggested that the phase choice for an individual wave should be independent of the
choice of other waves; it should be locally invariant. This principle was formalized
with non-Abelian gauge theories by Yang and Mills [35]. In order to maintain invari—
ance, the Dirac Lagrangian (using a simpliﬁed notation from Equation 2.3) would

need to be modiﬁed as in, Equation 2.6.

Etot 2 IF (ihCA/ﬂa'u — 777.62) ‘11 —->
__ 1
£tot = II! (mm/#8,, + 76/177 — me?) ‘11 — 4——F“VF7W.
I #0

(2.6)

When this equation is compared to the previous Dirac equation, the partial derivative
(9” is replaced by what is known as the covariant derivative, DMD = (874 + 76A”) III.
The covariant derivative was introduced explicitly to maintain the local gauge invari-
ance. However, it is found that the additional term describes the interaction between
the particle and an electromagnetic ﬁeld. The Flu/Ff” term represents the kinetic

energy of the electromagnetic ﬁeld itself.

 

l 0 0 0

T 0
1w is the adjoint spinor 1121370 and 70 = 0 l 0
0 0 —l 0
O 0 0 — 1

9

2.1.3 Symmetry and the Standard Model

The interactions necessary to preserve the phase symmetry described above can be
put into the language of group theory. The symmetry arising from the electromag-
netic interaction satisﬁes the conditions of a U(1) group. If this process is repeated
for SU(2)L, the weak interactions can be obtained, and for SU(3)c010r, the strong
interactions. While the strong interactions obey an exact symmetry, it is found that
the electromagnetic and weak interactions together form an SU(2) L <8) U(1)y sym—
metry. It is a linear combination of the gauge bosons predicted in this theory that
are responsible for interactions involving weak isospin and electromagnetic charge.
This symmetry is broken, and at low energies becomes the familiar U(1) symmetry

of electromagnetism.

2.1.4 Symmetry, Broken

The SU(2) L (E U(1)y symmetry of the electroweak interactions is only satisﬁed if
the gauge bosons are nearly massless (loop corrections would provide a mass of the
Z boson of 35 MeV). Additionally, fermion mass terms would also break this gauge
invariance and must also be missing from a gauge-invariant theory. Since the inter-
actions satisfy the electroweak symmetry, the syrmnetry must be broken to provide
particle masses [36]. The mechanism of mass generation through Goldstone bosons
that provide mass to the W and Z bosons, the Higgs mechanism, has been experi-
mentally veriﬁed. The speciﬁc dynarnics of the Higgs mechanism, however, are still
unknown [4].

Theories predicting the dynamics of the Higgs mechanism fall into two general
categories. First, is the addition of a weakly-interacting self-coupled elementary
scalar. The other option is to add additional strong-interaction dynamics among
new fermions. The simplest form of the Higgs mechanism in the electroweak sector is

the addition a single scalar doublet, which is the form that. is currently incorporated

10

into the standard model. One of the experimental consequences of this form is a
Single observable scalar particle, the Higgs boson. Even if one abandons the concept
of SU(2) L (8) U(1)y symmetry and simply adds the mass terms directly, the theory
would diverge for some interactions involving the weak gauge bosons, such as the
longitudinally-polarized W boson scattering process as seen in Figure 2.1. This di-
vergence violates the fundamental principle of unitarity in quantum theory, predicting
total probabilities greater than one. This Violation is shown to be universal and to
all orders, with a critical energy of ~ 1.2 TeV.

The standard model Higgs mechanism uses the fact that the electroweak interac—
tion symmetry can be preserved if the vacuum is deﬁned at a nonzero value incorpo-
rating what is called a vacuum expectation value. This lowest nonzero energy of the
vacuum is an energy density that. perrrreates all space. The SU(2) L 68> U(1)y sym-
metry is valid for the overall system until a speciﬁc vacuum grormd state is chosen,
then the symmetry is spontaneously broken. The ground state of the system could
have a minimum among a continuum of possible values. Nature must choose one of
these possibilities and once the choice is made, the symmetry of the system is gone.
Additional diagrams due to the Higgs boson, the observable scalar particle from the
vacuum, cancels divergent terms in gauge boson scattering. The diagrams in Figure
2.2 are complementary to those in Figure 2.1.

This idea is often Visualized through looking at simpler analogous symmetries.
For a pseudoscalar wave equation with charge symmetry (symmetric in (b, —+ —¢),
the minimum energy ground state has two symmetric possibilities. Nature would only
be able to choose one of them, breaking the symmetry of the overall equation. This

can be extended to a complex scalar ﬁeld where the vacuum ground state energy can
now choose among points on a circular minimum as seen in Figure 2.3, known as the
Mexican hat potential. The standard model symmetry is slightly more complicated,

but the idea is a generalization of the previous examples. The ﬁeld must choose a

11

.3
,5.

WI“ WI
((1)
“’7'. WE
y/Z
WI Wit
0))
w: w;
yIZ
wt WE
(C)

Figure 2.1: Longitudinal W boson scattering. This is one of the processes that would
have a divergent cross section without additional diagrams. In this thesis, the time
axes in Feynman diagrams run left to right.

12

E
I"'+
S
“'4-

(b)

Figure 2.2: Additional diagrams involving the Higgs boson that cancel divergences of
longitudinal W boson scattering in the standard model.

direction in SU(2) space breaking the symmetry. This creates a. Higgs doublet in
SU(2) and a singlet in U(1). Hints of the direction are shown in the experimental
observation of electromagnetic charge conservation.

Even if the Higgs mechanism does not satisfy the simple Higgs doublet assumption
of the standard model, if new physics are at considerably higher energies, the lightest
Higgs boson introduced in theories that use weak-coupling will mimic the properties
of the single Higgs boson of the standard model. The lack of evidence for physics
beyond the standard model from electroweak precision data (see Section 2.2.2) hint
that it may be unlikely to ﬁnd low—mass new physics, and a Higgs boson associated
With high-mass new physics would Show many of the same properties as the standard

Inode] Higgs.

13

 

Figure 2.3: The Mexican hat potential shown as an analogue of the spontaneous sym-
metry breaking of the standard model. The overall potential is completely symmetric,
but nature must choose a speciﬁc minimum within the potential for the vacuum ex-

pectation value [4].

2.2 The Standard Model

While the ideas above are useful in understanding how nature preserves basic sym-
metries, the standard model is typically described by the experimentally observed
particles and interactions. The couplings among the particles of the standard model
are determined from the gauge symmetries. Still, twenty-six parameters are deter—
mined from experiment. The similarity among these hint at possible greater under-
lying symmetries of a more general theory. The standard model would then be just

an effective low energy theory of this more general model.

14

2.2.1 Particles and Interactions

We observe particle interactions as forces that change a particle’s measurable prop—
erties. Three types of interactions are measurable at the quantum scale: the elec—
tromagnetic, weak, and strong forces. These forces are shown in Table 2.1, with an
approximation of their strength and range. Gravitation is included for completeness.

The particles observed in experiment and their properties are listed in Table 2.2.

Table 2.1: The four fundamental forces with their approximate interaction distances
and strengths [1].

 

 

 

 

 

 

 

 

 

Force Relative Strength“ Range (m) Carriers
electromagnetic 1036 inﬁnite photon
weak 1025 10—18 Wi, Z
strong 1038 10_ 15 gluons
gravitation 1 inﬁnite gravitonb

 

 

a The relative strengths are approximate and vary depending on the particles involved.

b The graviton has not been observed.

The intrinsic property of spin is used to differentiate two classes of particles.
Particles with integer spin are known as bosons, while those with half-integer spin
are called fermions. The known fundamental matter particles are spin-1/2 fermions
while the particles that mediate the interactions between the matter particles are
spin-1 bosons, called gauge bosons since they arise from the phase invariance of the
interaction Lagrangians.

The SU(2) L <8) U(1)y electroweak theory predicts two charged and two neutral
gauge bosons. From experiment, it is seen that only one of them is involved with
the known electromagnetic force seen at low energies. This is the massless photon.
The other types of particle exchange allowed in the electroweak theory are suppressed

because the gauge bosons are massive. Once the interaction energies approach the

15

Table 2.2: The fundamental particles with their force—related quantum numbers and
masses [2].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Particle EM Charge Spin Colored? Number of Particles Mass
6 —1 1/2 No 4 0.511 MeV
yea 0 1/2 No 2? < 2 eVb
,u —1 1/2 No 4 106 MeV
up“ 0 1/2 No 2? < 0.19 MeV
T —1 1/2 No 4 1.78 GeV
VTa 0 1/2 No 2"? < 18.2 MeV
u 2/3 1/2 Yes 12 1.5 — 3.3 MeV
d —1/3 1/2 Yes 12 3.5 — 6.0 MeV
c 2/3 1/2 Yes 12 1.27 GeV
3 —l/3 1/2 Yes 12 105 MeV
t 2/3 1/2 Yes 12 173.1 GeV
b —1/3 1/2 Yes 12 4.20 GeV
Wi i1 1 No 2 80.4 GeV
Z 0 1 No 1 91.2 GeV
7 0 1 No 1 0
gluon 0 1 Yes 8 ‘ 0
gravitonc 0 2 No 1 0

 

 

 

 

 

 

 

a . . . . . .
The neutrino mass eigenstates are heavrly mixed from the ﬂavor eigenstates. This means the
masses quoted here will be mixtures of the various neutrino ﬂavors, much more so than the
quarks.

This assumes CPT invariance. The limit comes from the antineutrino. There are much weaker
limits on the neutrino.

C O
The gravrton has not been observed.

16

masses of the gauge particles, these additional exchanges are observed. The charged
W bosons and neutral Z boson are the weak components observed from the elec-
troweak theory. The weak force is only visible to left-handed particles. This particle
property is related to the parity of the particle. These left—handed particles contain
a “charge” known as weak isospin which is mediated in much the same way as the
electromagnetic charge.

The interactions arising from the SU(3) symmetry are known as strong interac—
tions. They are mediated by a massless gluon. The exchange of color “charge” has a
couple complications that differentiate it from the electromagnetic charge. The color
charge comes in three types, and the charge carriers are colored objects as well. It is
found that colored objects cannot be directly observed in experiment. Each colored
object is drawn to create neutral “white” colored objects by proper combinations of
the individual colors. The strong force increases with distance, so as colored particles
move away from each other, eventually the energy will produce other colored objects
to create overall neutral measurable objects. As these colored objects are split apart
and form other objects, they produce a stream of colorless objects known as jets.
These are bound states of two quarks (one color with its anticolor) or three quarks
(one of each of color or one of each anticolor). The two quark states are known as
mesons while the three quark states are known as baryons. The proton and neutron
are examples of baryons (proton- [uud], neutron— [udd] ). Tire residual strong forces
from the proton and neutron are what hold together atomic nuclei, similar to how
residual electromagnetic forces in atoms hold together molecules.

Due to the additional interactions discussed in the above paragraphs, the table of
particles is actually incomplete. The expansion of the up quark which is subject to

all of the fundamental forces is shown in Table 2.3.

17

Table 2.3: Fundamental particles, revised. This is an example of the full particle
content of the standard model. Each particle listed has a corresponding antiparticle
with opposite electromagnetic charge. Furthermore, each particle has left-handed and
right-handed members to determine if they interact through the weak force. Addi-
tionally, quarks come in three types of colors. The gluons carry color combinations
and total eight separate particles.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Particle EM Charge Spin Color Weak Isospin
aged +2/3 1/ 2 red Yes
ﬂied —2/3 1/2 antired Yes
urﬁd +2/3 1/2 red N o
'ﬁﬁ’d —2/3 1/ 2 antired No
ull’llue +2/3 1/2 blue Yes
77721116 —2/ 3 1 / 2 antiblue Yes
ulélue +2/3 1/2 blue No
ﬁlizhm —2/3 1/2 antiblue N o
uglreen +2/3 1/2 green Yes
Hireen —2/3 1/ 2 antigreen Yes
ugzreen +2/3 1/2 green No
ﬂgé'een —2/3 1/2 antigreen No

 

2.2.2 Experimental Conﬁrmation

The theoretical picture of the standard model has been accepted after rigorous testing
by many types of experiments over many different channels. The most profound
veriﬁcation of the picture was the successful prediction of the W and Z bosons, and
the relation of their masses. Additionally, the standard model predicted the existence
of the gluon, charm and top quarks before their eventual discovery.

The most current measurements of the electroweak sector of the standard model

have been compiled and evaluated by the LEP Electroweak Working Group [5]. The

18

plot in Figure 2.4 shows the overall consistency of each of the complementary mea-
surements compared to their best ﬁt. The overall agreement is amazingly consistent.
The table includes masses of the W and Z bosons and the top quark, the heavy
boson widths (I‘), the hadronic cross section, the weak mixing angle, the hadronic
contribution to the running QED coupling constant at the Z -pole, and various asym-

metry measurrnents, A, (such as in charge or polarization) and decay width ratios,

. m5
R, (such as In W).

2.2.3 Difﬁculties with the Standard Model

The standard model is not a fundamental theory. Despite its success and its corn—
pelling derivation from symmetries, nruch of the information in the standard model
comes from experimental measurements. There are twenty-Six parameters whose val—
ues must be added to the standard model by hand, and it would be preferred to have
a theory where these were theoretically determined. The most obvious shortcoming
of the theory is its failure to incorporate gravity. While the current energy scales
probed are not sensitive to this interaction, it obviously must be incorporated into a
full theory. Surprisingly, the standard model has held up incredibly well in experi—
ments. Its imminent failure keeps being delayed as it has shown itself to be able to
make precision predictions beyond the point where it might be expected to fail. Most
of this discussion was adapted from a lecture by Guido Altarelli at the 2008 Hadron
Collider Summer School [37].

2.2.3.1 Theoretical Difﬁculties

The most fundamental shortcoming of the standard model is the lack of an explana—
tion of gravitation. Although the gravitational interaction is so weak that its effects
are not measurable at current experiments, it can be calculated when the gravita-

tional force would contribute noticeably to measurements. It is found that the center

19

Measurement Fit lO'“ea‘°’—O"t|/omeas

 

 

 

 

 

 

 

L.-m_1 A1 L 1 1-, LLLL SLEEELAS
Aagymz) 0.02758 4 0.00035 0.02768 -
mZ [GeV] 91.1875 4 0.0021 91.1874
rz [GeV] 2.4952 1 0.0023 2.4959 In
623d [nb] 41.540 i 0.037 41.478 '
R, 20.767 x 0.025 20.742
Af’b" 0.01714 2 0.00095 0.01645
A,(P,) 0.1465 x 0.0032 0.1481
Flb 0.21629 4 0.00066 0.21579
RC 0.1721 2 0.0030 0.1723
Aft” 0.0992 1 0.0016 0.1038
A9; 0.0707 : 0.0035 0.0742
Ab 0.923 a 0.020 0.935
Ac 0.670 2 0.027 0.668 r
AI(SLD) 0.1513 1 0.0021 0.1481
sinzeﬁi’mm) 0.2324 4 0.0012 0.2314 —
mW [GeV] 80.399 x 0.023 80.379 —
rw [GeV] 2.098 a 0.048 2.092 I
m, [GeV] 173.1 11.3 173.2 I
0 1 2 3

Figure 2.4: Many experiments measure values that are. intercor’rnected by the standard
model. This figure shows how much each measurement pulls on the overall fit. Most of
r

the measurements show excellent agreement. The value of A0122.) d(m Z) is taken front
low energy experiments; the next ﬁve are LEP I line shape and lepton asymmetries;
AAPT) is from LEP I tau polarization; the next six are from LEP I and SLD heavy—
ﬂavor measurements; sin2di?t(Qﬂ)) is from LEP I (76 asymmetry; the two IV boson
measurements are from both the Tevatron and LEP II, and the top mass is only from
the Tevatron [5].

20

of mass energy of an accelerator needed to to probe the gravitational sector would
need to be on the order of 1019 GeV, which is known as the Planck mass (MPlanck)-
This scale is impossible to probe with any foreseeable technology, and even the highest
energy cosmic rays are 1014 GeV. Information about this sector can only be gleaned
indirectly from observing the large-scale structure of the universe.

Another difficulty is known as the hierarchy problem. This refers to the difference
between the scales where the weak and gravitational interactions become important.
When calculating the loop corrections to the Higgs mass, there are quadratic diver-
gences that must cancel at the level of new physics (the Planck mass in the standard
model). While this is not explicitly forbidden, it seems unnatural.

Additionally, ﬂavor physics is not well-described. It is found that there are three
representations of the fundamental particles with different masses. Each of the mass
eigenstates of these ﬂavors are combinations of conserved interaction eigenstates. The
amount of mixing is now fairly well measured but not well—described. The standard
model contains no compelling explanation for the observed three generations of par-

ticles that seem identical in their interactions but vastly differing in mass.

2.2.3.2 Experimental Difﬁculties

As has been mentioned, the experimental conﬁrmation from particle colliders has
been exacting. The precision measurements in the electroweak sector have put con-
straints on many new physics models. There are a handful of experiments that Show
some disagreement, such as the muon anomalous magnetic moment, (9 — 2) It» the
forward-backward assymetry for bottom quark production, A335), and the frequency
of a B? meson spontaneously oscillating to its antiparticle B3, BS mixing. How-
ever, these disagreements do not point to a consistent compelling argument for new
physics, and it remains to be seen if these indirect inconsistencies are due to difﬁcul-

ties in prediction, experiment or actually are the effects of new physics. Most of the

21

unsettling experimental results are not based on a particular experiment but through
the interpretation of the data in general, some of which are described below. These
factors simply point to behavior that deviates from what would be expected from
our current understanding of nature or observed phenomena that the standard model
cannot describe.

First, the ftmdarnental forces vary their interaction strength as a function of en-
ergy. This can be thought of as a property of the vacuum. As energies get higher and
higher, they can probe closer and closer to the particle, penetrating ﬂuctuations from
the vacuum which can screen the charge of the object. The electromagnetic charge
becomes weaker as e'e+ pairs are created out of the vacuum and the dipole moment
of the pair screens the overall charge seen from the electron. The opposite happens
in the strong force where the charge screening creates not only quark-antiquark pairs
but also gluons. The gluons are aligned such that the overall color charge seen in-
creases with distance. In the standard model, the weak, strong, and electromagnetic
interactions begin to approach the same strength with an increase in energy. It is
unusual, however, that while the forces approach similar coupling strengths, they do
not seem to converge.

The recent discovery that neutrinos are massive also points to a theory beyond
the standard model. The neutrinos are found to be so much lighter than the other
particles of the standard model that the mass hierarchy is difﬁcult to explain. One
explanation for this phenomenon is that neutrinos are Majorana particles (particles
that are their own antiparticles) and get their masses through interactions that do
not conserve lepton number. These actions, however, seem to be suppressed by the
GUT scale (the grand uniﬁcation scale where the electromagnetic, weak, and strong

forces are merged into a uniﬁed ﬁeld theory).
Astronomical observations have shown that most of the matter in the universe is a

material that has not yet been seen in experiments (or anywhere else) on earth. This

22

matter is detected through its gravitational interactions with Visible matter. The
standard model provides no particles that can account for the amount of dark matter
seen in the universe.

Additionally, the vacuum expectation value would create an energy density of the
universe which is N 49 orders of magnitude above what is actually measured. The
constant of the vacuum energy is actually arbitrary, so this factor is not completely
inconsistent. However, again, as with the cancellation of terms in the Higgs mass,

the value seems unnatural.

2.3 Beyond

Knowing that the standard model can not be a ﬁnal theory, it is reasonable to predict
what a more ftmdamental theory may be that still satisﬁes all of the observed exper-
imental data. These theories look to explain the dynamics of the Higgs mechanism
that lead to electroweak symmetry breaking [38].

Three methods of doing this will be brieﬂy described. The ﬁrst is to reduce the
unnaturalness of the loop corrections to the Higgs mass, as in supersyrmnetry. The
second is to eliminate the hierarchy problem by introducing extra dimensions in which
gravity propagates, making the scales only appear different in our 4-D world. The
ﬁnal class of theories that will be explored are the technicolor models. These introduce
a new force which follows the pattern seen in the development of QCD, where the

interaction was originally thought to be mediated by pion exchange.

2 .3. 1 Supersymmetry

The hierarchy problem is a fundamental difﬁculty highlighting the enormous difference
between the scale of electroweak syrrmretry breaking and the GUT or Planck scale.

If the standard model is correct to gravitational energies, then all terms of this scale

23

can enter into loop corrections to the Higgs mass. A natural explanation to the
hierarchy problem is that there are fermionic partners for the standard model bosons
and bosonic partners for the standard model fermions. These partners allow the
cancellation of divergent loop corrections and would allow a natural Higgs mass up
to the GUT scale [39].

The incorporation of these effects could also give a light Higgs boson within current
electroweak constraints, the uniﬁcation of gauge coupling strengths at the GUT scale,
and a possible cold dark matter candidate. Other attempts to solve the naturalness
problem in the Higgs sector can yield difficulty in maintaining consistency in the
Yukawa couplings, but with SUSY, all of the observed masses are consistent.

It has so far not been possible to consistently explain experimental data with only
particles coming from the minimal supersymmetric standard model (MSSM). The
addition of a hidden sector that does not interact with the standard model particles
or the expansion of the theory to extra dimensions provide an additional variable
in considering how supersymmetry might be naturally realized. The phenomenology
of the underlying theory depends upon how the visible MSSM sector communicates

with the hidden sector (or across the bulk between the branes) [2].

2.3.2 Extra Dimensions

Extra dimensions in various guises have the ability to bring down the fundamental
scale of particle physics from MPlanck to M EW (the scale of electroweak symmetry
breaking) by allowing gravity to propagate in additional space-time dimensions. This
would allow the strength of gravity to be on the order of the other forces in the
universe and only appear weak in the 4-D brane in which we do experiments [2].
In ﬂat extra dimensions, only the graviton propagates outside of the observable
4—D brane. The size of the additional extra dimensions can be determined by moving

the Planck mass to a scale that is adequate for electroweak symmetry breaking. The

24

graviton propagating in a compactiﬁed dimension will have a tower of possible energy
states. For a large number of extra dimensions, the number of these states (Kaluza-
Klein Modes) that would be observable is small and the experimental signature would
be difﬁcult to see. If the number of dimensions is small 5 8, then these states would
have small mass splitting and would act like a massive non-interacting particle. This
process can be searched for directly in mono jet and monophoton states. Additionally
the large number of states can be checked indirectly by looking at differential cross
sections in dilepton production [40].

Warped extra dimensions act similarly. Gravitons originate in a separate Planck-
brane in 5-D space, and the strength of gravity is suppressed by a warp factor which
reduces its overall strength when it reaches the 4—D standard model brane. With
the extra dimensions now not needing to be small, the Kaluza-Klein modes can have
greater spatial differences. The lowest. mode would only couple with the strength
of gravity and be unobservable. The ﬁrst excited state could be produced at the
TeV scale and could be. relevant to collider searches, coupling to diphotons and

dileptons [41].

2.3.3 Technicolor

There seems to be a rather simple analogue to the difficulties seen in the electroweak
sector at 1 TeV, which are the difﬁculties with the pion description of QCD at energies
~ 1 GeV. This would signal a new force that is not easily seen in particle interactions
at detectors [2, 38].

The W bosons would be the analogues of the charged pions, and the Z boson
would be the analogue of the neutral pion. The trouble with this framework is that
there is no simple way to incorporate observed fermion masses. Extended technicolor
couples the fermion masses to technifermions at a scale much higher than TeV. This

18 broken to simple Technicolor at energies at the TeV scale. This would explain the

masses of ﬂavors but does not give a reason why no flavor-changing neutral currents
are observed. A variation of this called “Walking Technicolor” allows some terms to
be enhanced because of techniparticle interactions. This means that the couplings in
the theory must run, but not in an analogous way to QCD, The ﬁmdamental particles
of technicolor cannot become asymptotically free at high energies. This explanation
satisﬁes everything naturally except the top quark masses.

One ﬁnal variant yields “Top-Assisted Technicolor” which has the top quark in-
teracting with a new strong interaction. This would make the standard model top
quark part technifermion. This additional interaction would also predict massive

gluons, known as top gluons that have been the subject of collider searches.

2.3.4 Experimental Signatures

Each of these theories can yield different types of experimental signatures. In an R—
parity conserving supersymmetry2, for example, large amounts of missing transverse
energy would be expected. However, most of the signatures are very model—dependent
within their overarching framework. One important feature of all of these models is
that in order to bring naturalness to electroweak symmetry breaking, the scale of
these new phenomena must be around the TeV scale. This leads to new particles
that would tend to decay to standard model particles with very high momenta. This
is the singular common feature, which makes it difﬁcult to make a speciﬁc prediction.
Often many assumptions have to be made to reduce the parameter space of the theory

being presented.

 

21D supersymmetry, baryon and lepton numbers are no longer conserved. Since the conservation
of these quantities has been tested very precisely, R-parity is introduced to suprcss these violating
processes. It is deﬁned as R = (—1)2j+33+L, where j is the spin, B is the baryon number, and L is
the lepton number. In supersyrmnetric extensions of the standard model, standard model particles
have R-parity of 1, and supersymmetric particles have R-parity of -1.

2(5

2.4 Analysis Strategy

With the overabundance of experimental signatures, this thesis describes an attempt
to search for physics beyond the standard model, attempting to minimize the as—
sumptions about the nature of that physics. Generally, the extensions of the standard
model include particles decaying to high energy particles related to the electroweak
symmetry breaking mechanism. The standard model background modeling simula-
tions at DO that are cm‘rently most developed are for ﬁnal states containing leptons,
which will be the subject of this dissertation. The strategy involves three basic steps:
(1) the selection of high-pT events and addition of correction factors, (2) the compar-
ison of overall event cormts and histogram shapes, and (3) a check of the high-pT tails
of distributions. These steps are accomplished in (1) the DO MIS (model independent
search) analysis packages, and the experiment-independent (2) Vista and (3) Sleuth

algorithms.

2.4.1 DO MIS Analysis Packages

The DO MIS (model independent search) analysis packages are responsible for object
selection and implementation of the necessary correction factors. Events that contain
isolated high-pT leptons are selected. Final states are then deﬁned based on the
objects occurring in these ﬁnal states. The simulation used for the prediction does
not properly account for events arising from multijet processes. These events are
modeled by reversing certain object selection cuts used to deﬁne the electron, muon,
and tau. The selected events are separated into seven nonoverlapping ﬁnal states
that are dominated by a particular standard model process. These seven were chosen
based on the possible dominant lepton or lepton pairs in an event (0, )1, cc, up, er,
#7", ye). The states are inclusive in jets and use a series of cuts to establish a single

dominant process. For these states, a ﬁt is performed to ﬁnd individual scale factors

27

that are unaccounted for in the simulation. These ﬁts are based on three fundamental
observables W, 77, (b). After the scale factors are determined, additional check plots
are used to make sure that the ﬁts using simple variables match the more complicated

parameters of the events.

2.4.2 VISTA

The events and scale factors from the MIS analysis packages are then passed to the
experiment-independent VISTA program. The VISTA program attempts to see if the
selected data can be accommodated by the standard model background developed
for this analysis. This algoritlnn focuses on signiﬁcant discrepancies in exclusive ﬁnal
states and agreement in 1-D histogram shapes. In VISTA, the ﬁnal states are deﬁned
by the full object content in the event. A ﬁnal state with one jet would be placed
in a different ﬁnal state than one with two jets. Overall consistency among many
histograms and ﬁnal states assures us that we can pass this information to the more
narrowly focused SLEUTH algorithm. VISTA could ﬁnd new physics if there were a
general and broad discrepancy with the standard model that could not be explained
by detector or simulation problems. More information on VISTA can be found in

Section 8.1.

2.4.3 SLEUTH

SLEUTH combines various ﬁnal states to improve sensitivity and calculates the event

pT sum. This is the sum of the transverse momenta of all of the objects in the event,

 

Zobj [I’prj] and the missing transverse energy, ET]. The missing transverse en—
ergy (ET) is the negative of the vector sum of the observed energy of the objects in
the event. In a hadron collider, the transverse component of the energy should be

conserved, so invisible particles carrying energy can be partially reconstructed by cal-

Clllating the transverse energy imbalance. Each event in these ﬁnal states will have

28

exactly one value of this quantity. These values are put into increasing order and
compared to the Monte Carlo prediction. For each event in data, the number of data
events with ZPT equal to or larger than the 2 PT for that event are counted and
compared to the number of weighted Monte Carlo events found in the same region.
If there is a data excess, then the probability for the Monte Carlo to ﬂuctuate up to
or beyond a value as large as that seen in the data is calculated from the Poisson
distribution. This is done for each event. The region Of the Z pT distribution found
to have the largest data/ background discrepancy is chosen. Then, to quantify the
probability of seeing a discrepancy as large as what is seen in data from statistical
ﬂuctuations in the background, the experiment is repeated, by creating Poisson ﬂuc-
tuations in each of the bins of the background distribution. The difference between
the event 2 PT in this pseudoexperiment is compared to the actual background, and
the region of maximum discrepancy is found again. This procedure is repeated to
determine how many pseudoexperiments would need to be run to see a ﬂuctuation
as large as what is seen in data. This process is repeated for all of the ﬁnal states.
If the probability of any point ﬂuctuating up to what is seen in the data is less than
0.001, then the state is marked for further study. Additional information on SLEUTH

can be found in Section 8.2.

29

Chapter 3

The DO Experiment at the

Fermilab Tevatron Collider

The Fermilab Tevatron Collider was the highest energy collider in the world until the
Large Hadron Collider produced collisions at energies above those of the Tevatron
for the ﬁrst time on December 8th, 2009. During the time that data was collected
for this analysis, the Tevatron was the highest energy collider. The Tevatron collides
protons with antiprotons at two locations on a one kilometer radius ring. Two high
energy physics experiments, GDP and DO, sit at the two interaction points as can
be seen in Figure 3.1. The ﬁrst section will describe the acceleration process which
leads to the collisions seen at DO. The second section discusses the DO detector.
The detector consists of material and electronics used to measure characteristics of
particles emanating from collisions. Each particle has its own unique signature and
the detector may measure the path, charge, energy, momentum, and / or vertex of
the particle to try to determine the kinematics of the event corresponding to the
collision. All of the information from the collisions must be ﬁltered to reduce the
rate of incoming events and the overall data size to a manageable level. This data
must be collected and stored, and other qualities of the detector environment must

be measured to make the data collected meaningful.

30

There have been two major data taking periods at the Tevatron. The ﬁrst ran
from 1992 to 1996 and is referred to as Run I. The second began in March 2001 and
is ongoing. This period is known as Run II. Furthermore, additional upgrades were
performed in 2006. This splits Run II into the period before the upgrades, Run Ila,

and the period after, Run 11b [13].

3.1 The Fermilab Tevatron Collider

There are three major stages of the accelerator that lead to the p13 collisions at the
Tevatron. The ﬁrst is the creation and acceleration of H - ions. Second, the electrons
are stripped off and the remaining proton is accelerated for either eventual injection
into the Tevatron for collisions or toward the 1‘) target for antiproton production. The

third major process is the creation, debunching, and storage of the antiprotons [20].

3.1.1 Creation and Acceleration of H ”

The early stages of acceleration are completed by H — ions. Using an ion of opposite
charge from the ﬁnal product allows easier accumulation of protons in the Booster.
The ions are created in the preaccelerator source and accelerated in the Cockcroft-
Walton preaccelerator. They then undergo further acceleration in the Linac through
the low energy drift-tube Linac (DTL) and the side-coupled Linac (SCL). The Linac is
the last stage of the H ’ acceleration where it then enters the Booster and is stripped

of its electrons [8].

3.1 . 1. 1 Preaccelerator

The preaccelerator begins with a 30 ft3 bottle of H2 that contains enough hydrogen
for around six months of Tevatron operation [42]. This source is released into a

magnetron in an electrically-charged dome [7]. A magnetron uses a magnetic ﬁeld to

31

Fermilab’s Acceleration Chain

[KL-«l "“N— ,_ Main Injector

Tevatron
Target Hall

,2: ""13 4; \
1 /Debuncher

/Accumu|ator
\{( \ ./

. -- Booster
/

f \\\ LINAC

Cockcroft-Walton

724% Antiproton Proton
Direction Direction

4‘ 4..-

 

 

 

Figure 3.1: The Fermilab accelerator chain [6].

cause the light electrons to spiral around a cathode which is enclosed within an anode.
The heavier charged particles will be pulled into the cathode or anode, while neutral
particles will be hit with a barrage of electrons. A diagram of the magnetron is shown
in Figure 3.2. Some protons will pick up two electrons from the dense plasma, pulling
the newly formed ions toward the anode. The main mechanism is from sputtering off
hydrogen atoms from the surface of the cathode. The addition of cesium vapor raises
the probability that the hydrogen atom will pull off the necessary electrons to form
the H — ions. Some of these ions will be pulled through an aperture in the anode.
Once through the aperture, there is a magnetic right-angle bend which selects H "
ions while the electrons and other particles of different charge/ mass ratio that also
happen to pass through the aperture are sent into a dump and lost. The gas goes

from the dome containing the magnetron to a grounded wall where it reaches a ﬁnal

32

energy of 750 keV and enters a transfer line to the Linac [8]. The static ﬁeld of 750
kV is created by a Cockcroft-Walton accelerator using a smaller 75 kV source which
is then multiplied several times by a system of capacitors. The total ﬁeld strength is
limited by the size of the area where the acceleration is to take place and the electrical
breakdown point. This is the only point in the accelerator chain where static ﬁelds
are used for acceleration. At higher energies, static ﬁelds are too diﬂicult to maintain

to be of practical use.

Plasina ’ F H2 Gas [Anode

 

  

 

 

088mm .. . ._ . .
Vapor _ . . . __ GB
kExtt-actor
Plate
H‘Ions ‘[

 

Figure 3.2: The Magnetron: Creating H - [7].

3.1.1.2 Linac

The Linac takes the 750 keV H — ions and accelerates them to 400 MeV over 79
m. This is done in two sections, a low energy drift-tube Linac, and a higher energy
side—coupled Linac. The drift-tube Linac contains ﬁve radio frequency stations, while

the side-coupled Linac uses Klystrons for acceleration. The drift-tube Linac (DTL)

33

uses a single varying B-ﬁeld to produce a ﬂuctuating E—ﬁeld. The ions are exposed
to the ﬁeld when it pushes the ions forward and are shielded from it when it pushes
in the opposite direction. As the ions gain energy, the length of shielded pipe must
increase to compensate for the fact that the ions cover a larger distance over the same
period of time. A diagram of the DTL is shown in Figure 3.3. The increasing particle

energy from this process is shown in Figure 3.4.

 

 

 

 

‘I'r‘

 

 

 

 

 

Figure 3.3: The Drift Tube Linac [8]

The side-coupled Linac (SCL) uses Klystrons to produce the electric ﬁelds used
for acceleration. The Klystron produces a ﬂow of electrons which are bunched in
cavities, and then accelerated [43]. These electron bunches excite microwaves in an
output cavity that ﬂow into a waveguide. These waves are used to produce the electric
ﬁeld that is seen by the ions in the SCL. The electrons used to generate these waves are
then absorbed. While each chamber in the DTL uses the same ﬂuctuating magnetic
ﬁeld to produce the electric ﬁeld seen by the ions, the SCL cavities are separated
using different generated ﬁeld strengths. Upon leaving the linear accelerator, the ions

are next sent to the Booster.

34

Particle

Kinetic m

Energy ,
(no drift V tIme

 

 

 

 

 

 

 

 

 

tube)
Electrically-
grounded
? drift tubes
A _.

Particle

Kinetic

Energy ,

(with drift > "me

tubes)

Figure 3.4: The energy of particles as they travel through the DTL [8]

3.1.2 Creation and Acceleration of the Proton Beam

Once the ion reaches the Booster, it has reached an energy of 400 MeV. At the Booster
it is stripped of its electrons, and the remaining proton is accelerated to 8 GeV. After
this, the proton is sent to the Main Injector where it can be stored for injection into
the Tevatron, sent out a beam line to ﬁxed target experiments, or diverted to a target

for the production of antiprotons.

35

3.1.2.1 Booster

The Booster is a synchrotron that takes 400 MeV H _ ions, strips off both electrons
producing protons, and accelerates the protons to 8 GeV. The Booster is 75 m in
radius and accelerates the protons with 17 RF cavities before sending them to the
Main Injector [44]. When ﬁlled, the Booster contains 3- 1012 protons. Particles must
be aligned in a way such that they experience an accelerating E-ﬁeld at the same
time. At any time, each of the 17 RF locations could be used to accelerate particles.
The possible particle acceleration paths are known as buckets. If the bucket contains
particles, it is known as a bunch.

In the circular synchrotron machines, each particle arrives at an individual RF
cavity many times, each time with increasing energy. In order to ensure that an
accelerating ﬁeld is found inside the cavity, the radio frequency of the ﬁeld needs to
be modiﬁed.

Non-ideal particles will not be accelerated as expected, and each particle that is
slightly ahead of the ideal particle in phase will get less of an increase in E-ﬁeld, and
each particle behind the ideal will get a larger increase. This causes the non-ideal
particles to oscillate aroundthe ideal particle trajectory in what are called synchrotron
oscillations. Similarly, the restorative forces of quadrupoles used to focus the beam
will redirect wayward particles toward the ideal path, but it is necessary to continually
correct them to keep them in the beam. This type of oscillation due to the focusing
elements of the detector are called betatron oscillations [8].

In the Booster, particle energies reach a point where the stable synchrotron os-
cillations discussed above are no longer valid. As particle momenta are increased,
the velocities of the particles approach the speed of light, and there is little differ-
ence in speed across the particle bunch. This means that higher momenta particles
will still receive the increase in energy leading to a larger radius to traverse in the

Booster. With the same velocity, this requires a longer time than the synchronous

36

rJ

particle to complete a cycle. This means that the higher energy particles that were
arriving early, begin arriving late as speed approaches the speed of light and rela-
tivistic considerations dominate. At this point, the former restorative forces become
destabilizing, and the ﬁelds are modiﬁed to anticipate higher energy particles arriving
late and lower energy particles arriving early. This transition occurs ~ 4.2 GeV, and
is passed through quickly to minimize instabilities.

The H — ions enter the booster where a magnetic ﬁeld draws them toward an
already spimiing proton beam. As the two beams are brought together, the H —
beam hits a carbon foil where electrons are stripped producing additional protons.
Next, the entire beam is subjected to the same magnetic ﬁeld producing a dogleg
for the protons and putting them back into the normal path of the Booster. The
ﬁeld will cause the remaining H _ ions to be cast into a beam dmnp while neutral
hydrogen atoms continue along the original path and are subject to the same fate [7].
Using an H — ion beam, allows charge-exchange with the neutral carbon foil. Since
the charge-exchange is nonconservative, the conservation of phase space necessary to
satisfy Liouville’s theorem is not a necessary condition, and the new protons created
from H — ions can be fully merged with the existing proton beam. This was the
primary motivation for using the H “ beam rather than immediately creating and
accelerating protons. The process of electron stripping and merging of the beams can
be seen in Figure 3.5. Once particles pass through the Booster synchrotron loop 24

times, they reach an energy of 8 GeV and are sent to the Main Injector.

3.1.2.2 Main Injector

The main injector performs several functions [9]. Some of the 8 GeV incoming protons
are accelerated to 150 GeV and injected into the Tevatron for collisions. Others are
ramped up to 120 GeV and sent toward the antiproton target. Antiprotons also enter

the main injector and are similarly ramped to 150 GeV for insertion into the Tevatron.

37

ORBMPI ORBMPZ

 

 

Strlpplng Foil

Septum

if

Debunched 1cm I__
f 200 MeV H- In
Beam from Linac

Figure 3.5: The H 5 ion is stripped of its electrons and merged with an existing beam
of protons using a carbon foil and dogleg magnet [7].

Both the protons and antiprotons are coalesced at ﬂattop before moving to the
Tevatron. Flattop is the accelerator condition where the current in the accelerator is
maintained as constant and the accelerating voltage is dropped to nearly zero. This
releases some of the restorative bunching forces in the cavity, so bunches are able to
drift. Special RF cavities then make several bunches (7 for protons, 4 for antiprotons)
coalesce into a single bunch. The RF voltage is then turned back up with a newly
coalesced bunch structure. For proper insertion, the Main Injector and the Tevatron
are set to have the same RF frequencies and phase. To line up a particular MI bunch
with a Tevatron bucket, the RF is changed slightly in the MI until the desired Ml

bunch is aligned with the target Tevatron bunch. The RF frequency is then restored

38

and the transfer from the Main Injector to the Tevatron is made. This process is
known as transfer cogging and is described in the Accelerator Concepts Rookie Book,
[8], as follows: “Imagine two large gears meshed together. The Main Injector gear has
588 teeth (RF buckets), and the Tevatron gear has 1113. Once these gears are synched
up with each other, they are locked into position relative to each other as well, and
particle transfers can occur between them. We want to send protons in a given MI
bucket into any Tevatron bucket. The solution is to change the RF frequency in the
MI slightly, making the two machines out of phase with each other for a time. While
the two gears are out of phase with each other, they will rotate at different speeds,
causing different sets of teeth to come near to one another. If the MI frequency were
changed back to its original value at the appropriate time, any MI bucket could line
up with any Tevatron bucket.” The loading of the Tevatron from the Main Injector

can be seen in Figure 3.6.

/ Tevatron
Coalesced Protons .
Coalesced Antiprotons .

 

Figure 3.6: Loading the Tevatron from the coalesced protons and antiprotons in the
Main Injector [9].

39

Some protons are sent down a beam line that leads to ﬁxed targets and analysis
by other experiments at Fermilab. The rest are used in the production of antiprotons.
These 120 GeV protons are sent from the Main Injector, through a beam line near

the Tevatron and toward the Inconel (a nickel-ion alloy) antiproton target.

3.1.3 Antiproton Production and Storage

The Fermilab Tevatron Collider is a pf? collider. The 13’s are created at the Tevatron
using accelerated protons. The 120 GeV protons from the Main Injector are directed
into a target, the antiprotons from this collision are peeled off, debunched, stored,
and ﬁnally injected into the Tevatron for use in collisions. There are four parts of the
antiproton system: the target, Debuncher, Accumulator, and Recycler. The Recycler,
which was originally plarmed for storage of unused antiprotons from the Tevatron,
has instead become the ﬁnal step in antiproton storage and cooling before transfer

into the Tevatron.

3.1.3.1 Target

Energies of 120 GeV in the Main Injector were chosen speciﬁcally to best produce an—
tiprotons at 8 GeV. It takes approximately 50,000 protons to produce ~ 1 antiproton
[10].

The target is made of a single cylinder of Inconel, a nickel—ion alloy, chosen because
of its ability to withstand high stresses due to rapid beam heating.

Since the momentum spread is not important for protons about to hit the target,
the protons undergo bunch rotation reducing the time spread of the particles at
the expense of increased momentum spread. A lithium lens focuses the incoming
antiprotons in the :1: and y planes with a very strong magnetic ﬁeld. The lithium lens
was used rather than a traditional quadrupole because of its ability to focus in both

transverse planes and produce a very strong magnetic ﬁeld. It has the disadvantage of

40

losing ~ 18% of the antiprotons to absorption because the beam must pass through
beryllium end plates and the lithium conductor. Lithium was speciﬁcally chosen
because of its low density, to minimize the absorption and scattering effects. A

pulsed dipole then selects 8 GeV antiprotons. This is shown is Figure 3.7.

 

     

   

     

 
   

lnconel
Production Current = 0.5 MA
Target 4...
Lithium
Protons Lens

Secondaries

Figure 3.7: A ﬁgure showing the 1‘) target and the lithium lens used to select antipro—
tons at 8 GeV [7].

me here, the antiprotons follow a beam line to the Debuncher.

3.1 .3.2 Debuncher

When antiprotons enter the Debuncher, they have a wide momentum spread. A dipole
was used to select antiprotons of ~ 8 GeV, but the momentum spread of entering 17’s
is still large [7].

The Debuncher uses bunch rotation to reduce the 1') momentum spread. Bunch
rotation is the same process that was used on the protons before hitting the target,
but in the opposite direction with the opposite goal. By reducing the momentum
spread and broadening the time structure (phase), smaller magnetic apertures are
effective and stochastic cooling works much better.

After passing through the Debuncher, the Ap/p is reduced from 4% to 0.2% or
around 18 MeV. This principle is outline in Figure 3.8.

After the reduction in the momentum spread, the particles remain an additional

41

Bunch Narrowing with

 

 

 

 

  
     

RF voltage = 3.5 MV
15
%
; Phase(¢)
ﬂ .
2
n
m
E Bucket
B with RF
5 Voltage
E , 3.5 MV
0 Bunch StretchIng when
5 RF voltage is reduced
from 3.5 MV to 1.2 MV

E
o.
'3
-o
(6
2
g Phase(¢)
E
B
5 Bucket
E with RF with RF
g Voltage Voltage

1.2 MV 3.5 MV

 

Figure 3.8: This shows the process of bunch rotation. The phase of individual particles
is sacriﬁced to get a more consistent momentum in the beam [10].

42

 

‘sole "

. 0 'v
1 a ‘. l
‘[ I I
‘ l I.
.‘. t...« l

'l"
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n [l
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two seconds in the Debuncher where they undergo stochastic cooling. Stochastic
cooling is the process where the transverse position of a particle is found, related to
a betatron oscillation, and sent a corrective signal to dampen the oscillation. The

magnitude of betatron oscillations drops by a factor of around two in the Debuncher.

3.1 .3.3 Accumulator

The purpose of the Accumulator is to accumulate and store antiprotons. First, 8
GeV ﬁ’s are injected into the Accumulator [10]. The injected beam remains 80 mm
outside of central p orbit. Then, the beam is decelerated by 60 MeV to move it to
the stacktail (the edge of the central orbit). The RF is then turned off there, so
the beam is adiabatically debunched, and the momentum of the particles drops by a
total of 150 MeV from the injection point to the central Accumulator energy. After 20
minutes the antiprotons reach the core of the beam where they undergo momentum
and betatron cooling before transfer to the Recycler. The path of the 13’s within the

orbit of the Accumulator can be seen in Figure 3.9.

3.1.3.4 Recycler

The Recycler runs 47 inches above the Main Injector in the same tunnel. It cools the
antiproton beam and stores it before injection in the Tevatron, functioning much like a
larger and more complex version of the Accumulator. There are four stochastic cooling
systems within the Recycler, two horizontal, one vertical, and one longitudinal.

The Recycler also uses electron cooling to cool the antiproton beam [11]. Electron
cooling works by sending a beam of electrons parallel to the antiprotons. The 13’s
undergo Coulomb scattering with the electrons and lose energy until they reach a
thermal equilibrium. The cooling process is shown in Figure 3.10.

Once the antiprotons have been cooled in the Recycler, they are accelerated to

150 GeV in the Main Injector and sent into the Tevatron.

43

l —

 

 

Stack Core

Beam Intensity (Log Scale)

 

 

Freshly injected
pulse on injection

 
 

Outer edge
of Accumulator
(8lGeV)

I
0 Energy Difference from ‘1 50
Injection Energy (MeV)

lnneredge
of Accumulator

 

 

 

Figure 3.9: The ﬁgure shows the path of the antiprotons within the Accumulator as
a function of energy. As the particle begins to lose energy, it slowly moves into the
center of the orbit [7].

44

y _
...JII.

 

 

 

 

 

 

 

 

 

 

 

Electron Electron
Gun \ Collector
__ g "E __ Storage

 

far" L ..I ""”'--~..-Ei_pg

r

_-- l‘
'0“ Beam 1-5% of the ring ’"
circumference

Figure 3.10: The process of electron cooling. A stream of electrons is pushed over the
antiproton beam, absorbing energy until the antiprotons are at thermal equilibrium
with the cool electron beam [11].

3.1.4 The Tevatron

The Tevatron is a one kilometer radius, 1.96 TeV proton-antiproton collider. It uses
only superconducting magnets kept at 4.6 K with liquid helium. The beam pipe is
kept at 10—9 torr. The beam in the Tevatron is accelerated in eight separate cavities,
four are used for antiprotons and four for protons.

Protons and antiprotons are sent to the Tevatron with energies of 150 GeV, and
are ramped using the same magnets to 980 GeV. Once the energies in the beam have
reached their goal, the Tevatron begins what is called the low ﬂ squeeze.

The position of a particle will deviate from that. of the ideal. The area of transverse
phase space that is occupied by the particle beam is known as the emittance. The
amplitude of the beam spread is proportional to a term known as the ﬁ function. The
value of this function is typically on the order of meters (this is proportional to the
beam spread which is on the order of 100’s of microns). Focusing quadrupoles at the

interaction regions reduce the value of the 73 function at these areas (known as ,8*)

to 35 cm. This is equivalent to a beam spread of 10’s of microns.

 

 

p I ‘

r d L.
t—

|

' [lr' Tl
‘ . ‘. I
v 3 -
I Ill
. .u ‘

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Once the beam size is reduced, collisions commence, but the unstable portion of
the beam still needs to be removed. The part of the beam that falls outside of the
stable region is known as the beam halo. Collimators are pushed near the beam to
remove the unstable beam halo.

A period of collisions, typically lasting between one half to one full day is known as
a store. Thirty-six separate bunches are collided, divided into three superbunches of
12 bunches with a 2.6 [us spacing between the superbunches. Collisions at the Tevatron
happen every 396 ns within a superbunch. The bunch spacing at the Tevatron is
shown in Figure 3.11.

The luminosity is a measure of the number of collisions occurring in a unit time.

2

The average luminosity during Run IIa was on the order of 81- 1030 cm‘ 3‘1 while

030 cm"2 3‘1 or more. The average number of

this has recently increased to 2001
collisions in each crossing have gone from an average of around 2.3 early in Run 11a

to 5.8 at higher luminosities.

3.2 The DO Experiment

The DO detector was proposed in 1983 for pf? collisions at an energy 1.8 TeV. The
ﬁrst run of the Tevatron took place from 1992 to 1996, leading to the discovery of
the top quark among many other signiﬁcant achievements. The second run began in
2001 with an increase in energy to 1.96 TeV and decreased bunch spacing producing
more collisions and provided greater sensitivity to rare physics processes [13].

All the physics detectors at DO rely on an understanding of how high energy
particles from the pp collisions interact with matter. The Bethe equation shown in
Equation 3.1 describes charged particles interacting with matter through ionization
for mid to very high energy particles. The variables are deﬁned in [2] with units in
MeVg—lcm2. A common example is the interactions of a muon traveling through

Copper, shown in Figure 3.12. Electrons also interact through ionization, but high

46

   

BO CO

  

 
 
      

pbar bunches
proton bunches
colllslon areas

A0 DO

Figure 3.11: The Tevatron bunch structure. Collisions happen every 396 us within a
superbunch. There are three “Trains” of twelve bunches with an abort gap between
“Trains” of 2.617 as [12].

energy electrons at DO lose most their energy through bremsstrahlung emission of a

photon. The relative fraction of energy an electron loses in lead is shown in Figure

3.13. Photons at high energies typically interact through pair production.

 

dE 2Z 1 ll Q'mcC2132O/QTynaI _ £2 _ 6037)

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the interactions that inﬂuence that particle. A charged particle is sensitive to electro-

47

 

   
   
       
   

[*{I I I I I II

 

 

 

 

 

 

 

 

 

 

 

 

 

,_, " [1+ on Cu ‘
3’
NS 100 :— —E
g : Bethe-Bloch Radiative j
c I _
E 73.5 Ziegler a
s r- 3 E ‘1
B :5 ,2
8- 10 —.S (B , , __
be 5...: Radiative :
a 3 Minimum effects :
a. - ionization reach 1% ,,,,,,,, a
.8 _Nuclear —.- ______ _
”3 _ losses i ——————————————— L
[ Without 8
1 ; l l ' l I
0.001 0.01 0.1 1 10 l3 100 1000 104 105 106
Y
1 l l l J l l l l J
L01 1 10 100 I [1 10 100 I [1 10 100 ,
[MeV/c] [GeV/c] [TeV/c]

Muon momentum

Figure 3.12: The Bethe equation showing the stopping power for a muon traveling
through copper. The solid line represents the total energy loss [2].

magnetism, and through ionization leaves tracks in the DO central tracking system.
Electrons also interact through bremsstrahlung with nuclei in the material of the
detector. Once the material reaches the density of that in the EM calorimeter, the
electrons can lose most of their energy. Photons similarly lose energy in dense ma-
terials through pair production. This ties the decays and energy measurements of
these two types of particles together. A high energy electron can emit a high en-
ergy photon through bremsstrahlimg, which will then pair produce an electron and a
Positron, which can then emit additional photons. This chain of events can continue
until average photon energy drops below the pair creation threshold, after which time,
Compton scattering is the dominant process. This will ionize molecules by kicking
electrons from their bound states. At this point, the shower stops growing. The aver-
age energy lost by an electron or photon will be measured in this analysis in radiation

lengths (X0)- This is the amount of material for an electron energy to be reduced 1/e

48

 

 
     
 
 

 

 

 

I ‘\lll|lll I IFTIIIII l Tll|l|_W
_ ‘ . —- 0.20
‘ Pos1trons J
— \ Lead Z = 82
_ \/ ( ) A
Electrons \\ _
"T 1.0: \\\ _015 FT
>50 _ ‘\ Bremsstrahlung : also
as — I E
—0.10 v
HIE] F— Ionization .4
I _ s
0'5 Moller (e‘) _
Bhabha (e +) 4 0.05
__ Positron :
annihilation —
0 l l I l l l l I —~_._
1 10 100 1000

E (MeV)

Figure 3.13: High-energy electrons and positrons lose most of their energy from
bremsstrahlung. The relative energy loss for an electron or positron in lead per
radiation length is plotted against the electron or positron energy [2].

and also 7/9 of the mean free path for pair production of a high energy photon.

The high mass of the muon makes all but the most energetic at the Tevatron
below the threshold of signiﬁcant energy loss through bremsstrahlung. The muon
will still lose some energy through ionization, but this is typically of the order of
a few GeV. Since muons also do not interact hadronically, and their decay time is
considerably longer than it takes to exit the detector, the main way of identifying
muons is the fact that they get through the calorimeter to produce a path in the
muon system. This path can the be tied to a track in the central tracking system and
their signature within the calorimeter of minimum energy loss through ionization.
This type of minimum ionizing particle is known as a MIP.

Charged hadrons are also susceptible to ionization within the tracking system, but

49

the lower cross section of nuclear interactions allows them to pass through the EM
calorimeter without losing all of their energy. The hadronic calorimeter was designed
to provide enough material for hadronic particles to interact inelastically with atomic
nuclei to the point that most of their energy is lost. Hadronic particles shower in
a way similar to electrons and photons. As they interact with nuclei they decay
into less energetic particles which can decay again and again in a hadronic shower.
The no decays into two photons which can decay electromagnetically and provide an
electromagnetic component to the hadron showers. The energy grows until the lightest
hadronic particles, the pions, can no longer be produced. Particles that interact
hadronically, have an analogue to the radiation length, called the nuclear interaction
length (AA). This accounts for energy losses by all types of nuclear interactions.

There are three major detector subsystems: the central tracking system, the
calorimeter, and the muon system at the outside of the detector. The main subde-
tector components and relative detector size can be seen in Figure 3.14. The primary
sources used for the explanation of the detector physics were [45, 46], and the primary
resources for the DE implementation of these devices were [13, 47, 48].

D0 uses a right-handed cylindrical coordinate system with positive z oriented
along the proton direction and positive y pointing straight up. Given the right-
handed coordinate system, the x—axis points out from the center of the Tevatron ring.
Several other variables are used when measuring position with the D9 detector. The
azimuthal angle, (15, is measm'ed from the :c-axis in the Qty—plane. The polar angle,
6, is measured from the z-axis in the yz-plane. The perpendicular distance from the
z-axis, r is deﬁned as r = W. The polar angle is typically not used in favor

of 77, the pseudorapidity. This is deﬁned as

17 :2 —ln [tang] . (3.2)

The pseudorapidity approximates the true rapidity,

    
  

Muon Sclnﬁllatom

‘2 Muon Chambers

  

 

Figure 3.14: The DQ Detector— The z—axis is in the direction of the proton beam, the
y-axis is straight up, and the :r—axis points out, away from the center of the Tevatron.
The central tracking system is within the calorimeter [13].

1 [Epic] (3.3)

y = 2m E — pzc
for ﬁnite angles as mc2/E -—> 0. Rapidity is a Lorentz invariant quantity under
longitudinal boosts. The pseudorapidity is a more useful quantity than the polar
angle both for its invariance properties as well as the fact that particle ﬂux is rather

evenly distributed in pseudorapidity so that it is a convenient way to divide the

detector in the polar direction.

3.2.1 Central Tracking, Solenoidal Magnet, and Preshower

The central tracking system operates on the principle of ﬁmdamental particles mini—

mally interacting with detector components. The tracking system attempts to mea-

51

sure particle position without interacting strongly enough to change the particle di—
rection signiﬁcantly or absorbing a non-negligible fraction of the particle’s energy.
When these detectors are layered, the position measurements of each layer can be
combined to reconstruct tracks. Only particles with charge interact enough to pro-
vide position measurements. The tracking system lies within a solenoidal magnet
(causing the charged particles to bend) allowing for charge and momentum mea-
surements. Outside of the solenoidal magnet, preshower scintillators allow for quick
energy sampling to help identify electrons and to assist in tracking before the particles
hit the calorimeter, which will be discussed in Section 3.2.2.1. A view of these central

detector components can be seen in Figure 3.15.

Intercryostat
Detector

Central Fiber Tracker

  
  
  
 
   
 
  
  

Forward
Solenoidal Preshower
Detector

Luminosity
Monitor

D0
Beam

Pipe
End

Central Preshower
Detector Tracker

Figure 3.15: The inner tracking system showing the SMT, CFT, the solenoidal magnet
and preshower detectors [13].

52

3.2.1.1 Silicon Microstrip Tracker

The SMT is a silicon microstrip tracker that provides tracking and vertexing informa-
tion over the 77 range needed for objects detected in the calorimeter or muon system.
Additional information about the silicon detector comes primarily from [14]. In or-
der to produce hits at normal incidence over a range of 7] values across the extended
interaction region, a z 25 cm, the SMT system uses a series of 12.4 cm long barrels
interspersed with disks. Each barrel contains four concentric layers, the closest to the
beamline at a radius 2.6 cm and the furthest with a radius of 10 cm. This has been
complemented in Run IIb with an additional layer of silicon, layer 0, which resides
1.7 cm from the beamline [49]. Layer zero required a new beryllium beampipe of 1.5
cm radius onto which the detector was attached directly.

The SMT tracks position through the use of 300 pm thick silicon wafers. Two of
these 6 cm wafers are placed together in what is called a ladder. The silicon is slightly
n—doped, but as it encounters radiation, donor states are. removed and acceptor states
are created leading to type inversion, and the bulk becomes p—doped. Type inversion
allows the tracker to function for longer under heavy radiation than a design for only
a single type of doping. The depletion voltage needed to bring charge to the surface of
the each of the strips is decreased as the radiation adds impurities to the bulk. This
will reduce the depletion voltage until the type inversion, after which it will steadily
grow until the microstrip becomes unusable. Only the ﬁrst layer of the silicon appears
to eventually cross the utility threshold in the expected lifetime of the Tevatron.

There are three types of sensor design, single-sided, double-sided, and doubled-
sided double-metal. The single-sided modules are used in the Layers 1 and 3 of the
outer two barrels and only provide axial information. The double-sided modules are
used in Layers 2 and 4 for all barrels and the double-sided double-metal for layers
1 and 3 in the inner four barrels. The double-sided sensors have small stereo angles

of 2° while the double—sided double-metal are at larger angles of 90°, for gathering

53

3—D information for the primary vertex and secondary vertex ﬁnding, respectively.
Each of these has 50 pm pitch strips on the p—side, while the pitch of the n—side of
the double layers varies depending on the stereo angle. Layer 0 has a pitch of 75 pm
and a total of 256 channels which are readout outside of the active detector region to
minimize the mass that particles must travel through.

The SMT was designed to maximize the number of detector layers each particle
went through and to have some particles pass these layers perpendicularly to get the
best hit resolution. The SMT location close to the beampipe allows measurements
of secondary vertices. These are used in the identiﬁcation of b—quarks which brieﬂy
form B mesons. The B mesons live long enough to have a distinct secondary vertex.
Since the barrels will not measure forward particles well, disks have been included to
sample these particles with higher 7). There are twelve of these F—disks located at [z] =
12.5, 25.3, 38.2, 43.1, 48.1, 53.1 cm. The disks use twelve double—sided wedge detectors.
Additionally, in Run Ha there were four H—disks located at [z] = 100.4, 121.0 cm for
very high-17 particles. The SMT consists of nearly 800,000 strips providing a spatial

resolution of ~ 10 pm. The full barrel-disk structure used in Run He. can be seen in

Figure 3.16.

 

Figure 3.16: The layout of the silicon microstrip detector [13].
Estimates of the momentum and impact parameter resolution are shown in Figures

54

3.17, 3.18. The addition of layer zero improved the impact parameter resolution by
~ 55% and expected to improve heavy ﬂavor tagging ~ 15% [50]. The 2 resolution is
shown to be 35 pm for 90° stereo, and 450 pm for 2° stereo [51]. This is adequate for
the goals of primary vertex ﬁnding with the small angle stereo and secondary vertex

ﬁnding with large angle stereo.

 

    

100.0

T I IIIIII]

[J 1 Llllll

pT == 100 GeV

    
 

l llllllll

I IIIIII
l llLlllll

I

 

 

 

Figure 3.17: The pT resolution expectation with respect to 77 for different particle
momenta [13].

The currents from the SMT are readout with low—mass Kapton cables using 128-
channel SVXIIe chips. The input for one train of beam collisions (~ 12) is integrated,
and then reset during the gaps between the superbunches. On a Level 1 accept signal,
the pedestal values are subtracted, and the signals are sent to Wilkinson ADCs to

digitize the signal. The ﬁrst use of the SMT data is in the Level 2 trigger.

2D Impact Parameter Resolution

 

 

 

 

.150 [Fr r r F‘ iﬁi‘rFW Iii rf_
.. l | _
i: I
'— a
._ d
lb _
100 :—- —:
7: '3 3
t '- _
a" 50 z}- '1.
.4
b .- j
0 l I I I I I I I-
0

 

No B d'nks

 

""""" H disks :hchded

Figure 3.18: The impact parameter resolution expectation from the SMT technical
design report [14].

3.2.1.2 Central Fiber Tracker

The central ﬁber tracker uses a scintillating plastic to determine the position of
charged particles through eight concentric cylinders of two doublet layers. The radius
of the innermost cylinder is 20 cm, and the outermost is at 52 cm. The inner cylinders
are 1.66 m long to allow room for the H-disks in the SMT, and the outer cylinders
are 2.52 In providing [77] coverage to 1.7. One doublet layer in each cylinder is aligned
axially while the second alternates between 21:30 to give a stereo measurement in the
z-plane. The layout of the OFT within the tracking system is shown in Figure 3.19.

The 835 pm diameter ﬁbers consist primarily of polystyrene which when excited
transfers energy to paraterphenyl by dipole-dipole interactions. The paraterphenyl.

emits light at 340 nm, which would be quickly absorbed in the polystyrene. Therefore

Strain

  
  
  
       

relief ring
for CFI', CPS
waveguides
256-channel ﬁber
CFl' or CPS ,/" Central calorimeter
waveguide bun ” Q/ cryostat wall

Strain
relief

an]

a" , Eyh Clearance
' ' [f for FPS

3 waveguides

§‘ ) (not shown)

     

\§‘
a.

‘
‘\
\- .\

z-‘I‘ \
\\‘. .

      
        
   

  

."

      
     

   

. // ’llllllllﬂl \
Willi“ Solenoid

L]],,.]]/Z! services

/ "1\
(9": I
V, 1‘
\4/1 «-

\Calorimeter
support
structure
Vertical
waveguide
chutes
to D¢
readout platform
(VLPC cryostats)

Figure 3.19: The central ﬁber tracker with supports within the solenord [15]

57

an additional agent, 3-hydroxyﬂavone, is added which absorbs the 340 nm signal and
re—emits at 530 nm. This wavelength transmits easily through the polystyrene. Each
ﬁber contains two layers of cladding to maximize internal reﬂection, and is stopped at
one end with sputtered aluminum providing 90% reﬂectivity. The attenuation length
in the scintillating ﬁbers is 5 m. The ﬁbers are connected to clear waveguides ﬁbers
which transfer it out from the central tracking region through gaps in the calorimeter
to the housing of the VLPC (visible light photon counters) in a cryostat below the
central calorimeter. This covers a distance of 7.8 to 11.9 m. The attenuation length
of the waveguides is 8 In. All of the ﬁbers total 0.0028 radiation lengths, with the
carbon supports 0.0032 X0 and the various glues 0.0030 X0 for each of the eight CFT
layers. This allows high energy electrons to pass the OFT layers without losing a
large fraction of their energy.

The VLPC is an avalanche photodetector. It consists of impurity-band silicon
with the entering photons creating electron—hole pairs. The holes drift through a
depletion zone and into an impurity band colliding with neutral donors and releasing
an electron. The electron begins an avalanche by impact ionization with the neutral
donor impurities. The gain saturates at ~ 104. The process producing the electron
avalanche is shown in Figure 3.20. The VLPC boards are also used for the central

and forward preshower detectors discussed in Section 3.2.1.4.

3.2.1.3 Solenoidal Magnet

The solenoidal magnet was installed to improve the momentum resolution of charged
tracks passing through the tracking system. The magnet is 2.73 m in length and 1.42
m in diameter, determined by the available space within the calorimeter.

The magnet was designed to operate in both polarities, provide a uniform ﬁeld,
maximize the tracking area, minimize the materials used, and have adequate safety

mechanisms in place in the case of a quench. A ﬁeld of 2 T was found to be the

 

Figure 3.20: The process used to create the electron avalanche from the incoming
scintillated light in the VLPC. A photon enters the intrinsic region of undoped silicon
creating an electron—hole pair. The hole moves to the drift region where it removes
an electron from an atom. The electron accelerates through the gain region freeing
more electrons from atoms. The current from these freed electrons is then collected
to record the presence of the initial photon [15].

optimal ﬁeld to best satisfy the above conditions.

The magnet is constructed using strands of CusNbTi in a ratio of 1.34:1 and sta—
bilized with aluminum. Each strand is 0.848 mm in diameter with 18 strands in each
conductor. The material in the magnet totals 0.87 X0, and it is kept superconducting

with liquid helium. The full magnetic ﬁeld is shown in Figure 3.21.

3.2.1.4 Preshower Detectors

Outside of the solenoid, in the 5 cm gap before the calorimeter lie the central and
forward preshower detectors. These function in some ways similar to the tracking
detectors and others to the calorimeters. Measurements from the preshower can

help with electron identiﬁcation and background rejection by correcting EM shower

59

 
  
  

 

Toroid

V (cm)

 

 

I

2 (cm)

Figure 3.21: The magnetic ﬁeld seen by particle traveling through the D0 experiment
in kG [13].

60

measurements for energy losses in the solenoid and other upstream material. The
particle signals in the preshower detectors are measured quickly enough to allow their
inclusion in the Level 1 trigger.

The preshower scintillators are made of triangular strips of polystyrene, as with
the OFT. This is mixed with small amounts of p—terphenyl and diphenyl stilbene to
allow for transfer of the photon through the scintillator to wavelength-shifting ﬁbers
located at the middle of the triangle. These ﬁbers are attached to clear waveguides
and are sent to VLPCs, just as in the case of the CFT. The ﬁbers are 835 pm in
diameter. The triangular scintillators are shown for each of the detector types in
Figures 3.22, 3.23, and 3.24.

The central preshower consists of three cylindrical layers. Before the detectors
is roughly one radiation length of lead, with the thickness varied to provide ~ 2 X0
before reaching the preshower detectors for incoming particles in all directions. The
central preshower provides coverage of 77 < 1.3. Each of the CPS layers consists of
1280 separate scintillation strips.

The forward preshower is located between the luminosity monitor and the inter—
cryostat detector. It consists of two layers of two planes of scintillator strips. The ﬁrst
two layers are known as the MIP layers, referring to the minimum ionizing particle.
In these two layers, light particles are still not expected to shower too much, only
depositing the minimum ionizing energy. The MIP layers are made of 206 scintillator
strips. The outer layers are called shower layers. Between each two layers, 2 X0 of
lead-stainless steel absorber material are placed to induce showering. They are cre-
ated with 288 scintillator strips. Electrons easily shower in the absorber while heavier
charged particles tend to leave MIP signals both in the MIP and shower layers. Pho-
tons usually leave no signal in the MIP layer while depositing energy in the shower
layer. Each pair of FPS layers are at. a. 22.50 stereo angle from each other. The FPS

covers 1.5 < [77] < 2.5.

61

60°

 

t

 

 

 

/\ .
50° \ iii?”
6.858 mm Ref \\ (I) 0.991 mm 5 994 mm Ref
\;\\\\\ 5,309 mm.

,
1 .981

/_\ \\ Ami“. .

~— 2.972 mm —-
5.944 mm ——.-

R = 0.635 mm 6.858 mm Ref

 

 

  

 

 

 

 

 

Figure 3.22: The general scintillator geometry for the central and forward preshower
system [13].

3.2.2 Calorimeters and Intercryostat Detectors

The calorimeter is the primary tool for particle energy measurement at DC . A series
of absorber plates interspersed with liquid argon and signal boards induce and sample
the showering of electrons, jets, photons, and taus. The calorimeter information can
also provide shower shape identiﬁcation of these particles as well as muons. Also,
when combined with muon PT measurements outside the calorimeter, information
about non-interacting particles can be inferred from a transverse energy imbalance.

The DC experiment uses three sampling calorimeters with some additional detec—

62

 

 

2 Layers of Mylar (0.025 X 2 = 0.050 mm)

Figure 3.23: The arrangement of scintillation tiles in the central preshower [13].

 

2 Layers of Mylar (0.025 X 2 = 0.050 mm)

Figure 3.24: The arrangement of scintillation tiles in the forward preshower [13].

63

tors placed between separate calorimeter cryostats. The cryostats maintain tempera-
tures of 90 K necessary for the liquid argon to be the most effective as an active mate-
rial. The central calorimeter provides coverage for [n] < 1 while the end calorimeters
extend that to [17] < 4. All of the calorimeters are segmented into electromagnetic,
ﬁne hadronic and coarse hadronic layers. The EM and ﬁne hadronic use a uranium
absorber, while the coarse hadronic use copper or stainless steel, and all of the layers
use liquid argon for energy sampling. The layout of the calorimeters is shown in

Figure 3.25.

  
  
   
 
 
 

END CALORIMETER
Outer Hadronic
(Coarse)

Middle Hadronic
(Fine & Coarse)

  
      
 

a,

,4
.4

l§\ 4
..F §

i_\_.
,j 5‘}

    
    

(47/

4.
Jr

75/.

/
I

CALORIMETER
Electromagnetic
Fine Hadronic

  
    
 
 

Inner Hadronic

(Fine & Coarse) Coarse Hadronic

Electromagnetic

Figure 3.25: The three DO calorimeters showing the division into layers [13].

3.2.2. 1 Calorimeters

The EM calorimeter uses thin plates of 3 or 4 mm of nearly pure depleted uranium.
The ﬁne hadronic calorimeter is 6 mm thick with uranium and 2% niobium alloy.

Uranium is used because it is a dense material and energy loss is compensated by

64

nuclear ﬁssion. The coarse hadronic is 46.5 mm to ensure an energy measurement
of the most energetic particles using copper in the central calorimeter and stainless
steel in the end calorimeters. In all cases, liquid argon is chosen as the active material
because it is radiation hard, dense and its response is uniform and linear.

In each of the layers, the absorbers are kept grounded while the signal boards have
a voltage of 2.0 kV applied to them. Electrons drift across 2.3 mm of liquid argon in
about 450 us. An example of a calorimeter cell is shown in Figure 3.26. The ﬁrst two
EM layers are around 2.0 X0~ This close spacing is used to help differentiate photons
from neutral pions. It is this early shower shape that shows the largest contrast
between signatures. Before reaching the calorimeter, a particle would be subjected to
about 4.0 X0 at 77 = 0 and 4.4 X0 at [n] = 2. The total EM calorimeter thickness is ~
20 X0- The central calorimeter is a total of 6.9 A A at 77 = 0, and the end calorimeters
are 9.5 /\ A at smallest angles. The amount of material in each layer is shown in Table
3.1. The end calorimeter outer hadronic is not included. It is entirely coarse hadronic

stainless steel and N 6.0 A A thick.

\\

‘—---

 

|<—1 Unit Cell—>[

Figure 3.26: A calorimeter cell showing absorber plates, liquid argon and signal boards
[13].

The transverse size of the readout cells were chosen to match the transverse shower

size— 1—2 cm in EM and 10 cm for the hadronic cells. All of the readout towers were

65

Table 3.1: Amount of material in each of the calorimeter layers measured in
radiation lengths, X0, and nuclear interaction lengths, AA. The outer hadronic
is N 6.0 )‘A thick

 

CenCal x0 AA ECalIH x0 AA ECalMH X0 AA

 

<EM 1 4.0 <EM 1 4.4 <EM 1 4.4
EM 1 1.4 EM 1 1.6 EM 1 1.6
EM 2 2.0 EM 2 2.6 EM 2 2.6
EM 3 6.8 2 EM 3 7.9 EM 3 7.9

EM 4 9.8 tot 0.76 EM 4 9.3 tot 0.95 EM 4 9.3 tot 0.95

 

 

 

 

 

 

 

 

 

 

FH1 1.3 FH1 1.1 FH 1 0.9
FH 2 1.0 PH 2 1.1 FH 2 0.9
PH 3 0.76 FBI 3 1.1 PH 3 0.9
FH 4 X PH 4 1.1 PH 4 0.9
CH 1 3.2 CH 1 4.1 CH 1 4.4

 

divided into sections of An = 0.1 and Ac) 2 0.1 except the third EM layer with
An x A45 2 0.05 x 0.05. At Level 1 and Level 2 triggers, triggers are formed based

on a An x A90 2 0.2 x 0.2 tower sizes.

3.2.2.2 Intercryostat Detectors and Massless Gaps

The calorimeters have gaps in coverage due to their separate cryostats. This causes
incomplete coverage in the range 0.8 < [77] < 1.4. This is somewhat mitigated by
additional detectors in these regions to sample the energy there.

Single cell massless gaps are signal boards installed within the central and end
cryostats and are readout in front of the uranium.

The intercryostat detectors are attached to the exterior sm‘face of the end cryostats.

They provide coverage of 1.1 < [7)] < 1.4. Cabling from the central tracking system

66

does not allow a more complete coverage area.

The ICD is made of 0.5” thick scintillating tiles of Bicron BC-400 housed in light-
tight aluminum. Each tile covers An x M of 0.3 x 0.4 and is divided into 12 subtiles
to match the calorimeter divisions of 0.1 x 0.1. Each of the subtiles is read out by two
wavelength-shifting ﬁbers on the outside edges. These ﬁbers are connected to clear
optical ﬁbers which lead to a photomultiplier tube.

The photomultipliers operate by directing the incoming photons to a photocathode
which excites an electron via the photoelectric effect. An applied voltage directs the
electron toward a dynode, where it transfers its energy to electrons there. Some of
these secondary electrons are emitted and travel toward another dynode, and the
process is repeated. This causes an electron cascade, similar to that described for
the VLPCs in the CFT section. An anode at the bottom collects the current and

ampliﬁes it for analysis.

3.2.3 The Muon System

The calorimeter system is able to measure energy depositions for most particles ob-
served in collisions of interest at DO . Certain particles such as the neutrino interact
so weakly with material that observation of these particles is currently impossible
within the constraints of the experiment (or any non-specialized experiment for that
matter). Muons are charged particles, so they ionize the material they pass through.
The muons of most interest have large momenta. This, combined with its relatively
high mass compared to the electron cause the muons to only leave a small amount of
their energy in the detector after passing through the calorimeter. Once the muons
approach 200 GeV, they begin emitting photons through bremsstrahlung as with elec—
trons, but this energy is rarely reached in collisions at the Tevatron. Therefore, the
only muon signals that are seen are ionization tracks in the tracking system. For this

reason, additional tracking is added outside the calorimeter. This provides a veriﬁ-

67

cation of the tracks seen in the central tracking system, identiﬁes the particle as a
muon (mostly due to its survival through the thick absorber), and provides separate
PT and charge measurements. These measurements beneﬁt from the much cleaner
environment and could allow for better PT measurements of muons with PT > 100
GeV. The magnetic ﬁeld in the muon system is similar in strength to that of the
tracking system (1.8 T vs. 2.0 T). The greater distance between layers in the muon
system perpendicular to the magnetic ﬁeld (1-2 meters vs. 52 cm in tracking system)
will make the bend of a high-pT muon (and thus its momentum) easier to measure.
For lower momenta muons, the broader granularity and greater multiple scattering in
the muon system make the central tracking measurements more accurate. Currently,
the momentum measurements are taken exclusively from the central tracking system,
but a move to use the PT from the muon system for high-pT muons is currently under
consideration.

The system is divided into central and forward systems similar to the calorimeter.
The central muon system has coverage of [77] < 1.0, and the forward muon system

extends to [77] = 2.0. Both of these systems measure tracks on either side of a toriod.

3.2.3. 1 Toroidal Magnets

The muon toroids allow a separate PT measurement of the muons outside of the central
tracking system. The separate measm‘ement allows a quick muon pT measurement
to allow a pT cutoff in the L1 muon trigger, reject muons from pion and kaon decays,
and allow for cleaner matching of the muon to a track in central tracking.

The central toriod is a square annulus 109 cm thick. The inner surface of the
toroid is 318 cm from the beamline. It is made up of 20 coils of 10 turns.

The end toroids are located 454 3 [z] 3 610 cm. Each of the end toroids have

eight coils of eight turns. The magnet current is 1500 A providing a ﬁeld of 1.8 T.

68

3.2.3.2 Central Muon

The central muon system consists of proportional drift tubes for accurate position
measurement, cosmic cap and cosmic bottom for time correlations with the beam
crossing, and Act scintillation counters for fast triggering and additional position

measurements.

3.2.3.2.1 Muon Pr0portional Drift Tubes The central muon drift tubes con-
sist of three layers of drift tubes, one inside the toroid (the A layer) and two outside
(B and C). The B and C layers are separated by 1 m. Approximately 55% of the
ﬁducial area is covered by three layers and 90% has at least two. The individual
chambers are 2.6 x 5.6 m2 created from extruded aluminum. The A layer has four
decks except at the bottom which has three. The B and C layers have three decks
throughout their coverage. Each chamber consists of 72 or 96 cells, each of which is
10.1 cm wide. An anode wire is fed through the center of the cell. Vernier cathode
pads are attached above and below the wire to provide information about the hit
position.

Each cell is ganged with a partner. The arrival time at one wire is compared to
the arrival time of the partner. Using the time difference between the two hits, a
the location of the particle can be inferred. Additionally, the charge distributions
are checked for a more precise measurement. The resolution in the PDTs is 1 mm.
The charge division method is only used in the A layer. The B and C layers only
use this method in 10% of the cells for monitoring purposes. It was found that these
additional measurements would have minor improvement on the resolution at high
cost.

The PDTs use a gas mixture of 84% argon, 8% methane, and 8% CF4. The
anode wires are kept at 4.7 kV, the cathode pads at 2.3 kV, and the aluminum case

is grounded. The drift velocity of an electron in the gas was found to be 10 (rm/77s

69

which gives a maximum drift time of 500 us. There are a total of 164 proportional
drift chambers for 11,386 anode wire cells. The layout of all of the wire chambers
used in the central and forward regions can be seen in Figure 3.27.

“x

l \\

   

I
‘\

  
  

Proportional

~\ ,/ '

Alf/TREE

I
i
i
I

 

_ Drift
. (:11. 7 Tubes
+y
.: __ -x -z
I -, ‘ West North
'5‘»? +2 +x
, South -y East

Figure 3.27: The layout of the wire chambers used in the DO muon system [13].

3.2.3.2.2 Cosmic Cap and Cosmic Bottom The cosmic cap and bottom are
installed on all sides of the detector to provide timing information for scintillation hits.
These detectors associate a signal in the PDT with a bunch crossing to discriminate
against cosmic muons. The scintillators use 0.5” Bicron 404A and are readout with
a PMT. The layout of all of the scintillators in the central and forward muon system

are shown in Figure 3.28.

70

  
  
  

  

I ’ I
”Ii/II 6’9"

   

[III/I
I III],
0;, ”/

   

.0

o “.

O .0
d

      
 
  

"III
C . L”, I/
' .r'll

   

.__
3:.
\

1!.

"I
ll

   

‘ ' (I ' ’ .
1:71," ' '
III,
. III

 
 

v ’1
v ’1 ’01
“cl/II

I
a" ‘0

    
    
  

d r I” I
I I ’1
d I,”

  
 
   

     
    
    

  

       

\s
‘\\I
\‘ \\\"‘~
‘:\‘\\\\\\\\
c \\ \\\\\\ \ +
$\\\ «mm
\ssswx
§§$$‘ ~
“ ‘ 5; ‘
~‘=\~ ' ‘ . n'n ‘ \
.\ ‘ ‘ :1 - Z... ‘ I -z
-=~:-; ‘ .10‘. ‘
‘u'.::'-.': g 3:..- . North
‘ $0.1.”- ~..‘ .
v -' 11:3
‘ o a
‘,I'

Figure 3.28: The layout of the scintillators used in the DO muon system [13].

3.2.3.2.3 A43 Scintillation Counters The second layer of scintillation counters
is used inside the A layer for triggering and rejection of backseatter from the forward
system. This information is matched with CFT tracks for Level 1 triggering of single
high-pT muons and lower pT dimuons. These counters are segmented by 45° in (15 to
match the CFT segmentation. There are nine counters along the z direction. These
scintillators also use Bicron 404A and are connected to a PMT. The average muon

signal produces 50-60 photoelectrons.

3.2.3.3 Forward Muon

The forward muon system provides coverage up to [77] < 2.0. The forward system
consists of three layers of small proportional drift tubes called MDTs, 3 layers of trig-

ger scintillation counters, and shielding of the beam pipe to reduce energy depositions

71

from p and 7‘9 fragments and beam halo.

3.2.3.3.1 Mini Drift 'Ilubes The mini drift tubes follow the same principle as
the PDTs but with a shorter drift time and slightly better resolution. The drift
tubes in the forward region are smaller to account for the fact that muon ﬂuxes
are fairly constant in rapidity, so the forward regions need smaller cells to maintain
segmentation for the highest 77 values.

Three layers of MDTs are divided into octants, each of which contains three or
four planes of tubes. There are a total of 48,640 anode wire cells with a maximum
tube length of 5.8 m. Each MDT is divided into eight cells of 9.4 x 9.4 rmn2. The
wires are made of tungsten and gold with a diameter of 50 pm. As with the PDTs,
the MDTs are made from alInninInn extrusion combs and covered with stainless steel
foil inside of a PVC sleeve. The MDTs use a different gas mixture of 90% CF4 and
10% methane. The longest drift time in an MDT is 60 ns nearly a factor of ten shorter
than in the PDTs.

A voltage of -3.2 kV is applied to the cathode and the anode wire is grounded.
Each wire is connected to an ampliﬁer and discriminator. The ampliﬁer discriminator
boards link to 32 channels and can detect signals of 2.0 77A. All of this collected
information is sent to DAQ. The stand alone resolution of a 40 GeV muon is 20%,
and gives a better muon PT resolution than the central tracking after 100 GeV or in
the region 1.6 < 77 < 2.0 where there are fewer CFT layers. An example of the MDT

cells is shown in Figure 3.29.

3.2.3.3.2 Trigger Scintillation Counters The forward trigger scintillation coun—
ters are located on each MDT layer both inside and outside the end toroids. Each
layer is divided into octants of 96 counters each. The e5 segmentation is 45° match-
ing the OFT. These scintillators also use 0.5” thick Bicron 404A cut into trapezoids.

VVavelength—shifting bars are attached to the side of the plate and attach to a 1”

72

Envelope Cover Spacer
Comb Wire

    

Figure 3.29: A diagram of the individual MDT cells [13].

phototube with 15% quantum efficiency at 500 nm and a gain of ~ 106. After ampli-
ﬁcation, the signal is sent to a 10-bit ADC and to a discriminator. These signals are
passed to the Level 1 trigger and a scintillator front end TDC. After digitization, the
amplitude and time information is sent to the Level 2 trigger and the data acquisition

system.

3.2.3.3.3 Beam Pipe Shielding Three sources deposit signiﬁcant amounts of
energy and can limit the lifetime of the muon system without proper shielding. These

include the following:

1. 79, 7‘9 fragments from interacting with end calorimeter and beam pipe measured

in the A layer,

2. p, iv fragments interacting with the low 73 quadrupole sending hits to the B and

C layers, and

3. beam halos from the tunnel.

The beam pipe is covered with 16” of iron, 6” of polyethylene and 2" of lead to
reduce this background. The iron is a strong absorber of hadronic: and electromagnetic
particles with A A = 16.8 and X0 = 1.76. The polyethylene absorbs neutrons because

of its high hydrogen content, and the lead absorbs the high energy y ray photons.

73

This provides a factor of 50-100 reduction in energy deposition in the muon de-

tector elements, reducing aging effects and limiting interference in particle detection.

3.3 The Trigger System, Data Acquisition, and
Luminosity Measurement

The interactions of the particles with the detector have been discussed, but for physics
analysis, this information must be passed to permanent storage, reduced in size, and
properly interpreted. With an average of six inelastic collisions every half of a mi-
crosecond at current common luminosities, we would have to read out and store infor-
mation about 1.7 - 106 events every second. Full detector readout at this level would
be impossible, and the amount of information that would need to be stored would be
cost prohibitive and unmanageable. Additionally, even highly unlikely situations in
which the detector can mimic a process that has interesting physical properties be-
come relevant. This (as well as the quantum nature of the processes) necessitates the
use of statistics to differentiate the observation (or non-observation) of an interesting
physics process with a detector effect. In order to anticipate the rate of interesting
processes, it is necessary to understand the number of expected interesting collisions.

The luminosity system performs this task.

3.3.1 Trigger System

The proton and antiproton beams at the Tevatron cross at DO at a rate of 1.7 MHz.
In order to read out, reconstruct, and store adequate information for analysis, it was
found that the rate needed to be reduced to ~ 100 Hz. Most of the physics processes
of interest for DO analyses happen at rates much smaller than the storage rate, so
if the 100 events/ second are tuned to only store events which might be of interest,

very little useful information will be lost. The reduction in rate is the purpose of the

74

triggering system. The DO trigger system uses three layers. The ﬁrst uses hardware
to reduce the rate to 2 kHz, a second level system uses ﬁrmware and simple software
to drop that in half, and a third layer of more complex software provides the ﬁnal

reduction to 100 Hz. The basic layout of the trigger system is shown in Figure 3.30.

3.3.1.1 The Level 1 Trigger

The ﬁrst level trigger is divided into four sections corresponding to different parts of
the detector which are loosely brought together by the trigger framework system. The
trigger framework reads information from the subdetector triggers and the accelerator
and makes the decision to accept or reject the event.

Incoming events are stored in buffers giving the L1 system 3.5 as to make a
decision. This is roughly a factor of ten larger than the beam crossing rate within a

superbunch.

3.3.1.1.1 Trigger Framework The trigger framework is responsible for making
accept or reject decisions for Level 1. The framework itself does not provide any
further processing. It simply performs a logical OR of all of the trigger terms it
receives from the subsystems while accounting for beam conditions that are necessary
for each trigger to pass. The Level 1 system has 128 possible triggers, each with its own
beam condition requirements, which make a total of 256 terms that the framework
checks. On top of this, the framework also monitors trigger rates and deadtime,
coordinates trigger vetoes, and handles trigger prescaling if the trigger of interest

would ﬁre at a rate too high for the triggering or readout system to handle.

3.3.1.1.2 Level 1 Calorimeter Trigger The Level 1 Calorimeter Trigger mon-
itors 12 EM and 1280 Hadronic towers to look for energy patterns of interest and
make sure that events that have large or unusual energy signals are saved for further

analysis. The calorimeter is divided into A77 >< Act of 0.2 x 0.2 for triggering. This is

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coarser than the subdivisions used in reconstruction.

The triggers include the total sum of transverse energies and the missing transverse
energy, both at four thresholds. Also, individual towers are monitored, if a certain
number show transverse energy above a limit provided in the trigger list, the event
will pass. Additionally, 4 x 8 towers in A77 x Are are also checked. This roughly

corresponds to the energy deposited by a hadronic jet.

3.3.1.1.3 Level 1 Central Tracking Trigger The Level 1 Central Tracking
Trigger uses fast. discriminator data to look for matched hit patterns in three scintillator-
based systems, the CF T, CPS, and FPS. In all of these systems, the discriminator
bits from the analog front-end boards (AFEs) are read in and sent to the digital front-
end boards. After this point the data is handled differently depending on where the
information is coming from. One path handles the CFT and CPS axial information,

another deals with the CPS stereo, and a third processes the FPS.

3.3.1.1.3.1 CFT/ CPS axial The axial system compares the discriminator
information with thousands of predeﬁned tracking equations and looks for a match.
Each digital front-end board (DFE) unpacks the OFT data and stores the six highest
pT tr5101(8. This is done in four separate FPGAs with a ﬁfth that sorts the tracks,
matches them with CPS clusters, counts the tracks and total PT and calculates the
sector Occupancy.

These tracks are then sent over a coaxial cable to the Level 1 muon system which
is discussed below. The tracks are also sent to a board which combines 10 sectors
into an OCtant and ﬁnds which sector had the most ﬁber hits, and whether there were
any iSOIated tracks. This information is passed to another board which generates the
trigger terIns to send to the trigger framework.

If the AFE receives the L1 accept signal, the ﬁber data is digitized. The digitized

CFT SiFinals then travel to Level 2 and Level 3 to be used as seeds for track lists.

77

3.3.1.1.3.2 CPS stereo This is the information from the two CPS stereo
layers providing three—dimensional information for triggering. Here the digital front-
end boards (DFEs) store the discriminator bits but do not begin processing until after
receiving a. Level I accept. The processing consists of a search for hit clusters, and
then sorting these clusters to be sent to the Level 2 preshower (L2PS) crate and the

Level 3 readout.

3.3.1.1.3.3 FPS The forward preshower is processed in three steps, ﬁrst the
clusters are found, then they are combined, and ﬁnally the trigger terms are generated.
The DFE ﬁnds the clusters and saves the list for use in Level 2 (not implemented).
The cluster counts are then summed and passed to another board where the trigger
terms are produced.

On a Level I accept, the AFE digitizes the ﬁber data, and the DF Es extract the

cluster lists. The FPS then sorts the clusters to send to L2PS and the Level 3 readout.

3.3.1. 1 .3.4 STT On an L1 accept, the LICTT seed tracks are reformatted for
the L2STT system. First is a check for track overlaps, then each individual sextant is
checked for tracks. These tracks are then in the proper format to be sent to L2STT

by Optical ﬁber for use as seed tracks.

3.3.1.1.4 Level 1 Muon Trigger The Level 1 Muon trigger follows the same
principle as the central tracking trigger. The trigger looks for patterns that match
the inDUt L1 CTT tracks, wire hits from the MDT and PDT, and the scintillation
cormters, Scintillator trigger cards, MTC05, match tracks to muon scintillator hits,
and S€parate wire trigger cards, MTC 10, match the scintillator information to track
stubs in the wire chambers.

D eCiSiOns are made for each octant of the system, and this information is correlated

at. the muon trigger crate manager. The manager forms 256 L1 Muon triggers and

78

sends 32 of them to the trigger framework.

3.3.1.1.5 Level 1 Forward Proton Trigger The FPD trigger also follows the
CTT and Muon L1 triggers in operational principle. Discriminator signals are sent to
three DFES. These discriminator signals are matched against predeﬁned hit patterns.
If a match is found, the event is saved. Events that have very large hit multiplicities

are ignored because this is most likely due to beam halo.

3.3.1.2 The Level 2 rIrigger

The Level 2 trigger bridges the gap between the hardware for each of the detector
subsystems at Level 1, and the software algorithms using the full detector readout at
Level 3. The input rate to Level 2 is ~ 2.0 kHz, determined by the digitization rate
of the central ﬁber tracker. Level 2 cuts this rate approximately in half for the input
limit of 1 kHz needed for full calorimeter digitization needed at Level 3. Level 2 is
the ﬁrst place that information from all different subsystems is combined globally,
and the ﬁrst place that silicon tracking information is used.

The Level 2 system consists of ﬁve different preprocessors, each of which create
basic objects such as tracks, EM objects, jets, etc., and send these to the Level 2
Global Processor which combines information of these objects to make the trigger
decision. The L2 trigger system uses two buses, the VME backplane associated with
the crate, and a 128-bit custom MBUS. The MBUS can handle up to 320 Mbits/s.
The VME bus is used for the readout of the L2 crates to be sent to Level 3 and the
data acquisition system, as well as cormnunication with the run coordination system
and monitoring. The MBUS is used to pass inputs to the L2 processors.

Each Level 2 crate contains several types of common components: one single
board computer for controlling the readout of the L2 output over the VME backplane,
one dual‘Dort memory for communication between the run coordination system and

the . . . .
Level 2 processors, one MBT (Magic Bus Tr‘ctllSCGIVCI‘) card for collecting input

79

to be sent to the processors, queuing that information, collecting signals from the
serial command link (run and event nmnbers and information from run coordination
system), and transmitting information from the preprocessors to the global crate.
Additionally, most crates have ﬁber input converters and VME transition cards to
convert from optical ﬁbers to the Hotlinks used in the L2 system. The Beta card
is the card used for L2 processing. It is a dual 1 or 2 GHz processing card, with
one processor used exclusively for the L2 executable and a second for utilities and
monitoring. The STT and Muon crates have additional specialized cards that are
speciﬁc to those preprm‘fessors. They will be discussed in the section on the given

preprocessor.

3.3.1.2.1 Preprocessors Each of the major subsystems sends partial readout
information to the Level 2 system. The Level 2 system analyzes this information
using preprocessor crates to form simple objects. These objects are sent to the Global

processor Where they are reﬁned and combined for more complicated decisions.

3.3.1.2.1.1 L2CAL The Level 2 calorimeter preprocessor creates jets, EM
ObJBCtS and missing transverse energy out of 2560 trigger towers. The L2 system re-
ceives separate energy information for the electromagnetic and hadronic calorimeters.
Jets are formed out of 5 x 5 towers clustered around seed towers, which are deﬁned
as towers with ET > 2 GeV. The EM objects use EM towers within ET > 1 GeV
combined with the neighboring tower of the greatest energy. The missing transverse
energy Calculates the vector sum of ET from towers. The E T calculation can set dif-
ferent limits for the minimum tower ET used in the calculation with 77 ranges deﬁned

in conﬁguration ﬁles.

3-3-1.2.1.2 L2MUC and L2MUF Two preprocessors, L2MUC and LQMUF,

are responsible for creating preprocessor objects from the central and forward muon

80

systems. Unlike other preprocessors, the inputs for the muon are coaxial cables that
are sent to a CIC (Cable Input Converter) for conversion into the standard Hotlinks
format. The muon systems also have an extra stage of processing. The muon sectors
are ﬁrst sent to 800 200 Hz DSPs where an initial stage of processing is done. Each of
the DSPs searches for track segments in a small region of the detector. The DSPs are
spread over 11 central and ﬁve forward VME boards. After the track segments are
created, they are sent to the ﬁeta processors where the segments are used to make

muon candidates with pT and quality information.

3.3.1.2.].3 L2PS The Level 2 preshower processor takes Central Preshower
axial clusters and combines them into quadrants. The CPS cluster centroid looks for
clusters that match in three layers. These output clusters are checked for a track,
and then tagged as either electrons or photons. Currently, the forward preshower
information is not sent to Level 2, and the central preshower information is not sent

to L2 Global (so not used in the trigger decision).

3.3.1.2.1.4 L2CTT The L2CTT processor was designed to take input from
LlCTT and L2STT. Currently, only the L2STT information is used. Three different
variables are used to deﬁne the STT tracks: initial azimuthal angle (230, the azimuthal
angle at the third EM layer of the calorimeter, qbem3, and the isolation. This infor—
mation is used to provide two track lists sent to Global, one sorted in pT, and the

other sorted by impact parameter.

3-3-1-2.1.5 LZSTT Each event that passes Level 1 sends its LICTT infor—
mation t0 the STT. The track from LlCTT is established as the seed. A road is
established around the track into the SMT, and hits that are within the deﬁned road
are aSSOCiated with the track. The L2STT only looks at axial strips for the trigger

(180151011 The inner and outer CFT layers with at least three of the four SMT layers

81

are used to deﬁne the track parameters.

The L2STT processing takes place in three stages. First the Fiber Road Card, gets
the inputs from LlCTT and TFW and sends it the other modules while managing
the data buffers. Then, the Silicon Trigger Card receives SMT data, checks the SMT
clusters with the roads deﬁned from the LlCTT. Then, the Track Fit Card makes

the ﬁnal hit selection and applies the ﬁt. The LQSTT layout is shown in Figure 3.31.

 

 

 

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Figure 3.31: Data ﬂow in L2STT [13].

Heavy-ﬂavor events are selected by measuring the impact parameter, and to avoid
PT dependence, the impact parameter signiﬁcance. This more complex parameter

incorporates multiple scattering effects.

82

3.3.1.2.2 Global Processor The Level 2 Global processor is the ﬁrst part of the
trigger system to look across all subsystems and the object relations among them. The
decisions are based on the incoming list of 128 triggers decided at Level 1. Global uses
this list to determine which algorithms to run. All of the preprocessor information is
available to use, and the Global processor can further reﬁne or combine the objects
sent from the preprocessors to make a list of Global objects. The Global objects are
then used in the trigger algorithms to determine if the event should pass Level 2.

More information on the global processor can be formd in Appendix A.

3.3.1.3 The Level 3 Trigger

The Level 3 decision is based 011 a set of candidate objects or relations that use
algorithms called ﬁlter tools. The tools unpack the data, look for hits, create clusters,
and reconstruct the objects. The parameters for running these processes are stored in
COOR—deﬁned lists called refsets. All of the objects or relations that pass a particular
ﬁlter tool are cached in case they are needed in the future. As with the L2 trigger,
the Level 3 trigger has a set of algorithms associated with a particular L2 bit. If the

L2 bit is set, only then are these ﬁlters run.

3.3.1.3.1 Level 3 Jets and Electrons The jet tool at Level 3 uses a simple cone
algorithm, and the ability to suppress hot cells. It has more precise readout than at
Level 2, and uses the primary vertex position. Electrons use a jet cone of radius 0.25
in 77 and (25 along with ET, EM fraction and shower shape cuts. They can also require

a preshower match.

3.3.1.3.2 Level 3 Muons Level 3 muons use wire and scintillator hits as with
the other levels, however, Level 3 can also access information from the inner tracker
and the calorimeter. Additionally cosmic ray vetoes are applied using out-of—time

information and tracks that penetrate outside of a particular candidate. The muon

83

tracks are extrapolated to the central tracker, and the track is determined by the
ﬁt that minimizes X2. These candidates are further mapped to a MIP signal in the

calorimeter.

3.3.1.3.3 Level 3 ET The ET works by creating intermediate pseudorapidity
sums. The ET is calculated along with the qb value of the ET, the scalar ET, and

the E T signiﬁcance.

3.3.1.3.4 Level 3 Tracking The tracking works by ﬁrst ﬁtting a circle through
the axial layers, then using a link-and—tree method to join clustered hits from different
layers. It starts from the outer layer and works in. The track is then ﬁt to a helix
and the smallest X2 is found. The CFT vertex and beam spot info are also used for

a full 3—D vertex in every event.

3.3.1.3.5 Level 3 Relation Filters Additional ﬁlters can be added on top of
the individual object ﬁlters. Examples include the invariant mass, acoplanarity, and

the HT of the event.

3.3.2 Data Acquisition

The data acquisition system transports data from the VME readout for each crate
and transfers it to the Level 3 farms. These are then sent to the online host which uses
the information for logging and monitoring. The COOR system controls triggering
and data acquisition. The farm data is sent to the collector which then directs each
event to a data logger associated with the event’s output stream. A copy of the event
is also sent to the distributor where it is used for online monitoring in the trigger and
physics examines.

The datalogger writes the data to ﬁles based on their stream and also creates

metadata for storage in the database. DLSAM monitors local data buffers and re-

84

 

 

quests ﬁle storage in the EN STORE tape storage system, ~ 3 km from D0 . The

data path from the L3 farm nodes to storage on tape and the examines is shown in

Data Tape

Logger
- ﬂ 0 0
Disk
V 0. @ 0's“
a a
Level 3 “ “999'

Process w

Level 3
Process " '°

Figure3.32.

Level 3
Process

SDAQ
Process

e

Figure 3.32: Data path from the L3 farm nodes to tape storage and the online exam-
ines [13].

3.3.3 Luminosity

The luminosity system is responsible for determining the mnnber of hard collisions in
the D0 interaction region measured as a rate of particles per interaction cross section
per unit time. This value determines the likelihood of observing a particular process.
As the experiment sees more luminosity, increasingly rare processes may be observed.

The luminosity is derived by determining the number of inelastic collisions seen
with two scintillation counters at very high values of 77. It consists of two arrays of

24 scintillation counters attached to a photomultiplier. These detectors are found at

|z| = 140 cm in front of the end calorimeters between the beam pipe and the forward
preshower detector covering 2.7 < 77 < 4.4. The detector setup in the rz-plane can be

seen in Figure 3.33.

proton direction

 

 

 

 

 

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Forward 1 i x’ ' L
were :‘Eimfl‘f’naw ' t nae
--_.__._ m} l J beam pipe
l North h K Southilﬁﬂ
-140 cm Memo

Figure 3.33: The placement of the luminosity detector as seen in the T2: plane [16].

The luminosity system must differentiate between hits originating from the col-
lisions in the detector and scattered particles coming from the beam pipe (beam
halo). It does this by calculating the time difference between hits at either end of the

detector. Using this information it determines an interaction vertex using,

1 .
2: := §c(tz_ — tz+). (3.4)

If z is measured to be less than 100 cm than a collision is assumed because halos
will typically show a z vertex of ~ 140 cm [16].

Additionally, the possibility of multiple interactions in a single crossing must be
considered. To determine the number of multiple interactions at a given instanta-
neous luminosity, the number of zero interaction crossings are counted, and a Poisson
probability distribution is assumed to determine the average number of interactions.

The luminosit is measured with the followin r formula,
. s

86

_Ue;[*L —0 L —0 L
P(O)=e *(26 2% —e l ) (3.5)

where P(0) is the measured quantity that is determined separately for each of the 36
bunch crossings. These values are determined over the course of a minute so that the
measurement uncertainty drops to < 1% while the change in instantaneous luminosity
is negligible.

With the total inelastic cross section at 1.96 TeV of 60.7 d: 2.4 mb, the effective
cross section, Jeff, is found to be 48.0 mb and the single side cross section, 033, is
9.4 mb.

Luminosity is a one of the largest sources of uncertainty in precision measurements
made at DC . It has a 6.1% uncertainty mostly stemming from the Oeff measurement
(5.4%), half of that from the inelastic cross section and the other half from acceptance

and efﬁciency.

87

Chapter 4

Event Reconstruction and Object

Identiﬁcation

Experimental particle physics tests assumptions about the basic laws of particle inter-
actions. In order to perform these tests, physicists must translate the mathematical
predictions of the theory into energy clusters and ionization tracks in the detector.
Similarly, the signatures observed in the detector must be translated to determine
the underlying physics process between the partons within the colliding proton and
antiproton.

Fortunately, in fundamental physical interactions, there are relatively few con-
tributing particles. Of the fundamental particles, electrons, photons, muons, light
jets, heavy jets and taus and can be reasonably well distinguished from each other.
The light jets include gluons and up, down, strange and a substantial fraction of
charm and bottom quarks while the heavy jets are focused on bottom quarks, with
a substantial contribution from charm. In order to reconstruct these objects, some
basic preliminary information is ﬁrst calculated. Tracks, the interaction vertex, and
secondary vertices are useful in distinguishing among these objects, and they are.
complex enough that they are often used as independent objects rather than just

parameters associated with distinct particle types.

88

4.1 Tracks and Vertices

The tracking system registers small energyr deposits as ionizing charged particles pass
through the detector material. When these energy deposits reach a predeﬁned thresh—
old in the tracking system (either in the silicon strips of the SMT or the scinitillating
ﬁbers of the CFT), they are registered as hits and saved in the raw data. A combi-
nation of these hits are strung together to create the basis for particle tracks through
the tracking system (and extrapolated beyond). These tracks can then be traced
back to their point of origin providing the initial collision point, the primary vertex,

or delayed decay vertices (secondary vertices).

4.1.1 Tracks

Particle tracks are found using the Lorentz force equation to determine particle motion

in a magnetic ﬁeld, Equation 4.1.

d5}; = qv x B. (4.1)

When the magnetic ﬁeld is uniform, the equation describes a helix, with radius,

r — 5—9 where c is the speed of light and PT is the transverse momentum of the

_ PT’
particle. The reconstruction system propagates tracks across detector surfaces based
upon their geometry and material composition. A detailed look at the propagation
of tracks and their error matrices can be found in [52], and the addition of multiple
scattering and energy loss effects from material is described in [53].

Track reconstruction at DC uses two algorithms, the AA and HTF algoritlnns,
and one algorithm to improve the prediction of the path of the track, the Kalman

ﬁlter.

89

4.1.1.1 Alternate Algorithm (AA)

Track-ﬁnding with the AA involves looking for three axial hits in the SMT [54]. The
hits in the SMT are checked from the inside, closest to the beamspot and propagated
out. The algorithm begins by looking at all hits in a given layer. For each initial
axial hit, the SMT layers outside the one containing the initial hit are checked for a
second axial hit within Aqﬁ < 0.08 of the ﬁrst. If at least one second hit is found,
then a third axial hit in a layer outside of the second must deﬁne a circle with r > 30
cm, which corresponds to PT > 180 MeV. The track is kept if the impact parameter
is less than 2.5 cm, and the overall ﬁt has x2 < 16 for the three points. The initial
track stub ﬁnding can be seen in Figure 4.1.

Once these initial tracking hypotheses are determined, the hits are extrapolated
out to the remaining SMT and into the CF T. If an associated hit adds < 16 to the
x2 value, then the hit is added. If more than one hit satisﬁes this condition, the
track hypothesis is split, and all are kept. These axial hits can correspond to many
different stereo projections. As more hits are added, only certain stereo projections
are feasible. Tracks with several possible stereo projections may be part of a track
hypothesis with the stereo projection only determined after the determination of the
primary vertex.

After all of the tracking layers have been checked for hits, the track hypotheses

are reduced further by forcing the tracks to satisfy the following conditions:

1. At least 4 hits contain stereo and axial information

2. No more than three layers are missed between any two hits
3. No more than 6 misses in the extrapolation region

4. No more than two misses betwmn layers in the SMT

At least ﬁve times as many hits as misses

CI!

90'

 

impactMax ,
0”

Beam Spot

Figure 4.1: The Alternative Algorithm looks for at least three hits in the SMT and
extrapolates outward to the OFT [17].

6. If at least one miss between layers, no more than four total misses combining
between layers and outward extrapolation, and no more than three total misses

combining between layers and inward extrapolation

After this, the ﬁnal determination of AA tracks is done by eliminating tracks that
have too many shared hits.

Using this ﬁnal AA SMT—based track list, primary vertices are determined from
these tracks. Another round of ﬁtting then begins with CFT-based tracks that follow
the same seeding procedure except they must connect to the primary vertex with
daxial < 1.5 cm and dstereo < 1.5 cm. The tracks are connected through the OFT,

and then inward into the SMT.

91

 

 

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4.1.1.2 Histogramming Track Finder

In a homogeneous magnetic ﬁeld with no material, a track can be speciﬁed by three
parameters in a plane perpendicular to the ﬁeld [17]. The HTF algorithm speciﬁes
these as p, (b, dca while assuming that the dca (distance of closest approach) is small.
This reduces the track parameters to two variables which can then be plotted in a
histogram. If each pair of points were plotted, then the tracks could be found from

(72-1)
__2__

peaks in the histogram with an expected n entries for a track with n hits.
The HTF method, however, reduces the number of calculations by instead looking
at each individual hit, and plotting all possible p, Q6 values that could produce that
particular hit. This will produce a line of values in the 2-D histogram. Each hit in
the track will produce its own line of values, and the ﬁnal track parameters can be
determined by ﬁnding which of these histogram bins has the most hits. The actual
track values occur where the lines in p, Q5 space for all of the individual hits intersect.

The steps showing the transformation from tracks to peaks in histograms is shown in

Figure 4.2.

4.1.1.3 Kalman Filter and Fit

Once the tracks from the AA and HTF algorithms have been determined, they are
combined, and duplicates are removed. The points corresponding to each track are
then reworked to ﬁnd the best ﬁt using a Kalman ﬁlter and ﬁt [55]. The Kalman
ﬁlter begins with an individual point in the track and using information from the
material composition of the tracking elements (accounting for energy loss and multiple
scattering), provides best ﬁt estimates of the tracking parameters, and the associated
error matrix. As the track prediction extends inside to out, point-by-point, more
and more data points are added to the track parameter determination. The last
point should then have the most accurate tracking parameters. After this ﬁltering

is ﬁnished, the ﬁlter is then run in the opposite direction, from the outside in. The

92

 

 

 

v, cm
8 8

...................

YTWTTﬁ—Tl I
. s u
I I

 

0
9°

I'T

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

III) III! All I All ll ‘

(Po, deg (Po. deg

Figure 4.2: The Histogramming Method looks for at peaks in 2-D histograms plotting
p and 45. Histograms with the most hits deﬁne tracks [17].

ﬁnal parameters associated with each point are determined by a ﬁt between those
determined from both of these Kalman ﬁltering procedures. This is known as the

Kalman ﬁt.

4.1 .2 Primary Vertices

Primary vertices are selected by following the tracks back toward their origin and
ﬁnding where multiple tracks intersect. This is done in several stages [18]. First,
only tracks that have W > 0.5 GeV are chosen. These tracks are then classiﬁed
as either within or outside of the SMT ﬁducial region (~ [z] < 36 cm). For tracks
within the ﬁducial region, two SMT hits are required, while those outside have no

such requirement. All selected tracks within 2 cm of each other are then clustered.

93

Then, all of the selected tracks are combined to ﬁnd a best ﬁt. If the overall ﬁt has

a X2 per degree of freedom greater than ten, then the track contributing the largest

X2 is removed until the value drops below the threshold. The remaining tracks are

then subject to a cut in the impact parameter signiﬁcance, 3%0—33)’ of ﬁve. Once this
cut is applied, the remaining tracks enter the adaptive vertex ﬁtting algorithm, the
heart of primary vertex selection.

The adaptive ﬁtting algorithm was developed to replace a Kahnan ﬁlter, which
when applied directly, pulled the vertex parameters toward secondary vertices, and

2 or impact parameter resolution, lost too many tracks

when used with a strict cut in x
originating from the primary vertex. The adaptive algorithm begins with a normal
Kalman ﬁlter pass using all of the remaining tracks associated with a particular
vertex. Once the best ﬁt is found, a weight is assigned to each of the tracks based on
Equation 4.2,

1
W = 2 , (4-2)

2_
Xi Xcutoff
1+ 6 2T

 

 

where x3,” to f f is tunable and set to 10, and T is set to 1. This equation with T set
to zero would give the Kalman ﬁltering procedure with an additional X2 cutoff. The
given weights for various values of X2 and impact parameter resolution are shown in
Figure 4.3.

Once all of the weights are determined, another iteration is run to determine the
new best vertex position. The weights are then recalculated and the procedure is
repeated until the weights converge. This way all of the tracks can contribute to a
particular vertex, and if primary and secondary vertices are found simultaneously,
each track can contribute fractionally to each vertex.

Finally, after all of the vertices have been determined, one must be selected as the

primary vertex [56]. This last stage is done in the following four steps:

94

 

[ Weight Function”? = 10, T = 1 J

 

 

 

 
 

-6
f0 . o 2 4 6 8 1o
- -1 0 -8 dcaxl 6(dcax)

Figure 4.3: Values for the weighting function of a given track to its contribution to a
particular primary vertex given a ﬁxed X2 and various impact parameter resolutions
of the track-vertex system [18].

1. Tracks are clustered within 2 cm.

M

. The vertex with highest multiplicity within the cluster is selected.

00

. All vertices are given a minimum—bias probability based on the loglo(pT) of
the associated tracks. The probability of an individual track originating from a
minimum-bias is shown in Equation 4.3, and the probability that the vertex is

associated with a minimum—bias interaction is shown in Equation 4.4.

sh.

. The vertex with smallest minimum-bias probability is selected as the primary

vertex

fligwm) F (1711’)de
fizzwms) FlPTW’T’

 

P(pT) = (4.3)

where F is the minimum bias track [0910(pT) spectrum distribution obtained from a

Monte Carlo simulation.

PMB— HNZV ——l——"m, (4.4)

where H is the product of the indivklual probabilities of the tracks associated with
the vertex.

The only assumption made in determining the probability is that tracks from
a hard scatter have higher PT tracks than those from minimum-bias events. The
probability of a track with a particular pT to originate from a minimum-bias event.
is determined by integrating over a minimum-bias distribution. The probabilities
of all of the tracks in the event are multiplied together, and then the minimum-
bias probability for the vertex is determined after removing the track—multiplicity
dependence from the probability. The study of the efﬁciency of this method has been

determined for the dataset in this analysis in [57].

4.1.3 Secondary Vertices

Third generation particles are important in the study of many proposed new physics
signals as well as rare physics signals in the standard model [58]. Jets that originate
from the decay and hadronization of b—quarks are identiﬁable from a short-lived B-
rneson that exists long enough to isolate a decay vertex different from the primary
vertex. The reconstruction of secondary vertices uses a Kalman-ﬁltering technique
that is accomplished in ﬁve steps. The speciﬁc parameters used in identifying dis-
placed vertices may vary depending on the efficiency/mis—ID ratio determined for a

particular analysis. For the MIS search, we look to minimize misidentiﬁcation at the

96

expense of efﬁciency and choose a fairly tight list of parameters to identify b—quark
jets.

The ﬁve steps in secondary vertex identification are as follows:
1. Find track clusters of 5 GeV within a cone of R < 0.5.
2. Select tracks not associated with the primary vertex.

3. Find vertices by including all tracks within a cluster that add less than x?) for

the X2 of the vertex ﬁt, where for tight b—tags, x3 :- .

4. Additional vertex selection cuts are made 011 impact parameter signiﬁcance, dca,
decay length, etc. The parameters used to determine b—jets will be explained in

more detail in Section 4.4.2.3.

5. If more than one vertex share a particular track, only the best vertex (based on
smaller opening angle and X2 / do f ) will be kept. This is done until all tracks

are associated with a single vertex.

4.2 Electromagnetic Objects

Electrons and photons are objects that react in similar ways in the calorimeter. Elec-
trons emit photons through bremmstrahlung, which in turn pair produce electron—
positron pairs, each of these again producing brenmistrahlung radiation, with this
process repeating until the energy drops below the photon pair production thresh-
old. The photon produces a nearly identical signature in the calorimeter, where it
will initially pair produce an electron and positron which produce bremmstrahlung
radiation, producing photons that pair produce also giving an electromagnetic shower.

Fortunately, electrons and photons can be distinguished in the tracking system
because the electrons ionize the tracking material while the photons can pass through

undetected. Additionally, the preshower detector can produce tracking and early

97

Shower signals that can differentiate photons from neutral pions which decay to two
photons.

The ﬁrst step in electron and photon identiﬁcation is the same, electromagnetic
cluster reconstruction, and is outlined in [59]. The experiment uses two methods
to identify clusters, the Simple Cone Algorithm and the Single Cell N N . The
algorithm which is most commonly used is the Simple Cone Algorithm, which is
also the one implemented in this analysis.

The Simple Cone Algorithm is based on towers in the calorimeter. These towers
are deﬁned by the three electromagnetic layers as well as the ﬁrst layer of ﬁne hadronic
material. For EM objects reconstructed in the central calorimeter, the ﬁrst step is
to ﬁnd the layer with the highest ET- Then, all adjacent towers with ET > 50 MeV
Within a cone of ”R < 0.4 are added to the initial tower.

In the end calorimeters, the EM clusters are sets of adjacent cells with transverse
direction < 10 cm from the initial cell with the highest energy in the third EM layer.
This layer is chosen because it has a segmentation of 0.05 x 0.05 rather than the
coarser 0.1 x 0.1 in the other layers. .

After the candidate EM clusters have been determined, they are tested against
SC“53123.1 criteria to determine whether are not the will be accepted as EM objects. The

four conditions are listed below.

1 - Cluster ET > 1.5 GeV
2 - 40% of cluster energy must be concentrated in central tower

'3 - The electromagnetic fraction, deﬁned as the energy in the electromagnetic layers

divided by the energy in all layers except. the coarse hadronic, must be at least

0.9( (fEM Efflwm

4' The cluster must also be isolated, as the electrons and photons have narrow

Shower shapes compared to hadronic jets. A cut of 0.2 is put on the variable

98

Center of Gravlty of the

0.4 Cimle lnitlal Cluster

    

0.2 Cier:

 

 

 

 

iso = "/v \L/ the interactiontp'oin't

Figure 4.4: The isolation of EM objects is determined by looking at the fraction of
total energy in a cone of ’R, < 0.4 minus the amount of energy in the EM calorimeter
m a Cone of ’R. < 0.2 normalized to the EM energy. The CPS is the central preshower
detector [19].

f’ _ Et0t(R<0'4)—EEAI(R<0'2)
13° — EEAI(R<U'2)

The isolation algorithm variables are displayed in Figure 4.4.

The centroid of the deposit is determined from the energy deposition in the third
EM layer. A weighted average of energy depositions in this layer is combined with
prinnary vertex information to determine the kinematic quantities associated with
this EM object. After this, the preshower layers are checked for hits in areas near
the calorimeter cells. If they fall within A17 x M of 0.95 x 0.05 of the weighted
average, the energy is recalculated, and the centroid adds the preshower information
to determine the direction.

Electrons are then separated from photons by searching for a track. This process

Uses a hits-on-the—road method. It checks a road in 0.05 x 0.05 in A7] >< Aqb between

99

the cluster and primary vertex. If a track with pT > 1.5 GeV is found, the object is

considered an electron. Otherwise, it is considered a photon.

4.2. 1 Electrons

The method used above is the most basic way to identify an electron. Depending
on the analysis, several types of electron deﬁnitions may be chosen according to how
strictly electrons are to be differentiated from photons and jets (typically neutral
pions). The deﬁnitions of many of these separation variables is outlined in [60].

The f E M and fiso deﬁned above can help distinguish between electrons and jets.
Several other quantities are also useful in making the differentiation.

A variable called the H -Matrix looks at longitudinal and transverse shower shapes
and studies the covariance matrix to determine if the given shower shape is consistent
with an electron. The seven variables considered in the matrix are the EM energy
fractions in each of the EM layers (showing the longitudinal shower development),
the r — ()5 cluster width in EM3 (showing the transverse development), the log of the
total shower energy and the log of the longitudinal position of the primary vertex.
There is a separate matrix for each ring of calorimeter cells with a particular 17. The

2 2 value less

shower shape is classiﬁed by its X value. The matrix cut requires the X
than a given cut.

Another variable is the track match X2. This is based on the difference between
expected (15 and 2 values in the track and the cluster value in the third EM layer. The

~

2 value of the track match is deﬁned as 2 — 6—¢ 2 + 6—Z 2 where the a
X ' ’ ‘ Xspatial — 0415 07 ' ' ’
values are resolutions of the quantities.

Finally, the electron likelihood combines several variables [60]. The seven variables

used in the likelihood for p17 are the following:

1. P()(2 ), the probability of the track-match X2.

spatial

1 ()0

2. 377;: does the energy in calorimeter match a certain track?

3. dca (distance of closest approach) of track: is track associated with primary

vertex?
4. The H —matrix explained above.
5. The EM fraction explained above.
6. The number of tracks within ’R < 0.05 of the candidate electron track.

7. The total PT of the tracks within R < 0.4 of the candidate track

The likelihood uses these quantities to determine an overall jet separation. The
tighter the cut, the more electron-like the object, and the less jet-like. The likelihood
is constructed from a sample of real electrons and jets or photons misidentiﬁed as
electrons (fake electrons). For each of the seven variables probability distributions
for real electrons (P5(a:,-)) and fake electrons (PB(x,-)) are determined [61]. With
the variables assumed to be independent, an overall real electron and fake electron
probability can be determined as shown in Equation 4.5. The likelihood is the ratio
of the probability that the electron comes from a real electron over the probability

that it comes from either a real or fake electron, as shown in Equation 4.6.
=1:[1Pi5(1‘i), PB(.r :1:11Pi,B (172-) (4.5)

_. __ 133(5)
£e(l‘) — Ps(f) + PB(.E) (4.6)

The energy of the electrons taken directly is found to underestimate the expected
Z -peak in Drell-Yan distributions. The energy scale and offset is then determined to

best match the known Z boson peak [19].

101

 

In this analysis, we use electrons that are defined as Top Tight, which includes

the following:

likelihood > 0.85,

fiso < 0.15,

fEr’VI > 0.9,

2

H -1natrix X < 50,

track PT > 5,

Calorimeter energy to track momentum ratio < 2.5.

The speciﬁc analysis cuts can be found in Section 7.1.

4.2.2 Photons

The selection of photons is similar to the electron selection. The track-match proba-
bility can be reversed to discriminate between electrons and photons. The tighter the
cut put on the reverse track-match probability, the stronger the discriminating power
of the variable. The isolation, electromagnetic fraction, and the H—matrix are also
used to differentiate between the photon and jets, just as they are for the electron.
Photon identification is discussed in [62].

The photon also uses several other variables. The IsoHC4 ﬁnds the scalar sum
of tracks’ momenta in a hollow cone between 0.05 < R < 0.4, with the direction
measured in EM3. Only tracks with pT > 0.4 GeV and |zvtI — afffl < 1.0 cm are
included. Additionally, the preshower is used to determine the difference in shower
shapes between a photon produced in direct production and the decay of a neutral

pion. The cpsrms ﬁnds the spatial differences between the energy deposits in the

preshower and the those in EMB. This discriminates against. clusters with wide energy

102

deposits. A second CPS variable is the cpsrmssq which takes the square of the gb
and measures the difference in the energy squared distributions. This discriminates
against multiple peaks in the preshower as would be expected in the diphoton decay
of the neutral pion.

The photon energy also needs to be slightly modiﬁed from that expected from
electrons due to a slightly different longitudinal energy deposition in the calorimeter.

This correction varies from 2% in photons of 30 GeV to 0.1% in 150 GeV photons.

4.3 Muons

Muon objects at D0 are reconstructed based on information in tlu'ee subdetector
systems: the muon system, the calorimeter, and the central tracking system. All
other known standard model objects either shower in the calorimeter or leave no
trace in the detector at all. Only muons survive the calorimeter to deposit energy in
the outer muon tracking system. The main problem with reconstructing events with
muons is then less involved with object identiﬁcation and more with the provenance
of the muon and the quality of the associated properties.

Each muon is deﬁned by three types of object deﬁnitions described in [22]. The
ﬁr St regards the quality of the muon based on information from the local muon system.

There are four deﬁnitions. In decreasing order of quality, these are:

H

Tight

2~ Medium N scg 3
3- Medium

4 - Loose.

This analysis uses Arledz'um N 569 3. The Nscg : 3 refers to the three segments of

the IIluon system that must contain hits for the local tracks. The A layer is located

103

within the muon toroidal magnet while the B and C layers lay outside of the toriod.
For a muon to be referred to as N seg3, there must be hits on either side of the toroid.
For a Medium N 369 3, there must be at least two hits in the A layer drift tube wires,
at least 1 hit in an A-layer scintillator, at least 2 hits in the B or C layer drift tubes,
and at least one hit in the B or C layer scintillators (unless there are four hits in the
BC-layer drift tubes).

The second object deﬁnition is based on the quality of the track in the central
tracking detector. This analysis uses the tight track deﬁnition, but there are also
medium and loose options. For tight tracks, the distance of closest approach to the
vertex of the matched track must be < 0.02 cm. Additionally, the track must satisfy
a X2 / do f < 4. Also, there must be at least one hit in the SMT detector.

The ﬁnal parameter is the isolation of the muon. The physics of most interest in
leptonic ﬁnal states arise from muons that are the result of object decays from heavy
bosons. These objects produce isolated muons, while muons coming from the decay
of heavy-ﬂavor jets are produced within the cone of the decaying jet. To determine if
the muon is sufﬁciently isolated, several isolation deﬁnitions are given. This analysis
USES an isolation deﬁnition known as N PTz’ght.

For a muon to be N PTz'ght, it must satisfy conditions for the track halo and the
calorimeter halo. The track halo is deﬁned as I ZtraCkS pT| in a AR(track, muon track) <
0-5 Cone. For the calorimeter halo, I Seems ET], the calorimeter energy is calculated
in a cone of 0.1 < AR < 0.4. In N PTight, the track halo must be less than 2.5 GeV,
and the calorimeter halo must be less than 2.5 GeV as well. The cone used for muon
iSOla-tion is shown in Figure 4.5.

There are additional cuts to reject cosmic muons by restricting the time for the

muon to propagate out to the A, B, C layers to 10 ns.

104

 

 

 

Figure 4.5: The muon isolation cone for calorimeter isolation is a hollow cone of
0.1 < ’R < 0.4 [20].

4.4 Hadronic Objects

Hadronic objects produce hadrons and have object properties that are primarily de-
termined within the calorimeter. The two detector objects of this type that are

separately deﬁned in DC analyses are hadronic taus and jets.

4.4. 1 Taus

Taus can decay to electrons, muons, and hadrons. It is difﬁcult to determine whether
light, leptons in an event ﬁnal state originated from a tan, but the hadronic signature
from a tau differs fairly signiﬁcantly from that of a jet. Taus’ calorimeter quantities
are determined from two algorithms, the Cal Cluster and EA! Sub — Cluster. The
Cal Cluster uses a simple cone of R = 0.3, and an isolation cone of R = 0.5. The

EM Sub — Cluster is used to ﬁnd ads. This uses a nearest neighbor algorithm in

105

the third EM layer. If any clusters are found, cells in other layers are combined with
preshower information to determine the properties of the tau object. Tau reconstruc-
tion and identiﬁcation is discussed in detail in [63].

Next, the calorimeter clusters are matched to tracks in the central tracking system.
A tau typically produces three tracks or less. The best way to suppress a track from
jets is to ensure that the tan has no more than three tracks associated with it. The

track matching procedure is described below.

1- All tracks within IR 2 0.5I cone are sorted in pp

2- If a track has PT > 1.5 GeV, then an attempt is made to match it to a calorime-

ter cluster

3- Up to two more tracks may be added if they are within 2 cm in the Z-direction

from the base track

4 - A second associated track may be added if the invariant mass of the two tracks

is < 1.1GeV.

5. A third track may be added if the invariant mass of the three tracks is < 1.7
GeV (the mass of the 7') and the total charge of the tracks is one or negative

one.

Three types of hadronic tau decays deﬁne the three tau types at DC :

1‘ 7i —‘) Wil/T

2- 7i —> piI/T —> 71'07Ti1/7-

3, i :t

'T —-> 7T WTWi

Each of these taus with their unique decay properties are found in the detector

“71th different algorithms. The three types of tau decays are shown in Figure 4.6.

106

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A type 1 tau is based on an algorithm searching for the ﬁrst listed decay type.
There are two properties used to distinguish the tau from the jet in this algorithm.
The ﬁrst is the AR between the track and the calorimeter cluster. The second is the
ratio £11,. For a type 1 tau, the energy deposited in the calorimeter should be equal
to the momentum of the associated track since there is only one detectable object
associated with the tau.

A type 2 tau uses the AR between the track and the hadronic part of the cluster,
E; £183; 3356)::3; The ﬁnal parameter is the mass of the track combined

with the EM3 cluster. The EM3 cluster should correspond to the 7r0 and the track

 

the em3iso 2

to the charged pion. These two should never have a mass larger than the known 1.7
GeV mass of the tau.

Type 3 taus use the AR between the second track and the calorimeter cluster.
Also the number of tracks between 100 and 300 is checked to ensure there are not
other associated tracks expected in a jet. Also the energy deposited in the calorimeter
is compared to the sum of track momenta. Each of the tracks should be associated
with the calorimeter deposit with no additional energy from the ’T in the calorimeter.

Each of the objects then uses a neural network to cut on several variables asso—
ciated with each tau type. A neural network is a multivariate process that takes a
vector of 72 inputs and maps them onto m outputs without knowing the functional
fOI‘III of the mapping. The neural network works by repeatedly presenting inputs as-
SOCiated with certain outputs. In high energy physics, training signal and background
samples are presented to the network. With this sample the network is able to learn
how known inputs are mapped to outputs, and the neural network can be trained
to maximize its discrimination between signal and background. The trained neural
Iletvvork can then be used on a sample with unknown signal and background content.
More information can be found in [64].

Type 1 Neural Net I63]:

108

Ci!

E1+E2
. taup'r f —> i—I This variable compares the energy in the two highest towers

z' 2
2 ET . . . .
to the overall energy depos1ted. Since tau objects have narrower Slgnatures, the

fraction of energy deposited in the highest towers for taus should be higher than

for jets.

tauiso —+ E(O'g)(6§)(0'3) This determines the tau energy isolation. It measures

 

the energy deposited in a circle around the centroid. This again uses the fact
that taus have narrow signatures. Most of the tau energy should be deposited
within R = 0.3 in 77, (1). Additional energy outside of this region points to a

more jet-like object.

tauE A11 122190 f r The ratio of the transverse energy in the ﬁrst two layers of the
calorimeter to the total transverse energy in a cone of R < 0.5 centered at the

centroid of the calorimeter deposition.

tauettl/taupt This is just the ratio of the calorii'neter energy deposition to the

momentum of the track.

. tauettr/(tauettr +tauett1 + tauett2 + tauett3) The total transverse momentum

of all of the tracks in a cone of R < 0.5 that are not associated with the tau

divided by the total transverse momentum of all tracks.

Type 2 and 3 Neural Net:

1.

CO

taupr f Same as above.
tauiso Same as above.

tauettl/tauEtz-so The transverse mommitum of the leading track as a fraction

of the calorimeter energy in R < 0.5.

taueleQ/taupt The square root of the. product of the initial track PT and the

ET of the electromagnetic cluster-

10‘)

5. taudalpha/pz' ——+ The Opening angle between highest PT track and corresponding
EM cluster divided by the sin 6 where sin 6 is the sine of the azimuthal angle of

the calorimeter cluster centroid.

6- tauettr/(tauettr + tauettl + tauettQ + tauett3) Same as above.

The type two taus are very close to the signature of an electron with a single
track and energy deposition in the EM calorimeter. To remove these, the H-matrix
X2 (see Section 4.2.1) is required to be less than 30 within an R of 0.4. Additionally,

- E .
the fEM < 0.8, ? — 1 < 1, and IA¢(MET,TtTk)I < 0.5 to account for the energy
deposition of the charged pion in the hadronic calorimeter and the missing energy of

the 1: an neutrino that will be associated with the decay.

Discrilmnation among decay signatures of different quark ﬂavors and between gluons
and quarks is quite difﬁcult. Heavy-ﬂavor jets of b—quarks and to a lesser extent c-
qual‘ks have hadronization signatures that allow some minimal discrimination. With
the exeeption of bottom quarks, all quarks and gluons will be considered identical.
Predictions of decay properties from theory are determined from cross sections using
I)ertuarbative QCD. The predictions involve partonic objects that have yet to hadronize
and decay. Some Monte Carlo programs incorporate showering and fragmentation
II1C>Ciels to predict showers of hadrons known as particle jets. At D0 , measurable
properties of jets correspond to energy depositions in the calorimeter. These define
the three types of jets necessary to bridge fundamental theories to particle signatures:

DartOnic objects, particle jets, and detector jets as seen in Figure 4.7.

4 ’ 4 ~ 2 . 1 Jet Reconstruction

AS discussed in Section 3.2.2.1, the calorimeter is divided into cells of 77 and g'b. The

(IQ .
‘ 118 are put together into clusters that extend out roughly along rays from the center

110

of the detector. A group of these cells is a geometrical tower. In jet reconstruction

algorithms, each cell is treated kinematically as a massless object with its own energy
and momentum determined by the energy deposition and its projection from the
detector center. The full jet reconstruction procedure is outlined in [65].

The ﬁrst step in reconstructing jets is to create energy towers out of the geomet—
rical towers. The energy in each calorimeter cell is measured and compared to the
vvidth of the energy signal due to noise. If the energy is 2.5 0““, the cell’s energy can

be added to the overall tower energy. Generally, noise from electronics and radioac-

tivi ty can cause isolated cells with high energy. If the cells are sufficiently isolated
they lmay be removed with the NADA algoritlnn [66]. Additionally, the T42 algo-
ritllm removes any cell with an energy < 4 Joell that does not have a neighbor with
energy > 4 Joell. The details of the T42 algorithm can be found in [67]. The cells
that survive these noise cuts become part of the ﬁnal reconstructed tower. For each
tower , one then calculates full 4-momentum values, from which its energy, momen-
tum’ and directional properties can be calculated. These towers are then fed into the

Simple Cone Algorithm.

The Simple Cone Algorithm takes individual energy towers and loops over them
(treat ing preclusters. Any tower with with a transverse momentum of > 0.5 GeV
Will be checked as a seed for precluster construction. If the lead (highest energy) cell

Comes from a cell in the coarse hadronic calorimeter or is part of the end cap massless
gap, an additional condition must be met. Since these cells are typically noisy, the
tot a1 tower PT minus the lead cell PT still must be > 0.5 GeV.

Once the precluster seed has been determined, then all of the remaining towers
ar e looped over. If AR < 0.3 between the tower and the precluster, and the PT of
tlle tower is > 1 MeV, then the tower is combined with the precluster using the full
4‘lilornentum. In the creation of preclusters, the pseudorapidity is used in R. In later

tages, the actual rapidity is used in R calculations. Any precluster With PT > 1

111

GeV and with more than one tower is used in the jet creation algorithm.
Several jet reconstruction algorithms have been proposed, but this analysis and
nearly all others have relied on one algorithm called Run II Cone Algorithm [65].
This algorithm follows three steps to produce the ﬁnal jets that are used in analyses:

clustering, ﬁnding midpoint protojets, and merging/ splitting.

4-4-2.1.1 Clustering The clustering method takes each of the preclusters as
seeds to form protojets and the list of all of the towers to recalculate energy val-
ues when the preclusters are turned into proto jets. First, the preclusters are ordered
in pT - The distance AR between the precluster and any already created protojet
Inust be > 0.25. The protojet candidate then goes through an iterative process to
ﬁnd its ﬁnal conﬁguration as a protojet. A cone of R = 0.5 is created and all cells
Withiill the cone are combined to form a new protojet candidate. The values associ—
ated Within the new protojet are recalculated. A new cone is formed and the process

Continues. The iteration stops when any of the following conditions are met.

1 - The transverse momentum of the protojet candidate is < 3 GeV, in which case

the candidate is discarded.

2 - The cone stabilizes with AR between successive iterations of the protojet can-

didates < 0.001. This protojet passes to the next stage.

3 - The number of iterations reaches 50. Again, this protojet will be passed to the

next stage of reconstruction.

4“1.2.1.2 Finding Midpoint Protojets This step is new for Rim II. It was
fouIld that calculations from perturbative QCD with infrared and collinear cut—offs
Were unstable without the inclusion of midpoint protojets. In this step, pairs of
prOtojets with 0.5 < AR < 1.0 are considered. The midpoints in PT of these jets are

fol1nd and the same clustering algorithm as above is run with two differences. First,

112

 

there is no condition put on the minimum AR between the precluster and another
protojet. Second, there is no removal of duplicated jets.
The midpoint protojets are then added to the list of the proto jets created directly

frOIn preclusters as discussed above.

4-4-2.1.3 Merging and Splitting The energy depositions in the calorimeter
must only be used once. To ensure this, the list of protojets is checked for over-
laps- All protojets are looped over and checked for overlaps with other protojets. If a
prot 0 j et shares a calorimeter cell with another jet, then the fraction of energy of the
lower PT jet that is shared with the neighboring proto jet is calculated. If over half of
the energy is shared, then the two protojets are merged into one. If under half, the
PI‘Ot 0 j ets split the energy by their distance from the cell AR, where R is now using
the true rapidity rather than the pseudorapidity. In either case, the new jet or jets
ar e added to the protojet list, and the process is begun again. This is repeated until
thel‘ e are no protojets that share calorimeter cells. A ﬁnal cut of PT > 6 GeV is put

on the protojets, and the resulting list consists of the jets that are used in analyses.

4‘4~2- 2 Jet Energy Scale

Unlike other detector objects, jets are considerably removed in their properties from
the initial decay objects. To better understand the physics processes that led to a
particular detector signature, the detector jets are corrected to determine the energy
and direction of the original object that entered the detector. When this information
is determined, the detector signature can be better compared to the original physics
proCess of interest. The determination of the jet energy scale for p17 data can be
f(“Ind in [68]. The transition from partons to detector jets is Shown in Figure 4.7.

The particle jet energy can be related to the measured jet energy by the following

e’(lllation,

113

 

 

 

 

 

 

 

 

 

 

 

 

 

"‘- -n- -u- ..~ ‘
CII‘L~--h-- —“‘f‘:
E. . I
g |‘ :' M
I
5 FR | l
.5 ‘ hadrons ,
|
1
EM
—————————— -‘—-—-— E
E. i:
2
i
a.
|
............ +-
I
‘6
H
a
13
n.

 

 

Figure 4.7: The partons of the initial physics processes decay and hadronize to par-
tlcle jets which then leave tracks in the inner tracking system and energy in the
Ca‘loltimeters.

114

measured _ .
Epartiele _ jet E0

Jet cht Sjet

 

(4.7)

T he rest of the section will describe each of these variables.
E0 is the offset energy. This energy can be due to electronic noise signals and the
radioactive decay of the uranium absorber plates. Additionally, there can be more
than one 171‘) interaction in an event and also energy left over from previous beam

crossings.

‘I 'he amount of offset energy will depend on several variables:

0 The size of the cone used to create the jet, because a larger cone size is more

likely to include depositions from unrelated processes.

0 The pseudorapidity of the jet because the granularity changes in r), and the

response of different parts of the calorimeter are nonuniform.

. The number of vertices changes the probability that there will be additional

collisions for a particular beam crossing.

- The instantaneous luminosity also will determine the likelihood of multiple col-

lisions and the amount of energy that may left over from a previous crossing.

The variable Rjet is the fractional response in the calorimeter to a particle jet
Witll a particular energy. This value tends to be less than one because of energy
lost in the calorimeter, the uninstrumented regions between detector modules, the
IOWQI‘ response the calorimeter has to hadrons compared to electrons and photons,
and inhomogenieties among the modules. The calorimeter response will depend on
the energy of the jet, the cone size used, and the pseudorapidity.

The last variable is Sj‘et- This determines the fraction of energy deposited within
the cone deﬁned for the jet. This value would be less than one from parts of the

Jet energy that falls outside of the deﬁned cone. Additionally, energy from other jets

that falls into the jet cone, may push the 8 value above one.

115

 

A difﬁculty with this method is that the true values cannot be determined from
data. The offset energy will depend on the fraction of energy within cone, and the
response will also depend on the other factors. Monte Carlo can be used to get an

idea what additional correction factors need to be included to properly translate the
energy of a jet back to its particle state.

The offset energy is determined by special triggers that collect events that do not
have a hard scatter process. The calorimeter response is determined from ’7 + jet
events. The photon response is better measured and calibrated, so the jet energy

lneasurements can be determined by the photon energy depositions. The in—cone

fraction uses 7 + jet events in both data and Monte Carlo. When these events are
back-to—back, the amount of energy that falls within the cone can be determined.

Since the values of R and E0 are determined directly from data, they contain

bi ases, Additional multiplicative factors, k0 and k R can be determined from Monte

Carlo to correct the estimated factors in data to the simulated values determined

from the Monte Carlo.

Fllrther discussion of jet corrections (shifting, smearing, and removal) for Monte

Carlo are discussed in 6.2.1.

4‘4-2.3 Jets from Bottom Quarks

NIa-Ily new physics processes preferentially decay to heavy quarks. These events can
be distinguished from light jet events because bottom quarks form B-hadrons with
lifetimes long enough to provide a identiﬁable vertex distinct from the main vertex
in the event. The heavy quark jets can be identiﬁed from the secondary vertex and
the association of calorimeter jets to “track jets”, which are groups of tracks in the
tre'Ctking detectors. Track jets are deﬁned as tracks within R < 0.5 of a seed track of
131‘ > 1.0 GeV with at least 2 SMT hits. The track jet must have at least two tracks

With combined pT > 1.0 GeV. Several different algorithms have been used for b—jet

116

 

 

 

 

 

 

/“
/

 

b-Jet Efﬁciency (%)
N
O

 

 

 

 

 

 

 

 

.......................

 

8 10
Fake Rate (%)2
Flgﬂlre 4. 8: Efficiency versus fake late for various operating using the neural net and

Jet lifetime probability tagger-

ideIltiﬁcation. Three of these, the Jet Lifetime Probability (JLIP), Counting Signed
Impact Parameter (CSIP), and the Secondary Vertex Tagger (SVT) have been used
in a. neural network improving the discrimination between b—jets and light jets better
the-11 any of the individual algoritlnns. The description of this process is described

in detail in [69]. The performance beneﬁts over the J LIP tagger are shown in Figure
4.8.

The seven variables used in the neural network are:
1. SVTS L DLS: Decay length signiﬁcance of the secondaiy vertex.

2. CS I PComb: A weighted combination of impact parameter signiﬁcance of tracks

117

associated with jet.

3. J LI P Prob: Probability that a jet originated from the primary vertex. The

closer to zero, the more likely a b—jet. If there is not enough information to

make this determination, the variable is set to one.

4 . S VTS L Xc210 f: Chi-squared per degree of freedom for the secondary vertex.

3'

a - S VTL Nt'rks: Number of tracks used to reconstruct the secondary vertex.

6- S VTS L M ass: Mass of the secondary vertex. This is the combined rest mass

of the tracks, assuming they are all pions.

7 - S VTS L N um: Number of secondary vertices found in the event.

The subscript L in SVT refers to the Loose operating point for that algoritlnn.
The SL refers to super loose which is an operating point which was not used when
SVT was used as an individual tagger. For the neural network, more information
prO‘Vides greater discriminating power, so the cut was lowered to allow more multijet
background to pass the cuts.

The efficiency of the neural net to properly identify a b—quark is divided into two
parts - The ﬁrst is the efﬁciency for the b—quark to be reconstructed as a matched track
jet - If the track jet is identiﬁed, the jet is deﬁned as “taggable”. The taggability differs
betWeen the data and the Monte Carlo, so that a scale factor must be applied to the

Monte Carlo to appropriately simulate the data events. The b—tagging efﬁciency is
baSQd solely on the ability of the taggable jet to pass a certain b-tagging operating

p0lllt of the neural network. This is discussed in more detail in Sections 6.2.2 and

62.3.

118

4.5 Missing Transverse Energy (ET)

The initial longitudinal momentum of an event is not known a priori due to the fact

that the colliding partons are part of the larger hadronic particles being accelerated,
and the distribution of that energy among the partons is not well known. The trans—
verse energy of the system, however, should be approximately balanced. If an event
shows a large amount of transverse energy, it can be inferred that a non-interacting
particle passed through the detector. In the standard model, only the three neutrinos
are non-interacting. Many theories of new physics include massive non-interacting
particles that would show up in the detector as large amounts of missing transverse
energy, well beyond that expected from W boson or Z boson decays.

The missing transverse energy is calculated based on the common T42 algorithm,
as are all energy calculations of calorimeter objects. This means that the energy for
any calorimeter reconstructed ob ject only uses the subset of calorimeter cells that
have positive energy more than 40 from the width of their noise, and neighboring
Cells in all three spatial dimensions that have energy levels greater than 20.

The missing energy incorporates all of these cells into its energy calculations except
for those of the coarse hadronic calorimeter. The cells from the CH are only used
if they are included in the reconstruction of the jet. Additionally, muons deposit
Only a small fraction of their energy in the calorimeter. The calorimeter-based E T

must be adjusted to account for muon energy determined from the muon momentinn.
Furthermore, many objects undergo further corrections to relate them to the energies
of the initial particles before they enter the detector. Therefore, for consistency, these
corrections must also be applied to the ET. These include corrections for the jet,

e
leCtron, and tau energy scales.

119

Chapter 5

Data and Monte Carlo Samples

5- 1 Data Sample

This thesis is based on the D0 Run Ila data set which ran from 2002 to 2006. Each
dat a—taking session at DQ is separated into several hour runs with approximately the
salne running conditions. The run numbers associated with this analysis begin with
run 151817 and ﬁnish with run 219000. The full analysis code used at DC?) is also
C‘d’tegorized by versions, so that the full analysis structure can be understood based
on a. Single version number. The data from RunIIa used in this analysis was processed
with version p17.09.03 and converted to the standard root—tree—based analysis format
(CAF trees) using version p18.05.00. After the data is converted into the CAP tree
analysis format, it is divided into skims based on the object content of the event. This
analysis uses two skims: MUinclusive and EMinclusive which are deﬁned by an event
that passes certain basic object criteria. For a single muon, this is typically a loose
Object deﬁnition and a PT cut of 8 GeV. For a single em object (electron or photon),
a. leose object deﬁnition is also used but with a PT cut of 20 GeV. Each of the skims
also have options of looser object and PT requirements if the event contains other
Objects. We also apply an additional condition on the data from the ElVIinclusive

klm so that 1t 18 not also Included in the h*"IUlll(“lllSlV(.‘.. This prevents the poss1b111ty

120

of double counting events. The original data reconstruction, root tree production,
and skimming was performed by the D0 Common Analysis Format Group [70].
Once the data are collected, they are checked by subdectector groups to ensure
data quality. Each group will mark particular runs or luminosity blocks as bad if the
detector components were unable to provide reliable information during that time.
All runs and luminosity blocks that are marked as bad are removed from the run.
The total luminosity used in this analysis after data quality checks is 1.1 fb‘l.

In our analysis, we focus on events that contain objects with high values of trans-
verse momentum. In order to quickly incorporate changes to our analysis framework,
we perform a subskim on all data and Monte Carlo choosing only those with high—pT
Objects, and saving them in a condensed format. The details of this format and skim
can be found in Appendix B.

The events entering the high-pT data set have no speciﬁc trigger requirements.
Wye choose events at the MIS level beyond the trigger turn-on threshold, so that
there is no speciﬁc momentum or energy dependence in the trigger efﬁciency. The pT
dependence of each of the plots are shown in Figures 5.1(a), 5.2(a). The 77 dependence
is Shown in Figures 5.1(b), 5.2(b). These plateaued efﬁciencies allow the incorporation
of the trigger efficiencies in the normalization ﬁts performed at the MIS level as
discussed in Chapter 7. The exception is u n dependence, which along with a jet.

11111ltiplicity dependence led us to include trigger efficiencies directly in later versions

of the analysis.

5-2 Monte Carlo Samples

The primary way we represent our standard model background is with Monte Carlo
genErators. With a model-independent search we must incorporate many different
bacl(ground processes to properly model the data. We primarily use two generators

f . . .
or this purpose, ALPGEN for produclng processes where we need to accurately incor-

121

 

 

d

Trigger Efﬁciency
0
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0 III[TIITIIIIIITIIIIIIIIIIT—TTIIFF
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Figure 5.1: Trigger efﬁciencies for single muon triggers in single p ﬁnal state. The
H 77 distribution is shown to not be completely ﬂat. This, along with a multiplicity
ependence led us to incorporate trigger efﬁciencies directly in later analysis runs.

122

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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F18 ure 5.2: Trigger efﬁciencies for single electron triggers in single e ﬁnal states.

123

porate jets produced in the hard scatter, and PYTHIA where these are less important
and our focus is on accurate hadronization and showering. When using ALPGEN, we

match the jets produced in the hard-scatter to PYTHIA for appropriate hadronization

and showering.

5.2.1 Monte Carlo Production Process

For some objects, independent programs provide more accurate simulation of particle
processes and decays. Speciﬁcally, TAUOLA is used for T decays [71], and EVTGEN

is used for the decay of b hadrons [72]. More details on these programs can be found

in the references.

5.2.1.1 PYTHIA

PYTHIA includes hard and soft interactions, parton distributions, initial and ﬁnal
state parton showers, multiple interactions, fragmentation and decay [73]. Because
of its completeness, it is the ﬁrst choice to model the pp collisions at the Fermilab
Tevatron Collider. While much of the particle collision is modeled in PYTHIA, it
does not incorporate the parton content of the proton and antiproton. For these
Ineasurements, a parton distribution function determined by the CTEQ collaboration
is used [74]. For all of the processes used in this analysis, the CTEQ6L1 library is used.
These are the leading order parton distributions speciﬁcally designed for Monte Carlo
event generators. It uses leading order hard cross sections with NLO as values which

are appropriate for the event generation methods used in PYTHIA and ALPGEN.

5-2-1 .2 ALPGEN

ALP GEN calculates exact matrix elements at leading orders for QCD and electroweak
interactions [75]. The beneﬁt of using ALPGEN comes from its exact leading or—

der Calculations for processes that include high jet multiplicities. ALPGEN produces

124

parton-level events with information on color and ﬂavor, so that it may be matched
to PYTHIA for showering and hadronization.

Matching of partons from the ALPGEN calculation to PYTHIA showering has the
fundamental difficulty of trying to separate the hard interaction from the showering
process. We use the MLM matching scheme which showers all events and looks for
an appropriate AR match between the partons and the jets, rejecting those events
without a match and also those with an additional unmatched jet [76]. This eliminates
double-counting from collinear partons with overlapping matrix elements and partons
that are too soft to produce their own jet. PYTHIA controls the partonic showering
and hadronization.

Additionally, ﬁnal states with high jet multiplicities and heavy ﬂavors (b-quarks
and c-quarks) are particularly interesting in the search for new physics. Since the
MIS analysis considers events with b—tagged jets in separate ﬁnal states from those
with light quark jets, it is particularly important to ensure that the standard model
background has enough events to accurately reﬂect the expected background in these
rare processes. To ensure this, processes that include additional heavy-ﬂavor quark
pairs are produced separately from the light ﬂavor contributions. In order to avoid
double counting the events, the light quark jets need to be scanned for b quark and c
quark content, and the b quark events need to be searched for additional c quarks [77].
These checks are required because of overlaps in phase space. Two charmed quarks

may be produced in tree level diagrams and during the PYTHIA parton showering.
When these events are removed, then all of the processes can be combined into a
Single input with appropriate weights without fear of double-counting. The following
is Sumrnaly of the skimming performed on each ALPGEN input process that includes

the production of additional radiative jets.

0 X + N light partons— Events with (parton level) c'c' or bb added (by PYTHIA)

ill the initial state radiation (ISR) or ﬁnal state radiation (FSR) are removed.

1‘25

 

o X + CE + N light partons- All events are kept.

o X + bb + N light partons- Events with CE in ISR or FSR are removed.

The events produced from this combination of generators are then passed through

the D0 detector simulation and combined with minimum bias events taken from

actual data. The detector simulation, dOgstar, is based on GEANT 3.2.1 [78]. The

dOSim program tracks particles through these detector elements, simulates hits on
the detector, and then digitizes those hits. The events are then reconstructed and
converted to the standard DO) analysis root-based trees (CAF-trecs) using the same

chain of processors as data.

5 . 2 - 1 .3 Additional MC Corrections

A handful of additional corrections are made after the production of the CAP trees.
These corrections typically involve parameters that may be updated frequently and
would require a lengthy resimulation if performed at an earlier stage. These cor-
rect ions include muon smearing (to correct for better resolution in the simulation),
Calculation of the process weights, and jet smearing and shifting. More details about

these processes can be found in Chapter 6.

5.2.2 Monte Carlo Samples

The following physics background standard model processes are currently considered,

Where j is a light jet (gluon, u quark, d quark, s quark) and [p is a light parton:
1- W + N j
2° VV +cE+ Nj
3- VV + b5 + N j
4' 2/7* + N J'

126

.Z/nf" +cE+Nj

01

6. Z/7*+bb+Nj
7. tf—a (26+21/+2b)+Nj
8. tE—>(€u+2b+2j)+Nj
9. WW

10. l/VZ

11. ZZ

5.2.2.1 W boson + Jets

W boson + jets samples are grouped by the parton content of each event. In order to
ensure that there are no overlaps with heavy-ﬂavor samples, the samples are heavy
ﬂavor skimmed, as described in Section 5.2.1.2. The W boson + 5 light parton, W
boson + bb + 3 light partons, and IV boson + CE + 3 light partons samples are
inclusive in jet content. The W boson Monte Carlo uses ALPGEN v2.11. All of these
Samples use PYTHIA v6-413 for showerng and hadronization. A list of W Monte Carlo
Salnples with number of events, leading log cross sections, and effective exposure can
be Seen in Table 5.1.

The factorization scale used for W boson + jets is set by the interaction energy

scale of the process,

Q2 = MEV + 23%;). (5.1)

jets
T . . . . . .
he faCtorrzatron scale Is the scale chosen to div1de the hard scatter process calculated

b . . . .
y ALI3(2EN and the showerlng and hadronlzation by PYTHIA [7b].

127

Table 5.1: W + jets samples

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Monte Carlo Sample Number of Production 0 L L Effective
Events Release Exposure
fb-l
W —> €11 + 0lp exclusive 2914k p17.09.07 4520 pb 0.645
W —> 2V + llp exclusive 8478k p17.09.06 1277 pb 6.64
W —> €11 + 21p exclusive 4964k p17.09.06 304.8 pb 16.3
W ——> £11 + 3lp exclusive 2443k p17.09.06 72.4 pb 33.7
W —> 61/ + 4!}? exclusive 1718k p17.09.06 16.49 pb 104
W —> €12 + 5lp inclusive 521k p17.09.07 4.95 pb 105
W —> £11 + C? + 01p exclusive 1175k p17.09.08 23.96 pb 49.0
1V —+ 61/ + c'c' + 1119 exclusive 598k p17.09.08 13.35 pb 44.8
W —+ 61/ + CE + 211) exclusive 237k p17.09.08 5.38 pb 44.1
W —-> £12 + 05 + 311) inclusive 248k p17.09.08 2.50 pb 99.2
W -—> 61/ + bb + 011) exclusive 1041k p17.09.08 9.34 pb 111
W —) a + 55 + llp exclusive 663k p17.09.08 4.26 pb 156
W —-> a + 55 + 2lp exclusive 285k p17.09.08 1.55 pb 184
W —+ 131/ + 55 +3115 inclusive 349k p17.09.08 0.74 pb 471

 

128

 

5.2.2.2 Drell-Yan + Jets

The Drell-Yan process is the primary standard model production mechanism for dilep-
ton events in the high-pT processes considered in the MIS search. These are also
grouped by light parton content with Z / 7* + 3 light partons, Z / 7* + CE + 2 light
partons and Z / 7* + bb + 2 light partons inclusive in light parton content. The Drell-
Yan samples also use ALPGEN v2.11. A list of Drell-Yan Monte Carlo samples can
be seen in Table 5.2. The choice of factorization scale for this production process is

shown in the equation below,

()
Q2 2 Mg +p%~(Z). (52)

Table 5.2: Drell-Yan Monte Carlo samples

 

 

 

 

 

 

 

 

 

 

 

Monte Carlo Sample Generated Number 0 L L(pb) Eff.
Z / 7* mass of Events Exp.
fb—l
Z / 7* —> 66 + Olp exclusive 15-60 GeV 562k 311 1.81
Z / 7* —-+ 66 + llp exclusive 15-60 GeV 427k 35.1 12.2
Z /7* —-> 66 + 2lp exclusive 15—60 GeV 164k 8.79 18.7
Z / 7* ——> 66 + 31p inclusive 15-60 GeV 78k 2.49 31.3
Z / 7* —-> 68 + Olp exclusive 60-130 GeV 1025k 131 93.2
Z / 7* —~> 68 + 11p exclusive 60-130 GeV 177k 40.0 4.43
Z / 7* —+ 68 + 2lp exclusive 60-130 GeV 83k 9.40 8.83
Z / 7* —+ 66 + 31p inclusive 60-130 GeV 77k 2.84 27.1
Z / 7* —+ 66 + Olp exclusive 130-250 GeV 94k 0.887 106
Z / 7* —> 86 + llp exclusive 130-250 GeV 84k 0.346 243

 

 

 

 

 

 

 

Continued on Next Page. . .

129

Table 5.2 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Monte Carlo Sample Generated Number 0 L L(pb) Eff.
Z / 7* mass of Events Exp.
fb—l
Z / 7* —+ 66 + 2lp exclusive 130—250 GeV 87k 0.0881 988
Z / 7* —> 66 + 3lp inclusive 130-250 GeV 75k 0.0466 1610
Z / 7* —2 66 + Olp exclusive 250-1960 GeV 98k 0.0686 1430
Z/7* —> 66 + llp exclusive 250-1960 GeV 88k 0.0349 2520
Z / 7* —+ 66 + 2lp exclusive 250-1960 GeV 88k 0.0105 8380
Z /’y* —> 66 + 3lp inclusive 250-1960 GeV 74k 0.00548 13500
Z /7* -—+ 66 + 05 + Olp exclusive 60—130 GeV 47k 3.05 15.4
Z /7* —> ee + cc + llp exclusive 60—130 GeV 43k 1.07 40.2
Z /7* -—> ee + 05 + 2111 inclusive 60-130 GeV 22k 0.424 51.9
Z/y’“ —+ ee + 623 + Olp exclusive 60—130 GeV 230k 0.965 238
Z/v’“ —+ ee + bb + llp exclusive 60—130 GeV 48k 0.350 137
277* -—> 88 + bb + 2lp inclusive 60-130 GeV 21k 0.132 159
Z / 7* -—> 1111 + Olp exclusive 15—60 GeV 552k 309 1.79
Z /7* ——> 1111 + llp exclusive 15-60 GeV 423k 34.3 12.3
Z/7* —+ 1111 + 2lp exclusive 15-60 GeV 163k 8.64 18.9
Z / 7* -—+ 1111 + 3lp inclusive 15-60 GeV 77k 2.52 30.6
Z /7* —> 1111 + Olp exclusive 60—130 GeV 985k 133 7.41
Z /7* -+ 1111. + 111) exclusive 60—130 GeV 198k 39.6 5.00
Z /7* —-> 1111 + 2lp exclusive 60—130 GeV 93k 9.32 9.98
Z /7* -—+ 1111 + 3lp inclusive 60—130 GeV 86k 2.77 31.0
Z /’7* —> 1111 + Olp exclusive. 130-250 GeV 101k 0.885 114

 

 

 

 

 

Continued on Next Page. . .

130

 

Table 5.2 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Monte Carlo Sample Generated Number 0 L L(pb) Eff.
Z / 7* mass of Events Exp.
fb—l
Z / 7* —> 1111 + llp exclusive 130—250 GeV 91k 0.345 264
Z / 7* —+ 1111 + 2lp exclusive 130-250 GeV 86k 0.0885 972
Z / 7* —> 1111 + 31p inclusive 130—250 GeV 73k 0.0455 1600
Z / 7* -—> 1111 + Olp exclusive 250—1960 GeV 93k 0.0678 1370
Z/7* —+ 1111 + Up exclusive 250-1960 ch 88k 0.0351 ' 2510
Z / 7* —+ 1111 + 2lp exclusive 250-1960 GeV 82k 0.0105 7810
Z / 7* —> 1111 + 3lp inclusive 250—1960 GeV: 77k 0.00559 13800
Z / 7* -—> 1111 + cc + Olp exclusive 60-130 GeV 47k 3.05 15.4
Z / 7* —1 1111 + cc + llp exclusive 60—130 GeV 43k 1.07 40.2
Z/'y* —> 1111 + c7: + 2lp inclusive 60—130 GeV 23k 0.412 55.8
Z/7* —> 1111 + 65 + Olp exclusive 60-130 ch 267k 0.967 276
Z/7* _. 1111 + 66 + llp exclusive 60-130 ch 48k 0.351 137
Z / 7* —-> 1111 + bb + 2lp inclusive 60—130 GeV 22k 0.132 167
Z / 7* —-> 77 + Olp exclusive 15—60 GeV 535k 310 1.73
Z/‘y” —+ 77 + Up exclusive 15-60 GeV 431k 34.3 12.6
Z / 7* —> 77 + 2lp exclusive 15-60 GeV 167k 8.73 19.1
Z / 7* ——> 77 + 3lp inclusive 15-60 GeV 76k 2.48 30.6
Z / 7* —> 77 + Olp exclusive 60-130 GeV 868k 133 6.52
Z /7* -—> 77 + llp exclusive 60—130 GeV 193k 39.7 4.86
Z / 7* —> 77 + 2119 exclusive 60—130 GeV 87k 9.70 8.97
Z / 7* —> 77' + 31]) inclusive 60-130 GeV 78k 2.78 28.1

 

Continued on Next. Page. . .

131

 

Table 5.2 (cont ’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Monte Carlo Sample Generated Number 0 L L(pb) Eff.
Z / 7* mass of Events Exp.
fl)”1
Z / 7* ——-> 77 + 011) exclusive 130—250 GeV 100k 0.888 113
Z / 7* ——> 77 + llp exclusive 130-250 GeV 90k 0.352 256
Z / 7* ——> 77 + 211) exclusive 130-250 GeV 80k 0.0915 874
Z /7* -—> 77 + 3119 inclusive 130-250 GeV 71k 0.0451 1570
Z / 7* ——> 77 + Olp exclusive 250-1960 GeV 93k 0.0680 1370
Z / 7* ——> 77 + Up exclusive 250—1960 GeV 88k 0.0351 2510
Z / "1* —-+ 77 + 211) exclusive 250-1960 GeV 82k 0.0104 7880
Z / 7* ——> 77 + 31p inclusive 250—1960 GeV 76k 0.00569 13400
Z / 7* —-> 77 + of: + Olp exclusive 60-130 GeV 39k 3.05 12.8
Z / 7* —-> 77 + 06 + 111) exclusive 60—130 GeV 43k 1.08 39.8
Z /7* —> 77 + CE + 2lp inclusive 60—130 GeV 21k 0.420 50.0
Z / 7* —> 77 + b5 + Olp exclusive 60-130 GeV 93k 0.967 96.1
Z/7* ——> 77 + 523 + Up exclusive 60-130 GeV 182k 0.351 519
Z / 7* —> 77 + 05 + 2lp inclusive 60—130 GeV 87k 0.132 659

 

5.2.2.3 ti

The t? samples also use the ALPGEN/PYTHIA generation method and are grouped

by light parton content and the decay results of the W bosons produced in the top

quark decay. A top quark mass of 172 GeV was assumed. All of the t? samples were

produced with ALPGEN v2.11 and PYTHIA v6-413. The samples are listed in Table

5.3. For ti, the choice of factorization scales is given by,

132

 

Q2 : A1301) + ZPCQTU)

jets

Table 5.3: tt samples

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Monte Carlo Sample Number of a L L(pb) Eff. Exp. fb’1
Events * Kfactor

tt —+ 2b + 41p exclusive 97k 1.91 50.8
tt ——> 2b + 5lp exclusive 90k 0.792 114
tt —+ 2b + 6lp inclusive 24k 0.389 61.7
t? —> [V + 2b + 2119 exclusive 518k 1.83 283
tt —-> 811 + 2b + 311) exclusive 98k 0.761 129
tt —+ (’12 + 2b + 41p inclusive 93k 0.374 249
tt —-> 26’ + 2V + 2b + Olp exclusive 368k 0.438 840
tt —-+ 28 + 211 + 2b + llp exclusive 236k 0.183 1290
tt ——> 25 + 21/ + 2b + 211) inclusive 242k 0.0899 2690

 

 

5.2.2.4 Diboson

The dibosons were produced using PYTHIA v6-413. The samples were produced

inclusively in parton content and decay and are listed in Table 5.4.

5.3 Multijets Background from Data

The multijets background is determined based on the inclusive final state considered.
For 6 + jets and 611 the jet background is determined from an electron background
sample. For 11 + jets, the background comes from non-isolated muons. For 117 and 67

the loose tau objects are used to provide the appropriate backgrounds. The multijet

133

Table 5.4: Diboson samples

 

 

 

 

 

 

 

 

 

Monte Carlo Sample Number of 0L0(pb) Effective Ex-
Events posure fb"l

WW inclusive 2460k 11.6 pb 212

WZ inclusive 602k 3.25 pb 185

ZZ inclusive 593k 0.425 pb 444

 

contribution in 1111 and ee ﬁnal states are insignificant, with the given event selection

cuts.

5.3.1 Multijets Background Using Loose Electrons

Ill order to estimate the multijets background arising from jets misidentiﬁed as elec-
trons, a sample of loose electrons is chosen by using loose electron likelihood criteria.
The sample uses the same cuts as those for Monte Carlo and data except for the
likelihood. The additional cut is determined by reversing the selection cuts used for
the MIS electron objects in e + jets and e11 ﬁnal states. Based on the plots shown
in Figures 5.3(a), 5.3(b), it was determined that the best reﬂection of electron-like
jets could be fOImd using an electron selection with likelihood values between 0.2
and 0.8, in contrast to electrons in the dielectron inclusive ﬁnal states which require
likelihoods greater than 0.85 and electrons in the e + jets ﬁnal state which require
likelihoods greater than 0.95.

The contamination of this background from real electrons decaying from the W’

boson was found to be only about 0.5% of the sample.

134

 

 

 

 

 

 

 

 

 

 

 

31800
c E I Data minus MC
$1600 T
Lu : ("as ..
u51400 _— j‘ Multijet Background
3; I .._.1
"831200 E—
31000 7
Z I
800 ‘_'
600 P
400 :—
200 E -_
: ‘ . "7L1 .1
0_ —I--—‘i—'“""’:l=“-"‘
".m_1.l.1.1|lln.1...1I.1..I.1.1|....1.44.1
2O 30 4O 50 60 70 80 90 1 )0
Electron pT (GeV)
(3)
1 j.
43 Real electrons
">’
LU r
"6 ,
3 -1 / Jets faking electrons
.0 1
510
3
z
‘o
2
ﬁ
-2
10 a

      

 

_ .I._ ' ' . - ~ . 1- - ﬁn.) -. '
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Electron Likelihood

Figure 5.3: A comparison of the multijets background to the data minus MC for the
electron PT in (5.3(a)) and the likelihood for electrons from the Z peak vs. those from
back-to—back electron-jet in (5.3(b)).

135

5.3.2 Multijets Background Using Non-isolated Muons

The main contribution of multijets backgrounds that involve muon ﬁnal states come
from real decays of heavy quarks decaying to muons. These muons are typically close
to the jets they decay from, so loosened isolation criteria are used to identify this
contribution.

The muon object criteria are the same as for other objects with the exception of
the ET track cone and ET calorimeter halo variables. The criteria for these in the
11 + jets and 1111 ﬁnal states is < 2.5 GeV. To best sample jets that contribute to
these ﬁnal states, these cuts are changed to 4.0 < X < 8.0 GeV, where X represents
both the track cone and the calorimeter halo. The distributions associated with the
background cuts can be seen in Figures 5.4(a), 54(1)).

The pollution in this sample from real muons is substantial. This will affect
the overall normalization factors as the W process Monte Carlo values will decrease
because some of this background is in the multijets selection. This affects the nor-

malization values but should only slightly affect the distributions’ overall sensitivity.

5.3.3 Multijets Background Using Loose Taus

In 67 and 117 ﬁnal states, multijets background is primarily from jets misidentiﬁed as
7 leptons. Based on Figures 5.5(a), 5.5(b), the best values of the tau NN to identify
jets are between 0.3 and 0.8. These best represent the shapes seen with higher NN
values and minimize the pollution from real tau leptons from W boson and Drell-Yan

decays.

136

 

   
  
 

+ Data_minus_MC

 

 

§§§§§§

O llllilll11111[IIHIIHHIIIHIITTIIIllllllllTlll

Number of Events

‘s’

 

 

 
 

 

 

100

90
”pr (GeV)

 

Real 115

  
  

_l
o
L.

 

7 115 from jets

 

 

Scaled N_umber of Events
O
:1:

 

 

9 1 0
Calorimeter Isolation (GeV)

0))

Figure 5.4: A comparison of the multijets background to the data minus MC for the
muon PT in (5.4(a)) and the calorimeter halo for muons from the Z peak vs. those
from back—to-back muon—jet ill (5.4(b)).

137

 

I Data minus MC

   

.—

 

 

D Multijet Background

 

  
 

Number of Events
U!
0
11413111 11,113 1 1 [ti 1 {bf 71‘! ‘l- 11‘

 

 

U‘llll-llll

 

_-

 

_n

lllllll

D I NN forjet mis-ID
D T NN for real I

_I
O
L.

llllll

fﬁlfr+m++1~1~+x JP - .

Scaled Number of Events

     

 

 

 

:A;';;..'.'.L.ll:.' ”1.5;. I; :; .'§;7..l}.i it 1173......
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1: NN Value

 

(b)

Figure 5.5: A comparison of the multijets background to the data minus MC for the
tau PT in (5.5(a)) and the neural network output value for Monte Carlo taus vs.
Monte Carlo jets reconstructed as taus (5.5(b)).

138

Chapter 6

Corrections to Monte Carlo

The Monte Carlo event generators are required to model ﬁnite approximations of
processes and GEANT detector simulations must accurately model an extremely com-
plex detector that is not completely static. Given the complexity of the task, some
additional corrections must be added to the simulation in order to properly model

the data.

6.1 Lepton Smearing and Efﬁciency

The Monte Carlo simulation of leptons shows higher reconstruction and identiﬁcation
efﬁciency and better energy resolution than is seen in the data. The efﬁciency is
corrected by applying a scale factor to the events to reduce the event weight. The
efficiency factor is chosen by comparing actual and Monte Carlo efﬁciency of events in
the Z ~peak. The resolution factor comes from matching the invariant mass spectrum

of the Z boson in each of the dilepton states.

6.1.1 Muon Smearing

The muon resolution in data is found to not exactly match that estimated in the Monte

Carlo, so an additional “smearing” parameter is applied. “Smearing” convolves the

139

calculated spectrum with additional resolution effects to match observation. This is
determined by looking at data and Monte Carlo events from Z —> 1111 and J / \II —-> 1111
processes. The widths of these distributions can be seen in Table 6.1. It is found
that the correction in the charge to transverse momentum ratio can best be adjusted
using a double Gaussian. The equation used is shown below,

B .
—q— —> —q—+AGl(0,1)+-———W

PT PT PT
with A found to have the best ﬁt at 0.007 GeV—1 and B at 0.009, where G1 and Gg

02(0, 1), (6.1)

are two independent Gaussian random numbers of mean 0 and 0 = 1.0.

Table 6.1: The width of the peaks using a best ﬁt to a double Gaussian. In both the
Z boson and J / ‘1' peaks, the Monte Carlo has a better energy resolution than the
data. This table was taken from [3].

 

Data Monte Carlo

 

U(Z -—> 11hr) 6.85 GeV 4.84 GeV

 

 

 

 

 

0(J/t1’) —> 1+1; ) 0.0651 GeV 0.0647 GeV

 

The J / 2,1) distribution before smearing can be seen in Figure 6.1. The Z and J / z/J
peaks after smearing can be seen in Figures 6.2(a), 62(1)).
The resolution is shown to vary from 2.5% from a muon of pr = 5 GeV to 9% at

PT = 40 GeV, after requiring IUCFTI = 0 and at least one SMT hit.

6.1.2 Electron Smearing

Electrons also show better resolution ill Monte Carlo than in the data [21]. The
general form of the electron smearing is given in [21], but a simpliﬁcation of this
general form is found to be sufficient to match our data in the Z -—> ee distributions,

as shown in Equation 6.2.

140

 

le —>1l*11' Invariant Mass

 

 

 

 

 

 

    

 

 

 

25000 L + Data
: MC

zoooo :—
15000 :—
1oooo :—
5000 :—

- :1." ‘ ‘ l l l I l l l l l 1 I l l l l l 3 4 L

" 2.8 2 9 3.2 3.3 3.4

Mass (GeV)

Figure 6.1: The J / 1b peak before applying muon smearing [3].

E’ = EG(0, a c) (6.2)

After the ﬁt, the parameters were found to be a : 1.004 and c = 0.0305 for the ﬁducial
region, where G is again an independent Gaussian random number with mean of 0
and a 2 ac. A ﬁgure showing the Z peak after application of the smearing is shown

in Figure 6.3.

6. 1 .3 Muon Efﬁciency

The muon reconstruction and identiﬁcation were discussed in Chapter 4. Each of
three muon identiﬁcation criteria (local muon ID, track type, isolation) introduce
scale factors with respect to the Monte Carlo [22]. These efficiencies are calculated
for each muon ill the event, so the overall event weight may incorporate. factors for

multiple muons.

141

 

[ Z —>1l*1l'lnvariant Mass 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

1000
1 + Data
_ — MC
800 F
000 —
400 —
zone—
0 — I I l I I l I I I I 1 I I l I l l I l I I I I I I J_ L I
60 0 90 100 110 1 20
Mass (GeV)
(a)
le —>1l*1l' Invariant Mass
20000 :—
15000 _—
1—
l.
10000 :-
5000 _—
o ‘— I I I I I I l l I 1 I l I I l I l l l I I I I I I I I l I I I
2.8 2.9 3 3.1 3.2 3 3 3 4

 

 

'Mass (Gav)

(b)

Figure 6.2: 11 smearing effects in the Z and J / 1/1 peaks. Figures taken from [3].

142

M(e,e) with two electrons in CC

 

 

'Data

Number of Entries
3 a

9 o
2 8
ITIIIIITerTIIIITIIIIIII

0.02

IllllllLJLLJllllllLlllllllle

so as so 95 100 105
M(e,e) (GeV)

 

 

 

Figure 6.3: Electron smearing effects in the Z peak. Figure taken from [21].

The efﬁciencies for each of the muon identiﬁcation criteria are determined by the
tag—and—probe method [22]. This method uses tight reconstruction cuts on one muon
and loose parameters on a second while choosing events that correspond to the Z
boson peak. The muon with tight cuts is called the tag leg, and for data events,
this object must have been able to trigger the event. The efficiencies for each of the
criteria are determined by looking at the other muon that was only required to pass
loose cuts. The fraction of objects passing each of these criteria for the probe leg
determines the efficiency.

For the local muon identiﬁcation efficiency, the detector 77 and 96 are used to pa-
rameterize the efﬁciency of the M edium N SegB muons. This averages to a data
efﬁciency of 81.5% and a necessary scale factor of 0.91 (since the Monte Carlo efﬁ-

ciency is 89.6%). For tracks, the parameters z and 770 FT deﬁne the efﬁciency for

143

tight tracks used in this analysis. The efﬁciency of the tight tracks is around 80.2%
with a scale factor of 0.97. Finally, the N PTight isolation efﬁciency is parameterized
by the particle 71. This is an average efﬁciency of 0.92 and also a scale factor of about

0.92. The efﬁciencies for each of these can be seen in Figures 6.1.3, 6.1.3, 6.1.3.

|eff__eta_phi_muid_medium_nse93 |

 

 

Figure 6.4: Combination 11 efﬁciency for local muon system, cosmic veto, and track
match. The hole is due to supports for the calorimeter preventing placement of muon
chambers. Figure taken from [22].

6. 1 .4 Electron Efﬁciency

The electrons from the simulation also show a higher reconstruction efficiency than
that seen in data. The efﬁciency calculations for electrons use the same tag-and-probe
method as was described above for the muons.

The electron efﬁciencies are measured for two sets of criteria [23]. The ﬁrst is the

preselection Where the efﬁciency of the probe electron is measured for object type,

144

 

eff_z_track_tight

 

        
 

was ....; ...... ....... i ..... M ..... :. ...... g ....... ...... .
0.3 ...... 5. ...... 1'95, ...... ....... iA'i' ...... ....... ...... .
0.7 ...... ... ...... g! ..... . ...... . ....... .....I... ...... ....... _. .......
0.6 ...-g..-...JE.......i......§....‘....?......?.-.uni....-"gnuuuéuuuu
0.5 ----- ------ ' ------- :- ------ . ....... : ...... .:. ...... : ....... .. ...... .
0.4 . ....... ...... ....... ...... = ..... ...... .
0.2 ....... ...... ....... ...... é. ......... ...... .
0.1 5 ---------------- ....... .. ...... .

I . . . . .

 

Figure 6.5: 11 efficiency for tight track reconstruction. Figure taken from [22].

isolation and electromagnetic fraction quantities. The preselection is parameterized
in ndet» with an average efﬁciency of around 97%. The top tight electron selection
used in this analysis, has a further efﬁciency relative to the preselection. The top tight
deﬁnition includes information on the H -matrix and likelihood. Its efﬁciency is pa-
rameterized in 77det and ¢det and is found to average 73%. The efﬁciencies are shown

in Figures 6.7(a), 6.7(b).

6.2 Jet Weights

Jets at DC have the same type of difficulties as the leptons: the jet efficiency and

energy resolution are better in Monte Carlo than in data. Additionally, the probabil-

Isolation Cut Efﬁciency on 2 —) 1111 DATA

 

 

m
-L

I I
ﬁl-

ll

Il_rl

EEEsgsgtttagsesttaﬁﬁﬂ

l-

 

0.9
0.8
0.7
0.6 ' NPLoose

Illl

 

llll

 

 

 

 

llll

 

llll

 

0.5 NPTight

 

 

 

 

 

”-4-2 -10 i i

77

Figure 6.6: 11 isolation efﬁciency for NPTight isolation requirement. Figure taken
from [22].

ities to ﬁnd a track jet (taggability), and to identify a b—quark are also higher in the

Monte Carlo.

6.2.1 JSSR

The JSSR correction stands for jet smearing, shifting and removal [24]. It has been
formd that additional corrections are needed when considering jet modeling beyond
those discussed in the section 011 the jet energy scale. These are the relative jet energy

scales, jet energy resolutions, and efﬁciencies.

146

Preselection Efﬁciency in CC

 

 

 

 

>
U
.5 31.0 W
U
E L-O.8
LLI _
0.6 1'
0.4 — -o-data p17
‘ —MC p17
0.2 _— —--|
o . I . I | x I

 

 

 

 

 

 

 

 

 

 

ndet

Figure 6.7: Electron efﬁciencies for preselection and top tight. Figures taken from
[23].

147

These values are determined by looking at 7 + jet and Z /7* + jet data and
Monte Carlo. In both cases most of the relevant information can be found in the
momentum imbalance between the photon and the jet.

pjet _ py/ Z
AS = T T (63)

Z
19;!

 

The differences in the momentum distributions between data and Monte Carlo show
the additional corrections to Monte Carlo that need to be added to give appropriate
jet distributions.

At high values of 7 PT» these AS distributions are Gaussian. At lower values,
there are some threshold effects. The two distributions can be deconvolved into a
Gaussian and error function representing the threshold effects. The turn-on curves
plateau by 15 GeV, below which jets are removed. Additional n-dependent efﬁciencies
are applied where the efﬁciency plateaus. This is only relevant for jets falling in the
InterCryostat Region where the efﬁciency is noticeably lower than 100%. The AS
distribution showing the convolved Gaussian and error function is shown in Figure
6.8.

The differences ill the means of the AS Gaussian ﬁts are used to determine the
shifting in the Monte Carlo, and the widths of the Gaussians are used as an additional
shifting parameter. These frmctions were derived based on the PT values of the 'y or
Z boson, so the reconstructed jet energies must be mapped to approximations of the
recoil energy of the boson-jet system.

The ﬁnal pT values of the jets are modiﬁed according to the following equation

after the removal of jets below 15 GeV.

paw = PT + p34/lehz'mp31/Z) + Gm. swampy/Z)», (6.4)

where 3112' f t is the relative jet energy scale, smear is the. oversmearing factor, and

148

 

”a
Q

IllllllllllllIll‘I—IIIIIIIIIIII

I40
120

number of events

100
80

40
20

\

 

 

 

 

'Q
:HI‘I
I
N
I
9
£11
0

0.5 1 1.5
AS

Figure 6.8: The difference in the energy measurements between the photon and a
jet in back-to—back events. The distribution can be approximated by convolving a
Gaussian distribution with an error ﬁmction [24].

G is a Gaussian random number with mean of 0 and a : smearwgs/Z). If jets fail
our jet criteria after adjusting the PT values, these jets are removed. We used the

common RunJSSR CAF processor to implement these modiﬁcations.

6.2.2 b—tagging Rate Correction

The b—tagging in this analysis uses direct tagging of the Monte Carlo jets to determine
the overall b—tagging rate. Direct tagging makes a One—to-one correspondence between
a jet and b—quark. Each jet will have a probability to originate from a b—quark, and
based on that probability a certain fraction will be labeled b—quark jets. This differs
from the tagging rate flmction method, in which the fractional probability for each jet

to originate from a b—quark is kept, and each jet is effectively a fractional b-quark jet.

149

The probability to tag a b—quark jet in Monte Carlo is higher than that seen in data
[25]. The b—tagging algorithm group looked at samples tagged with the neural network
tagger used in this analysis and compared it to rates seen using a soft lepton tagger,
which is independent of the neural network. It set up a system of eight equations with
eight unknowns, two of which were the tagging efﬁciency of each of the taggers. The
“Tight” operating point used in this analysis has an average data efﬁciency of 47%,
which requires a Monte Carlo scale factor of approximately 0.87. The parameterized
efﬁciency and scale factor can be seen ill Figure 6.9.

Sometimes jets are tagged as b—jets, which are not actually jets from b—quark
fragmentation. The rate of mistagging depends strongly on the ﬂavor of the actual
parton with which the tagged jet is associated. The jet is matched to a quark or
gluon within a ’R < 0.4. The ﬂavor—dependent scale factor is then determined using

the following equation,

TRFdataQDT, 77, flavor)

6.5
TRFMCQQT, 77, flavor) ( )

 

SFb—jet :

where the T RF are the b—tagging rates in data and Monte Carlo. The average fake
tag rate with the “Tight” operating point is 0.55%. The parameterized fake tag rate

can be seen in Figure 6.10.

6.2.3 Track Jet Finding (Taggability) Scale Factors

The efficiency to tag a b-quark is divided into two parts. The probability for a
particular tagger to tag a jet, and the probability for a calorimeter cone jet to qualify
as a track jet (“taggability”). The Monte Carlo is found to have a signiﬁcantly higher
efficiency than data, so a scale factor must be added to properly model the data.

In this analysis, the taggability (track jet-matching efficiency) is derived based
on a parameterization in 77, PT» and z vertex position developed by Yuji Enari for

the Higgs and W to dilepton, neutrino, and HM analysis [79]. The reconstructed

150

 

0 MC bmplos
+ System 8 b-mu
E 1‘1 Tagger: Tight Range: Alln I — seal. Factor
E’

I”

 

 

 

 

 

 

 

 

 

. MC b-sanplos

 

 

~I~ System eb-mu

 

 

  
 

 

 

 

 

>
g 1'_[ Tagger: Tight Range: pT > 15 1 _ Scale Factor
E : ‘
Ill _ .. .
0.3 -—"
0.6 —
1
0.4 _
[—
0.2 -
- I L ;l J l I l I I L 1 L4 i I I 1 I l l l J l i
0 0.5 1 1.5 2 2.5
I'll

(b)

Figure 6.9: The efﬁciency and scale factor necessary to apply to the Monte Carlo for
the “Tight” operating point using the NN b—tagger [25].

— cc
— lCR
Sample: COMB Tagger: Tight I —EC

 

 

 

 

0.012

Fake Rate

-L

lTT[ITTT||l[lll[lll[lll

0.008

0.006

0.004

  

0.002

 

 

I

 

I I l I I I I I
20 40 60 80 100 120
p, (GeV)

Figure 6.10: The fake tag rate for the “Tigllt” operating point using the NN b-tagger
[25].

cone jet is required to be within AR < 0.5 of a track jet. The track jet requires a
hit ill the SMT system or on all F —disk, so the taggability is highly dependent on
the (longitudinal) z—vertex position and pseudorapidity. The scale factor used ill this
analysis for W and Drell—Yan processes including heavy quarks, which contribute to

single muon ﬁnal states is shown ill Figure 6.11.

6.3 Common Analysis Reweighting

Several Monte Carlo reweighting functions were implemented because tlle integration
of the necessary changes in the Monte Carlo and detector modeling algorithms is
nontrivial. These reweighting functions are implemented ill a standard way across

the collaboration and include ﬁxes to the weak gauge boson spectrum, a reweighting

 

Taggability scale factor vs. 11 j

1 .65

 

 

 

‘

.0
lo
U'I

:.;IIllllll[lllllIlIl

9
o

  

 

Taggability Scale Factor

 

Figure 6.11: The taggability used in this analysis for W and Drell—Yan heavy—ﬂavor
processes that are binned as single muon plus jets ﬁnal states.

for luminosity and one for the z—vertex position.

6.3.1 Weak Gauge Boson pT Reweighting

The Monte Carlo method of using ALPGEN matched to PYTHIA is inconsistent with
data in the Z and W boson PT spectra at low values of boson PT [80]. Because of
this, a Z PT reweighting is performed to carefully match the behavior seen in the
measured Z PT distribution from the Z ——> 66 process [81].

The Z boson pT reweighting is carried over to the W boson PT by utilizing the
theoretical ratio of the W/ Z PT spectra [82, 26]. The scale factor used in the W PT

reweighting is shown in Figure 6.12.

153

 

 

 

| W p_r Re-weugﬁtmg]

 

 

........... ...........
2 ----------- ----- ++ ----- ~+~
15 f? -------------- ------------- . . ------------
1 """""" r """"""" :' """"""" *
05 ..................................................... - ..............

 

 

 

I I I I I
IlllIlllllllljlllllllllll

0 50 100 150 200 250
W pT I GeV

 

Figure 6.12: The generator-level reweighting function extracted from the cross-section
ratio of W boson to Z boson production [26].

154

6.3.2 Luminosity and z Vertex Reweighting

The Monte Carlo at D@ uses real zero—bias events to model the beam background.
Zero—bias events are collected to add the additional beam-interaction background to
the hard process modeled in the simulation. In early Run II, there were an average of
2.3 collisions in each beam crossing, and by the end of Run II, the average increased to
5.8. The zero-bias events, however, were taken over a different luminosity distribution
than that for the data. Therefore, both of these distributions are plotted, and the
Monte Carlo is reweighted to match the actual luminosity distribution of the data
[83].

Also, the z vertex position is assumed to be Gaussian in the Monte Carlo. The
data shows the vertex position is slightly non-Gaussian, so the Monte Carlo is again

reweighted to match the vertex distribution found in data [84].

6.4 Analysis-speciﬁc Weights

After applying all of the efficiencies and collaboration weights, the MIS group found
it necessary to add two more weighting distributions, a same-sign correction and Aqﬁ

correction.

6.4.1 Same Sign Reweighting

Electrons in this analysis have their energy 111easured in the calorimeter. However, the
energy deposition does not give the sign of the electron. The sign is determined by the
direction that the associated track bends in a magnetic ﬁeld. This is not a problem
for low momentum, well-deﬁned tracks, but for high-momentum or muddled tracks, it
may be difﬁcult to determine the direction of the bend. If the curve is assumed to be
in the wrong direction, the electron will end up with the wrong sign. This difﬁculty

is also present for hadronic taus (and to a lesser extent muons). The pion used in

155

the tau reconstruction also has its energy measurement in the calorimeter and sign
determined from the tracking system. Muons also get their sign from the tracking
system, but this is then conﬁrmed in the outer muon system to ensure that there is
agreement. This last condition makes Sign misidentiﬁcation signiﬁcantly lower in the
muon system.

The rate of sign misidentiﬁcation will be directly related to the resolution in
the tracking system. The problem is not that there is some sign misidentiﬁcation.
The difﬁculty has in the fact that the amount of sign misidentiﬁcation is not properly
modeled in the detector simulation. In order to properly model the data, we therefore
add another scale factor to the electron and tau Monte Carlo to approximate the
appropriate rate of sign mis—ID.

The incorporation of this scale factor is difﬁcult because a direct fit to the full data
sample would bias us in our search for new physics. We therefore restrict our sample
to dielectron events that have invariant masses in the Z boson peak [27]. For this
study, we are only looking at the electron calorimeter energies, and we do not use the
track PT or look at the sign of the electrons. In the mass range used in this study, 60
GeV < Mim, < 120 GeV, we see very little contribution from multijet processes. We
can therefore assume that the events in this region come exclusively from Drell-Yan
production. Figure 6.13 shows the invariant mass distributions of the same-sign and
opposite-sign data and Monte Carlo.

The Monte Carlo scale factors for same—sign and'opposite-sign events is determined
by looking at the data/ Monte Carlo ratios of the above distributions. The following

equation was used to determine the scale factor.

 

 

NSS,Data 2 5F55 Nss,MC
NSS,Data + NOS,Data Nss,MC + Nos,MC (G 6)
NSS,Data Nss,MC + Nos,MC '
SFSS = —————-— X

 

NSSMC NSS,Data + NOSData

156

 

 

 

 

8
g 0.22 5— —— 05 Data
2 0.2 E— -- OS MC
‘° : —- SS Data
g 0.18 E [ i __ SS MC
C 0.16 :—
- +
N‘ ;_ ...
£ 0.14 I l
> '— _r.
8 0.12 E [
N 0.1 E a: T
g 0.08 E— +
8 0.06 :— it A;
E 0.04;- i [3:
LL] 0.02 :— i'
0:1114bf-FWAEE'3 52Flllllllllr+ﬁtfm “‘IL111

130

)

o 60 70 30 90 100 110 120
ee mass (GeV/c

U'l

2

Figure 6.13: The dielectron invariant mass for oppositely charged data (black), oppo-
sitely charged MC (red), same sign data (blue), and same Sign MC (green). The plot
integrals are all normalized to 1.0. These plots are for electrons with 77 < 2.5 [27].

with a similar equation for S F0 5' The overall scale factor found for same-sign and
opposite-sign dielectron events was found to be SF S S = 2.049 and SFOS = 0.994.
The scale factor’s detector 77 dependence is shown in Figures 6.14(a), 6.14(b). While
some 77 dependence was found, the factors were driven by the large number of events
in the high-77 bins. A separate scale factor for the central bins was not particularly
well-motivated, given the few same-sign events with central electrons.

The pions are expected to follow the same sort of distribution because the pious
in this analysis are also based on single tracks. Therefore, the same scale factors
are applied to the e + T ﬁnal states. For 6 + u and T + [.L, the same rate of sign
misidentiﬁcation is assumed for scale factors of 1.52 for same-sign states and 0.997

for opposite—sign states. These assume the same probability of a charge flip of the

 

60

50

40

30

SS electron Scale Factor

20

10

 

 

 

. "let ll...w ..

 

ll[IIlI[llll[llll]lFIl[llTl[llll[I
m
I

 

 

 

 

 

1.05

[llll

 

OS electron Scale Factor

 

 

 

1 ‘ N wan—’d- 4.4.
] l + +++
0.95 [
L- +
0.9:—
0.85:—
” 1 . . L l . i l
0.8 _2 0 2
n

det
(b)

Figure 6.14: Same sign 6.14(a) and opposite sign 6.14(b) scale factors vs. Met The
black line shows the scale factors that are incorporated into the analysis.

electron or tau, but reduce the scale factor in half to account for a single electron or

tau.

6.4.2 Aqb Correction

The Monte Carlo also shows some signiﬁcant differences between the data and Monte
Carlo A05 distributions between objects in events. Large discrepancies were seen be-
tween leptons in dilepton ﬁnal states and between the lepton and E T in single lepton
+ jets ﬁnal states. We must make an assumption here: that these distributions are not
expected to reveal new physics, but rather indicate a modeling deﬁciency. With that
assumption, we apply a reweighting scheme to the A03 distributions. This reweight-
ing affected not only the A45 distributions themselves, but also other quantities that
depend on the spatial distribution of particles such as W boson PT-

For the p + jets state, we ﬁrst applied an ET cut of ‘20 GeV. The ET direction
for events with ET less than 20 GeV is not well known and should not be used in
calculating the A05 weights between p. and ET. The results of A4301, ET) is shown in
Figure 6.15(a). This correction is ﬁt to a parabola to Act < 2.5 where it is smoothed
into a linear ﬁt, and continuity is forced at the transition.

In the e + jets ﬁnal state, we also have an ET cut of 20 GeV, so the ﬁt can be
applied directly. The result of the e + jets ﬁt is shown in Figure 6.15(b). The ﬁt here
is not obviously different from ﬂat, so no additional scale factor is applied.

The dilepton ﬁnal states only need adjustments at A05 values that imply nearly
back-to—back leptons. This can be seen in Figures 6.16(a) and 6.16(b). In ,up, a
weight of 1.1 is used for 2.8 < A43 < 3.0 and 0.93 for Art > 3.0. For ee, the weight is
1.06 for 2.8 < Ad) < 3.0 and 0.93 for A0) > 3.0.

159

 

d
c
O

[IIIIIIIIIIII

.-‘
a

 

 

3"
l0

 

Scale Factor

9
a

 

 

I

 

 

1.5

IIIII]

 

Scale Factor

9
on
IIIIIIIIIT

-0.5

 

 

I
d
0']

l A l l l A I I A L i l J L l L A L A l l A A l I
0.5 1 1.5 2 2.5 3

 

A4) (e,MET)

(b)

Figure 6.15: Ratio of A05 distributions between data and Monte Carlo in inclusive
single lepton ﬁnal states.

160

 

‘
o
N

llllllf

‘
I

d
m

 

d
o
-‘

 

 

‘
'8

O
THIWIIHIHHIIIH Tll

 

Scale Factor

‘

 

 

 

 

 

”8
bI-
l-

1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 1 1 1 .1.

12.7‘ 1 2.8 29
A¢(u,u)

 

(a)

 

I

d

2..

0|
[T

d
L.
HrTIII

 

l
I

 

 

 

Scale Factor

 

0.“

 

 

 

0.9

 

 

 

bl]llTT]llll[Irl

Figure 6.16: Ratio of Art distributions between data and Monte Carlo in inclusive
dilepton ﬁnal states.

161

Chapter 7

MIS Analysis Packages

After all known Monte Carlo corrections are applied, the whole data set is divided into
seven non-overlapping ﬁnal states. The overall Monte Carlo normalization weights
are adjusted for input processes that contribute to each of the inclusive ﬁnal states.
The ﬁt process uses several histograms of basic object quantities (simple, single-object
kinematic variables) and ﬁts a single parameter for each of the input processes, so that
the X2 probability is minimized for the combined ﬁt. Once the ﬁt values are found,
the histograms are plotted again, taking into account the values obtained from the
general ﬁt. Several other quantities are also plotted before and after the application
of the ﬁt parameters to see how the general ﬁt affects more complex distributions.
Note: Most of this chapter is adapted from the internal DC analysis note, and from

the publicly available conference note [27, 85].

7 .1 Inclusive Final States

The seven states are inclusive in jets and additional objects. as speciﬁed in Table 7.1,
where each state is listed with the objects that deﬁne it and the associated object

cuts. The additional objects (X in the table) require cuts as seen in Table 7.2.

162

Table 7.1: Table of ﬁnal state object cuts: The seven inclusive ﬁnal states that are
being considered, along with their basic object cuts.

 

 

 

 

 

 

 

 

 

 

 

MIS Final State Object Min pT (GeV) Max |7}|
e 35 1.1
e + jets + X“ jet 20 2.5
ET 20 NA
ph 25 1.7
p + jets + X” jet 20 2.5
ET 20 NA
66 + X.C e 15 1.1
up + Xd ch 15 2.0
uh 15 2.0
m + X8
T 15 2.5
e 15 2.5
67' + Xf
T 15 2.5
ph 15 2.0
he + X9
e 15 2.5
a X 75 e, p, 7', 7
b X # 6, [1, T
cX¢mr
dx¢a1
e X 75 e
f X may be any object
9 X 75 7'

h Muons have an additional maximum pT cut of 300 GeV.

163

Table 7.2: Table of object cuts required for inclusion as additional objects (X) in one
of the seven ﬁnal states listed in Table 7.1.

 

 

 

 

 

 

Object Min pT (GeV) Max [7}]
e 15 2.5
[10' 15 2.0
T 15 2.5
jet 20 2.5
'7 15 1.1

 

 

 

a Muons have an additional maximum pT cut of 300 GeV.

7.1.1 it + jets

The ,u + jets ﬁnal state is dominated by the production and decay of W bosons. This
state is deﬁned by exactly one muon with PT > 25 GeV and with n < 1.7. 111 order
to reduce the amount of multijet background, at least one jet with ET > 20 GeV is
also required, as well as ET > 20 GeV. The muon must satisfy the NIedz’um Nseg3
Conditions for the local muon system, the tight track requirements, and the N PTz’ ght
isolation requirements as discussed in Chapter 4. The ﬁnal state is inclusive in jets
and photons, but any other additional objects would push the event into a different

ﬁnal state.

7.1.2 6 + jets

The electron + jets ﬁnal state parallels the muon + jets ﬁnal state. Jets are more
easily IniSidentiﬁed as electrons, so the cuts on this ﬁnal state are slightly tighter to
minimize the contribution from the multijet ﬁnal states. The electron PT cut is at 35

GeV With 77 < 1.1 and ET > 20 GeV. The likelihood cut, Ce > 0.95, is tighter than

the default top tight deﬁnition.

164

7.1.3 up

The dimuon ﬁnal state requires at least two muons with the same quality deﬁnitions as
the muon from the p + jets ﬁnal state. The muon I’T cut is dropped to PT > 15 GeV
because of the smaller contribution from multijet background. If this state includes
jets, jet PT must be > 20 GeV. It is inclusive in jets and muons, but an additional 6

or T would place the event in the pe or in ﬁnal states.

7.1.4 66

The dielectron ﬁnal states require each electron to have 6 PT > 20 GeV and likelihood
> 0.85. The electrons are also conﬁned to the central calorimeter and use the same
jet cuts as the other ﬁnal states. The end calorimeters were excluded for this analysis
because of inconsistencies between electrons measured in the central calorimeter and
electrons measured in the end caps when attempting to ﬁt histograms in the dielectron

ﬁnal state normalization ﬁt.

7.1.5 ,uT

The [17' states contain at least one muon and one tau. It is inclusive in all objects
except electrons, which would move the state into the he ﬁnal state. The requirements
are a PT > 15 GeV and T PT > 15 GeV. The T NNT > 0.9, and the T of type 2 has

an additional electron separation cut of N Ne > 0.2.

7.1.6 eT

The electron + tau objects are inclusive in all objects. The electron and tau PT cuts
are PT > 15 GeV. The electron likelihood is at > 0.95, for this state to differentiate
it from a large multijet background (since many apparent T‘s are misidentiﬁed jets).

The hadronic NN cuts are the same as uT, but the electron separation NN is set to

 

0.8 to remove the dielectron events.

7.1.7 ,ue

The ac ﬁnal state requires pT cuts of 15 GeV for the muon and the electron. It is
inclusive except for T’s which would fall into the eT ﬁnal state. The electrons can be
identiﬁed normally as top tight with likelihood > 0.85 or as misidentiﬁed T’s with the

electron separation NN < 0.2.

7 .2 The MIS Fit

The ﬁts for normalization use several histograms of basic object quantities to deter-
mine a scale factor, altering the overall normalization of each input process, so that
the X2 probability is minimized for the combined ﬁt. In order to avoid ﬁtting to the
high—pT tails that will eventually be searched for new physics, we check each object
in the event to see if the object PT is outside the bulk of the distribution. Basic
histograms like ET, pp, 77, cos(cf>0bj — ngT) for the leptons and jets are used to ﬁt
while we reserve more complex variables to check the ﬁt quality. These more complex
variables include the mass or transverse mass of two or more objects, jet multiplici-
ties, Aqﬁ between two objects, inclusive jet PT, W and Z pT, etc. If an event contains
any object in the tails, then none of the objects in the event will be used in the ﬁt.
A full list of the processes which are normalized based on these inclusive ﬁts,
along with the ﬁnal states that are used to determine their values, are shown in Table
7.3. A slightly simpliﬁed example using the electron + jets + X ﬁnal state (X is not
an e, ,u or T) would work as follows. We know this state to be dominated by the
W processes, but it also has a signiﬁcant contribution from multijet and Drell-Yan.
We use a constant normalization factor for the Drell—Yan process, determined by a

separate ﬁt to the 66 + X ﬁnal state (X 54$ ,u or T). This parameter will be held ﬁxed

166

in the e + jets ﬁt, along with other rare processes which have contributions which
would be too small to ﬁt accurately. Then, the W and multijet contributions will
ﬁnd the best agreement to ﬁt the given histograms and two scale factors will be used
to give an overall weight to the W —> 8V and multijet —* e + jets contributions.
Once the ﬁt values are found, the histograms are plotted again taking into account
the values obtained from this ﬁt. The total background contribution for a particular

ﬁnal state would be,
#ka
B = 2 35,8,- (7.1)

2
where the scale factors (S 17,-) for each background process (Bi) are determined only
once in the ﬁnal state in which their contribution is the most important, and then
held ﬁxed in any other ﬁnal state to which they contribute.

Our simpliﬁed modelng implementation does not directly account for certain
normalization factors due to such things as trigger efﬁciencies and some K-factors
(corrections for Monte Carlo leading order or leading logarithm cross sections to the
observed cross section for a process). In order to avoid gross errors in normalization,
we perform a ﬁt, described below, for each of these states to obtain the scale factors
which reproduce the distributions of the selected data with the background from
standard model Monte Carlo and multijet background determined from data. These
seven states were selected so that each is dominated by a speciﬁc standard model
process. Since the seven states are non-overlapping, they can be combined as an
input to the VISTA algorithm without fear of double-counting.

The ﬁt itself minimizes the negative logarithm of the likelihood function for each
set of parameters and converts this value to a X2- The ﬁt is performed with the Minuit
ﬁtter [86]. It minimizes the X2 of the ﬁtting histograms by looking at the differences,
bin-by-bin, between the data and the standard model background. The ﬂoating
parameters are modiﬁed until a minimum is found. Only two or three parameters for

each of the ﬁnal states are modiﬁed. The plots are not varied explicitly by shape.

167

Table 7.3: Table of input processes for which the normalization is
determined from inclusive ﬁnal state ﬁts along with the ﬁnal states
that are used in determining its value.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Input Process Final States
W ——> 611 + light partons e + jets
e multijet background (e + jets) e + jets
W —> 1w + light partons p + jets
a multijet background (a + jets) u + jets
Z /7 ——+ 68 + light partons 66
Z / 7 —> up. + light partons Mt
Heavy ﬂavor/ light ﬂavor content 6 + jets, ,u + jets, ee, up
Z / 7: >0 light partons/0 light partons 66, [All
Z / 7 —> TT + light partons (6T) 6T
T multijet background (6T) 6T
Z/'y —-» TT + light partons (,uT) 11.7”, T types (1,2) and 3
T multijet background (pT, T types 1,2) in, T types 1,2
T multijet background (pT, T type 3) ,uT, T type 3
Z /7 —> TT + light partons (,ue) ‘ he
6 multijet background (he) he

 

168

The ﬁnal results are the best ﬁt parameters corresponding to the normalization of
the ﬂoating input processes. For the single lepton states and the T ﬁnal states, the
multijet background is a signiﬁcant contribution. It is assumed that the contribution
from the other Monte Carlo samples to the multijet background is small. The input
process scale factors for the Monte Carlo should already include the contributions
of the process to the multijet background from data. The main effect of process
contributions to the multijet background would be that the multijet state would
resemble the process Monte Carlo, making it difﬁcult for the ﬁt to reliably ﬁnd the
multijet contribution.

The ﬁts are then checked for qualitative agreement. The main purpose of the
MIS normalization process is to make sure that the fundamental processes are well-
modeled. A Kolmogorov-Smirnov (KS) probability is determined for each of the
histograms to provide a quantitative check for comparison. Additionally, the overall
scale factors are checked to compare to those of other analyses. If all normalization
factors were properly included in the Monte Carlo, the scale factors would all ﬁt to
1.0. No speciﬁc cut is required for the KS probability because the main quantitative
analysis will be done at the later VISTA and SLEUTH stages. Two histograms that are
included in the overall ﬁt and two checking histograms that are not part of the ﬁt are
shown for each of the seven ﬁnal states in Figures 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8,
7.9, 7.10, 7.11, 7.12, 7.13, 7.14.

After the ﬁrst stage of ﬁtting is ﬁnished, several constraints are imposed upon
the ﬁtted condition. The ratio of light-parton to no—parton content that is ﬁt for
the dimuon and dielectron states is constrained to the same value. W »* expect this
ratio to be independent of ﬂavor, so a weighted average of the two states is taken and
then ﬁxed for a ﬁnal ﬁt. The same is done for the heavy-ﬂavor states. The ratio of
heavy—ﬂavor to light-parton content is ﬁxed for the dilepton and single lepton ﬁnal

states. An example equation showing the averaging process is shown in Equation 7.2.

169

Number of Entries

Number of Entries

 

 

   
  
   
 

 

 

E ' Data
40° :— - Diboson
200 :— tl

: - Multijets
°°° F n W( uv) + hf
800 E - Z0111)
600 E_ L: W(uv) + lp
400 E
200 :—

5

 

 

 

90 100
l1 FT (68V)

 

 

2o 25 30 35 4o 45 50 55 60
ET (GeV)

(1))

Figure 7.1: a + jets ﬁnal state ﬁtting histograms: ,u pT, ET.

170

 

  
 
  
  

 

+ Data

- Diboson
- '

- tltllultijets
W(l1V)+ hf
- 20111)
I—._- W(LW)+ lp

 
 
  
   
  

Number of Entries

2000

 

 

llllll'lTIIIIIIIIIII]Illl]llll[lll|]llll
l

 

 

 

     

140 160 180 200
Transverse Mass (GeV)

 

l lllll

  
  
  
  
  

0

l l llllll]

Numer of Entries

—1
our
I lllllll]

_I
l l llllll]

l l llllll]

 

 

_l
llllll]

4 5 6 7 8
Number of Jets (Light + Heavy)
(b)

Figure 7.2: a + jets ﬁnal state checking histograms: transverse mass (14. ET), number
of jets.

171

.1

Number of Entries

Number of Entries

 

   
 
  
     

 

' Data
200 - Diboson
tt
°°° - Multijets
E] W (ev) + hf

80° 2 (ee) + lp
600 - Z (ee)

, :l W(e v)
400
200

 

40 50 60 7o 80 90 100
e pT(GeV)

 

llll[llll[|lll[llll[llll]ll

  

 

 

400
350
300
-1 0 5 0 0 5 1
TI
0))

Figure 7.3: e + jets ﬁnal state ﬁtting histograms: 6 PT) e n.

172

 

 

 
   

 

 

 

W
m :
'5 : + Data
LEI 3000 _— - Diboson
“5 E t’f
g 2500 E - Multijets
g t_ +——~ w (e v) + hf
22°00: ameeHIp

1500 E—

1000 :—

500:—

o—

 

 

60 80 100 120 140 160 180 200
Transverse Mass (GeV)

(3)

 

Number of Entries

100

50

 

llll[lll|[lTliT['7|ll[llll]

 

 

20 40 60 80 100 120 140 160 180 200
Invariant Mass (leading jet, otherjet) (Gev)

(b)

Figure 7.4: e + jets ﬁnal state checking histograms: transverse mass (6, ET). invariant
mass of leading jet with other jets in the event.

173

 

   
   

      
   

 

 

 

 

1000 _ ° Data
_5 — - Diboson
g - t;
“6 800_— -Z(uu)+hf
2 : E 2( 1110+ '0

5 60° f - 201p)
2 l—

400 ;
200 F
20 30 40 50 6O 70 80 90 100
Leading u pT (GeV)
(0)

.3

E

“5

E

.Q

E

3

z

lllllllll[llll[rlll[

 

 

 

0 -2 -1.5 -1 05 0 0.5 1 1.5 2
Second [in

(b)

Figure 7.5: all ﬁnal state ﬁtting histograms: leading ,u pT, second a n.

174

 

+ Data
- Diboson

   

2500

   
  

a Z0111) + hf
- Zlulu) + In
- Z( w)

§

rlj]Ij—[T[Illllllll]llllll

Number of Entries

 

 

§

500

 

 

30 4o 50 60 70 80 90 100 110 120 130
Invariant Mass (u. u) (GeV)

 

t
2000

    
    

Number of Entries
3' 33
O O
O O

_I
O
O
O

 

 

   

        

30 35 40 45

Z Boson
pr

50

(b)

Figure 7.6: pp, ﬁnal state checking histograms: invariant mass (,u, ,u). Z boson PT-

175

 

   
 
  
  

 

 

 

 

 

 

no, ; ° Data
.3; : - Diboson
:5; 1000 _— - ti
o _
g 800; D Z (ee) + hf
E 3 D Z (ee) + In
6‘”:— - Z (ee)
400 :—
200 :—
° 30 4o 50 60 70 80
Leading e pT (GeV)
(3)
300
§
E, 250
“é .
3 200
E
:5
z
150
100
50

 

 

60 65 70

90 25 3o 35 4o 45 50 55
Leading Jet pT (GeV)

0))

Figure 7.7: cc ﬁnal state ﬁtting histograms: leading 6 pp, leading jet PT-

176

 

 

     
   
    

@3000 “*T Data *
3‘3 - Diboson

3 2500 - I

8 , t

E2000 —— Z (ee) + hf

 

:5 Z (ee) + lp
- Z (ee)

 

 

 

 

lllllllllllIII[llII[llll[llll[|lI

 

 

50 60 7o 80 90 100 110 120
Invariant Mass (e,e) (GeV)

 

O\
O
O
I [ I I I I TI II
If“: .
+'

s

FII]IIII]IIII[IIII[I.I

Number of Entries
.3.

U)
0
O

N
O
O

100

 

 

  

-5 -4 -3 -2 -1 0 1 2 3 4 5
Z Boson TI

Figure 7.8: cc ﬁnal state checking histograms: invariant mass (e,e), Z boson 77.
Several distributions, such as the Z 7) show some several bin discrepancies. When the
trials-corrected probabilities are determined for these discrepancies, the signiﬁcance
is shown to be at the level of one sigma. We work to generally improve the standard
model background modeling. but the focus is 011 statistically signiﬁcant discrepancies.

177

 

    
  
  
  

 

. ° Data
{$250 -D Diboson
a“: a ti
g 200 D Z(T’E)
'3 I:l Z(rr) + hf
2150 - 20m)
- W( (nv) & Multijets

 
 
 

 

 

100

50

40

50 55
u ween

 

_I
O
O

\D
O

00
O

70

60

Number of Entries

50

40

30

20

 

 

15 20 25 30 35 40 45
T P (GeV)
T
(b)

Figure 7.9: pT ﬁnal state ﬁtting histograms: a PT, T PT-

178

 

   
   

 

 

 

 

9,1500 7—0— tau type
do - —+—
'5 i - Diboson
,5 1400 _ -
H5 _ tt
51200 5 - Z(1."L')
E E ”—5- Z(tt) + hf
2 1000 _ - 20111)
3 - W( uv) + Multijets

800 _—

600 :-

400 :—

200 :—

00 0.5 1 15 2 25 3 35 4
1: Type
(a)

 

Number of Entries
‘6’
O

 

 

Tllllllllllll[llIl]lIII[IlIl[IllITTIIT

 

60 7o 80 9o
Invariant Mass( HT) (GeV)

0))

Figure 7.10: pT ﬁnal state checking histograms: T type, invariant mass (11, T). Low
values of invariant mass show single—bin discrepancies in the three ﬁnal states that
are dominated by the Drell—Yan TT process. These are related to PT threshold issues
with the taus, and when accounting for trials are not statistically signiﬁcant.

179

Number of Entries

Number of Entries

   

 

   
  
     
 

° Data
- Diboson

tt
- zo r)
- 2(n)+ hf
Z (ee)

- W(e v) & Multijets

 

 

50 55
e pT (GeV)

 

lll[lll[lll[lll[lII[l

l
1

 

(b)

  
   

50

 

60
ET(GeV)

Figure 7.11: eT ﬁnal state ﬁtting histograms: e PT, ET.

180

 

\O
O
O

  
  
 
 
  

 

+ Data
- Diboson
11

800

Number of Entries
\1
O
O

600
Z(tt)
500
e Z( 151') + hf

- Z(ee)

30° - W(e v) & Multijets

 

 

  

 

200

100

 

0 10 20 30 40 50 60 7o 80
Transverse Mass (e, ET ) (GeV)

((1)

 

300

N
U1
0

Number of Entries
N
O
O

150

 

llll TIIIWIIIIITIIIlI—l’l
I” I I I I

 

20 40 60

80 _ 100 120
lnvanant Mass (e,t) (GeV)

0))

Figure 7.12: eT ﬁnal state checking histograms: transverse mass (e,ET), invariant
mass (e,T).

181

 

Number of Entries

20

 

Ill[|ll[|Il[Ill|lIl[l

 

 

 

N
U!
0

Number of Entries
8
O

_0
U1
0

100

 

 

0 70
e PT(GeV)

(b)

Figure 7.13: he ﬁnal state ﬁtting histograms: ,u 17, e PT-

182

 

  
 
  
    

 

 

 

_g 200
5 + Data
C 180 _ _ .
g tt
g 140 E Z(rt)
z 120 E Z(tt)+hf

100 - Z( 1111)

- W( 11v) & Multijets

 

 

0 10 20 30 4o 50 60 7o 80 90 100
Transverse Mass (e, 111- ) (GeV)

((1)

 

Number of Entries

 

5‘
O
ll[l!l[lll[llI[Ill]lll[lll[1ll[lll[lll

 

 

10 20 3o 40 50 6O 70 80 90 100
Invariant Mass (e, u) (GeV)

Figure 7.14: [1.6 ﬁnal state checking histograms: transverse mass (e,ET). invariant
mass (e,e).

183

A ﬁnal ﬁt with these conditions imposed can be seen for the dimuon state in Figure

 

 

 

  

 

 

7.15.
. t.‘ t‘
SF : SFee #even s(ee) + ‘9pr #even 501a) (7‘2)
#events(ee + up) #events(ee + MM)
W
.0.)
L _
E1000 — ° Data
u.1 _
$ I—
O 1—
5 800 :- . All Drell-Yan
_Q _
g _
Z 600 _—
400 .—
200
0 20 30 40 50 6O 30 90 100
Leading u pT (GeV)

Figure 7.15: One ﬁnal ﬁt is performed after ﬁxing the ratios of light-parton to no—
parton and heavy—ﬂavor to light—parton. This ﬁgure shows the dimuon ﬁnal state
after these ratios are averaged with the dielectron and then ﬁxed.

A ﬁnal check is made to see the effect of the inclusion of the rare ﬁnal states,
ti and diboson. The tf contribution can be checked in histograms such as the 4—jet
HT as shown in Figure 7.16. The diboson contribution can be seen in many of the

histograms in the pe ﬁnal state.

184

 

   
  
     

 

8
”E 25 ' Data
E. - Diboson
“6 - t;
a 20 - Multijets
2 u wen/1+ hf
g - Z(uu)

15 l:| W(uV)

 

llll[|I|l[|lll[llll[llll[

 

 

 

       

250 300 350 400 450 500

HT (4 jets) (GeV)

       

50 100 150 200

Figure 7.16: The scalar sum of the transverse energy of jets in a + jets events with
at least 4 jets. This ﬁnal state shows the necessity of ti Monte Carlo to properly
describe the data.

7 .3 Text File Production

Once all of the normalization weights have been determined and the input processes
checked for agreement, the input ﬁles for the experiment—independent VISTA and
SLEUTH algorithms are created. These algorithms take text ﬁle inputs which only
contain the most basic information about the objects. The overall event weight,
run/ event number and vertex position are kept along the object PT: 17 and 0'). Using
this simple information, the algorithms quantify the overall agreement.

The text ﬁles are created in the same way that the histograms were created for
the ﬁt. The same computer code is used in their production, with the addition of one

input weight that comes from the inclusive state normalization ﬁts.

185

An example of one line of a In text ﬁle can be seen in Figure 7.17.

mutau12_ztt 1.113 0.000239137 ppbar 1960 409.05713.9419
mu- 61.563 0.135986 139.865 tau+ 162.489 -1.20636 317.824 j 0
21.319 4.64867 131.604 uncl 0 41.058 0 -37.7612 ;

Figure 7.17: The ﬁgm'e shows one line of a [17‘ text ﬁle used as input into the VISTA
algorithm. Only the run and event numbers, the vertex position, weight, and the
object PT, 17, (z) information are kept for each event. In the ﬁgure, each object is

shown in a different color.

186

 

Chapter 8

VISTA and SLEUTH

Once all of the event selection cuts and correction factors are determined in the
MIS analysis packages, VISTA and SLEUTH consolidate this information and use it to
quantify the agreement between the data and the standard model background. The
SLEUTH algorithm was developed for DO Run I [87, 88, 89] and later modiﬁed at the
H1 experiment [90]. The VISTA algorithm was developed at CDF [91, 28]. All of the

algorithms are discussed in detail in [92].

8.1 VISTA

VISTA is an experiment-independent program developed by the CDF experiment to
compare event counts and 1-D histogram shapes between data and the standard model
expectation, while explicitly taking into account the trials factor associated with the
number of places checked. While the original algorithm provided the capability to
make reﬁnements in object identiﬁcation, event selection, and correction factors, the
DO version of VISTA removes this functionality and only provides the quantitative
comparison between the samples.

VISTA checks overall event counts and Kolmogorov-Smirnov probabilities, so it is

most sensitive to differences in the central parts (not tails) of distributions. This

187

 

would provide sensitivity to new physics with large cross-sections or modeling issues
affecting variables across ﬁnal states. The SLEU TH algorithm is most sensitive to the

possibility of new physics in the tails of distributions.

8.1.1 Exclusive Final States

The seven ﬁnal states used to create the input text ﬁles described in the last chapter
are fully deﬁned in the input to VISTA. The objects deﬁned in each event are then
used to place each of the events into a particular ﬁnal state. For example, if the event
contained a muon and two jets, this would go into a separate ﬁnal state from an event.
with a muon and three jets. The object content completely deﬁnes the exclusive ﬁnal
states used for event counts and histogram checking in VISTA. The full list of ﬁnal
states with the event counts for each ﬁnal state and trials corrected discrepancies

measured in units of equivalent Gaussian standard deviation are shown in Table 8.1.

Table 8.1: The 180 VISTA ﬁnal states.

 

 

 

 

 

 

 

 

 

 

 

VISTA Final State Number of Data Events Expected Background 0
4j/1i ET TT 1 1.5513 0
4j #5 ET 99 83.7532 0
4j pi #5 ET 2 1751.2 0
4j11=t 5T 2 1551.2 0
3j pi FF 1 0.8511 0
3j pi ET TT 3 10.652 0
3j pi ET 750 68458.5 0
3j [Li 7 ET 6 3.3518 0
3j11i ,fF ET 15 21951.6 0
3 j pi ,fF 7 1 0.251 0

 

 

 

 

 

 

Continued 011 Next Page. . .

188

 

Table 8.1 (cont’d)

 

VISTA Final State

Number of Data Events

Expected Background

q

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 j 5i #4: 25 24.9517 0
2 pi ET 11 5.6516 0
2 ﬁt 70? ET 1 1251.1 0
2 pi 1 1.4512 0
2j ,ui Ti 2 5.3519 0
2j 5i 7? 11 10.4519 0
2j pi ET H: 55 46.353 0
2j 5i ET Ti 14 19.8528 0
2 j at ET 6213 53625292 +9.-
2j11i 7 ET 7? 1 0.8511 0
2j 5i 7 ET 34 1852.4 0
2j 5* 76?: ET 118 136.6525 0
2j pi 112': 7 ET 2 0.7:t1.1 0
2j pi ﬁ 7 1 1.3511 0
2 j ui ,ﬁ 216 22553.2 0
2 ei 2 j 7 ET 1 051 0
2 ei 2 j 2 0.9511 0
2 ei ET 3 3.4514 0
2 ei 7 2 1.6514 0
2 ei j 5 751.5 0
2 at eZF ET 1 1251.1 0
2 3i 82F '77 ET 1 Oil 0
2 at 28 24.6522 0

 

 

 

 

Continued on Next Page. . .

189

 

 

Table 8.1 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VISTA Final State Number of Data Events Expected Background 0
2 b 2j 5i ET 11 17.552 0
2 b #5 ET 26 29352.1 0
2 b #5 7 ET 1 0.251 0
2 bj #5 ET 15 15.3513 0
2 b :5t 2 j ET 6 14.4514 0
2 b e3E ET 18 20.5517 0
2 b 8d: #ZF ET 5 3i1 0
2 b ei j ET 11 13.2514 0
pi vi 194 138.8561 +2
#5 74: 828 84355101 0
#5 ET Ti 273 285.7579 0
#5 ET 5? 1239 120885124 0
#5 7 ’TZF 39 29.7525 0
pi 7 ET Ti 6 5.152 0
[1i 7 ET TlF 35 23.7525 0
,ui a; 2 7 1 0.2i1.1 0
#5 ,ﬁ Ti 18 29252.7 0
pi ,fF ET #3 19 3052.8 0
#5 53‘ ET 3559 319535214 +4.7
pi 1F 7 ET 29 13.4518 +0.6
,ui ”:1: 'y 178 111.6:t3.5 +4.2
#5 ”IF 22801 23048651368 0
j 2 5i ET 1 0.8512 0

 

 

Continued on Next Page. . .

190

 

Table 8.1 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VISTA Final State Number of Data Events Expected Background 0
j 2 pi 1 0.151 0
j ,ui H: 83 90.7539 0
j pi Ti 33 29.1532 0
j pi ET Ti 77 97254.9 0
j ,ui ET 73F 225 260.4561 0
j ,ui ET 41154 41816752225 0
j pi 7 ET 7?: 7 5.3516 0
j pi 7 ET Ti 2 1651.6 0
j [ft 7 ET 197 101.8545 +6.6
j pi p4: Ti 2 7.4:l:1.9 0
j #5 71? ET Ti 2 8.1519 0
j 7135 54: ET 871 758.6557 +2
j pi Iﬂ: 7 ET 3 3.8i1.3 0
j [ft ,1? 7 29 1251.5 +1.6
j #5 ,E 2070 21245136 0
ei 4j ET 69 69.4523 0
at 3j ET 5? 2 2.8514 0
ei 3j ET 457 439.755 0
ei 3j ﬂ ET 1 1.7511 0
ei 2j TZF 8 8.7519 0
at 2j Ti 3 3.9518 0
ei 2 j ET Ti 5 6.352 0
e=t 2j ET 7? 21 19.5523 0

 

Continued on Next Page. . .

191

 

 

Table 8.1 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VISTA Final State Number of Data Events Expected Background 0
ei 2j ET 3627 3479.85185 0
e=t 2j 7 TZF 1 0.5511 0
ei 2j 7 ET 7? 1 1.2513 0
ei 2j 53F ET 7 11651.4 0
ei 2j #5 ET 2 0.4511 0
ei 2j ,EF 1 1.8512 0
ei Ti 167 1216556 +1.1
ei T? 612 651.1593 0
ei ET 711: 556 532.558 0
5i ET Ti 111 96.455 0
ei 7 Ti 5 1551.5 0
ei 7 T? 38 38.353 0
ei 7 ET 7? 8 10.9519 0
e:h 7 ET Ti 1 1.4515 0
ed: ”:1: 72F 1 0.7:l:1.2 0
ei pi Ti 1 0.4513 0
5i ,fF ET 7'4: 1 151.2 0
ei 71? ET 204 208.6544 0
ei #5 ET 19 8.5516 0
ed: #3}: 7 ET 5 5.5:l:1.6 0
ei ,ui 7 ET 3 0.7512 0
ei 1F 7 11 11.652 0
ei pi 7 1 0.3512 0

 

 

Continued on Next Page. . .

192

 

 

T able. 8.1 (cont’d)

 

VISTA Final State

Number of Data Events

Expected Background

q

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e=t pi ﬂ ET 5 5.3514 0
5i ,ui 1F 8 9.1516 0
ei p? 343 350.3563 0
e:t #5 16 6.2516 0
ei j T? 65 71353.6 0
ei j Ti 30 24.253 0
ei jET Ti 39 26653.1 0
ei jET T? 112 116.8542 0
ei j ET 24482 24817551283 0
ei j7 r? 2 551.4 0
ei j 7 ET 7? 4 3.5514 0
ei jﬁ ET 64 54.8523 0
ei jpi ET 6 2.7513 0
ei j IF 7 ET 2 1751.2 0
ei j a; 7 1 0.3i1.1 0
at jpi ﬂ 3 0.9511 0
ei j ,ﬁ 14 16.3518 0
ei j #5 1 0.7512 0
ei e? 4j ET 1 0.6511 0
ei e? 4 j 1 2.4512 0
ei e=F 3j ET 4 4.3513 0
6i 82F 3j 7 1 O.5:l:1.1 O
ei (27+: 3 j 25 751.6 0

 

 

 

 

Continued on Next Page. ..

193

 

Table 8.1 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VISTA Final State Number of Data Events Expected Background 0
ei e? 2j ET 23 2151.7 0
«9t e4: 27' 7 4 5.3513 0
ei e‘T' 2 j 242 247.4535 0
ei .2? ET 180 16955.1 0
e:t 63F 7 ET 6 63:18 0
ei E 7 254 270.8556 0
5i e4: ,ui ET 1 2.2512 0
ei eZF #5 1 0.6511 0
ei e$ jET 84 69252.4 0
6i 6; j 7 ET 3 2i1.3 0
e=t eT j7 35 38952.1 0
ei eiF j 1854 188085103 0
ei e4: 16152 16083151051 0
b 3] pi ET 31 37552.1 0
b 3 J pi IE ET 0 0.551 0
b 27155 ET 76 83.2537 0
b 2 J 5i 5*" ET 2 3.2512 0
b 2j #5 IF 1 2.7512 0
b pi ET 620 70215106 0
b H 7 ET 3 4252.1 0
b #5 5* ET 12 18351.5 0
b pi a; 7 1 0.3:l:1.1 0
b #5 ,ﬁ 35 3651.8 0

 

 

 

 

Continued on Next Page. . .

194

 

 

Table 8.1 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VISTA Final State Number of Data Events Expected Background 0
bj #5 ET 266 306.3573 0
bj pi 7 ET 3 1251.1 0
bj E 54: ET 7 13.1513 0
b j pi IEF 8 12.8514 0
b ei 3j ET 31 3251.6 0
b e=t 2 j ET TT 0 0.751 0
b ei 2 j ET 67 56.852 0
b ei 2113 ET 6 1.751 0
b ei H: 0 1.751 0
b ei Ti 0 0.551 0
b ei ET 73F 2 3151.4 0
b ei ET Ti 0 0.651 0
b ei ET 414 4232566 0
b ei ﬂ ET 5 3551.1 0
b ei ﬂ 1 0.351 0
b ei 7'73: 0 0.651 0
b ei j ET 7? 6 2.9515 0
b ei jET 187 187.5537 0
b ei j 13 ET 1 6.7511 0
b at e? 2 j 0 2.751 0
b ei e=F ET 5 3.6512 0
b ei e3: 7 0 0.751 0
b e:t eT j ET 0 551 0

 

 

 

Continued on Next Page. . .

 

Table 8.1 (cont’d)

 

VISTA Final State Number of Data Events Expected Background 0

 

b 5i 6; j 6 16.5514 0

 

b 6i ezF 50 36.8-51.7 0

 

 

 

 

 

 

8.1.2 Final State Populations

VISTA checks the agreement in ﬁnal state populations by determining the Poisson
probability for the background estimation to ﬂuctuate to what is seen in data. The
calculation of the probability of data ﬂuctuating from a perfectly known background
is shown in Equation 8.1, with pd the probability of getting d or more background
events, d the number of data events, and b the weighted number of background events.
This probability then needs to take into account the fact that many ﬁnal states were
searched by reducing the signiﬁcance of any individual ﬂuctuation. The probability
formula is directly derived from the binomial probability. If the probability of a
ﬂuctuation is cc, and there are N 3 distributions that could have a ﬂuctuated to that.
probability, then the probability that any of the distributions would have ﬂuctuated

to :1: follows the binomial probability formula, shown in Eqs. 8.2 and 8.3.

00

hi" _
pd = 2: 56 b (8.1)
i=d '
_ N3! 16 Ns—k .
13“? 0111t0f N3) - m(19f5)(1 — Pfs) (82)

where k would be the number of distributions more signiﬁcant than p f3. We are
interested in a situation where any of the distributions is more signiﬁcant than p f3,

so the probability would equal 1) = 1 — P(O out 0 f NS) 1,

 

1For states that show a data excess, 1) f S is given for the probability of data to ﬂuctuate up to
the background. In cases where there is a data deﬁcit, the Poisson probability is calculated in the

196

 

p =1— (1— pfS)NS (8.3)

The reduced probability can then be converted into units of standard deviation by

solving for a in Equation 8.4.

00 1 _12
[a Vic 76116:]? (84)
with the value in a positive for data events exceeding standard model background
and negative for the opposite situation.

As an example of determining the agreement consider a ﬁnal state with 167 data
events and 121.6 :1: 5.6 events predicted from the standard model background. The
statistical error in the background is determined by the number of events in back-
ground sample. Since the nurnber of events is determined from a variety of sources,
the individual contributions from each of the bins must be combined to determine
expected statistical errors.

The probability for a precisely known background of 121.6 to ﬂuctuate up to 167
or more is 1.572 10‘5. Since the background is not known precisely, the Poisson
distribution is convolved with a Gaussian with a width of the expected background
uncertainty, 5.6 events to give a probability of 8.12 1041. This probability is then
adjusted to take into account the number of trials (in this case 180) to arrive at final
probability of 0.136, which corresponds to 1.1 standard deviations: Since this value
is below the 30 threshold, it is not reported as signiﬁcantly discrepant.

The ﬁnal state populations with the a values after trials factor for each of the

ﬁnal states can be found in Table 8.1.

 

opposite direction. It is the probability of seeing d or less data events given the background I), so
the sum in Equation 8.1 would run from i = O to d, rather than from d to 00.

197

8.1 .3 Histogram Shapes

VISTA also considers l-D histograms to quantify data/ background agreement. The
probability of the data being a statistical ﬂuctuation from the expected background
distribution uses a probability determined from the Kolmogorov—Smirnov statistic.
The Kolmogorov—Smirnov test is based on the empirical cumulative probability dis-
tributions of the data and background and ﬁnds the largest deviation in the distribu-
tion. After determination of the initial probability, it follows the same basic method
as the event counts discussed above, reducing signiﬁcance by the trials factor and
converting into units of a.

The histograms plotted for each ﬁnal state include the pp, 77, and 45 for each object
in the event, ET, spatial differences between each pair of objects in the event, Aqb,
AR, invariant mass among all object combinations, transverse mass among all object
combinations with ET, and a few other specialized variables.

An example of a full set of histogram shape plots for one ﬁnal state with only two

objects is shown in Figures 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7,88, 8.9, and 8.10.

8.2 SLEUTH

SLEUTH is a check of the high—pT tails of ﬁnal states. This will ﬁnd any new physics

that are in accord with the basic SLEUTH assumptions.

0 The new physics ﬁnal states have objects with high-pT relative to the standard

model and instrumental backgrounds.
o The new physics occurs in a small subset of final states.

0 The new physics occurs as excesses of data over standard model background.

198

Run II Preliminary (1 fb'1)

 

 

 

 

 

 

 

   
 

 

 

9+7
0 DO Run Ila Data
— Other
w _ Z —) up : 10.2%
.2. 100 — Multijets:15%
q, t _ Z—>11:,type3:17.6%
l.l>.l 5 _ Z—>tt,types1,2:44.3%
h
° +
L-
d3
.0
E
3
2
° 20 + 40 60
ll PT (GeV)
(50
+ - . . -1

ll 15 Run II Preliminary (1 fb )

7 0 D0 Run Ila Data

” — Other
:1: 5_ Z—>uu:10.2%
E- 601’_ Multijets:15%
0 5 _ Z—)rt,type3:17.6%
11>] r — Z —> TI, types 1,2 : 44.3%
“6 405 +
L-
.. l
.0
g 20F
Z

0 -2 .1 2 1 2
ll 71

Figure 8.1: All of the histograms plotted for the VISTA state with one muon and one
tau. The 14 PT and ,u 7) distributions.

199

u t Run II Preliminary (1 fb'1)

 

 

   
 

 

 

 

 

   
 

30— 0 DO Run Ila Data
- _ Other
in -— Z—>uu=10-2%
.... r — Multijets:15%
E, 60 = Z—>tt,type3. 17.6%
0
ll>.| Z—>tt,types1,2: 44.3/6
“5
._ 40— + + l
w .—
.n
E
z 20
° -2 o 2
11+ (1) (radians)
(a)
+ - I . -
H T Run ll Preliminary (1 fb 1)
‘ 0 130 Run Ila Data
_ — Other
«I: 7— Z—>uu=10-2%
E 60’— Multijets : 15%
ﬂ _ — Z—)tr,type3:17.6%
“>1 ‘ Z —> 11', types 1,2 : 44.3%
"6 40— +
h k
.. i
n
S 20
Z

 

 

11+ det n
(b)

Figure 8.2: All of the histograms plotted for the VISTA state with one muon and one
tau. The p o and a detector 7) distributions.

200

 

 

 

 

 

 

 

+ - -
H T Run II Preliminary (1 fb 1)
0 00 Run Ila Data
100 — Other
m — Z —> up : 10.2%
‘E — Multijets:15%
a — Z—>tt,type3:17.6%
“>1 __ z ——> 11, types 1,2 : 44.3%
h
o
I-
a:
.n
E
:1
2
0
20 30 40 50
1 p1. (GeV)
('4)
+ - . . -1
ll T Run ll Preliminary (1 fb )
_ 0 DO Run Ila Data
80T_ Other
m _ _ Z—>uu:10.2%
'E — — Multijets : 15%
q, ;— Z—atr,type3:17.6%
”>1 60 — Z —> It, types 1,2 : 44.3%
.._ -
. 7 +
‘5 40—
.n -
g i
z 20f

 

 

   

-2 _o 2
I n
(b)

Figure 8.3: All of the histograms plotted for the VISTA state with one muon and one
tau. The 7 PT and the 7' 77 distributions.

201

 

 

 

 

 

 

 

 

+- _ _ -
ll 13 Run II Prellmlnary (1 fb 1)
80* 0 D0 Run lla Data
_ — Other
,0 —— 2599:10-2%
E — — Multijets : 15%
d3 60__ Z—>It,type3:17.6%
“>1 : — Z —> “CT, types 1,2 : 44.3%
n- _
o .—
I—
o _
.E _
3
z 5
° .2 0 2
T 4) (radians)
(a)
Run II Preliminary (1 fb'1)
: Do Run Ila Data
— ' Other
‘0 80— ﬂ “'7 Z—>uu:10.2%
‘E ' — Multijets:15%
d) 60;— Z—>tr,type3:17.6%
If, __— z—m, types1,2 : 44.3%
k _
° — +1
3 40—
.D _
g i
z 20f

 

  

 

 

0 2
1:" det n

(b)

Figure 8.4: All of the histograms plotted for the VISTA state with one muon and one
tau. The 7' 45 and the ’7' detector 7) distributions.

202

b 1? Run II Preliminary (1 fb'1)

 

 

   
 

 

 

 

 

 

‘ 0 D0 Run Ila Data
‘ _ Other
60—— Z —> uuz10.2%
3 — — Multijets:15%
g _ — Z—>rt,type3:17.6%
> — Z —> 11, types 1,2 : 44.3%
I“
u. 40— +
o + +
I-
0
‘s’
3 20
Z
0 1o 15
p1. (GeV)
(9)
+ " . . .1
H T Run II Prellmlnary (1 fb )
150_ 0 00 Run lla Data
_ Other
a, 5 5. "‘ Z —>p.u:10.2%
‘E ,_ _ Multijets : 15%
g 100_- 2 an, type 3: 17.6%
In - — Z—>t1:,types1,2:44.3%
“5 ‘ i
h
d}
.D
E
3
Z

 

 

 

30
min(l p1.) (GeV)

(b)

Figure 8.5: All of the histograms plotted for the VISTA state with one muon and one
tau. The ET and minimum PT of the ,u and 7.

203

 

 

 

      

 

 

 
 

 

 

 

+ - .
9 1 Run II Preliminary (1 fb 1)
DO Run Ila Data
Other
0, BOTTTHHT Z ——>uu : 10.2%
‘E - _ Multijets:15%
a: — _ Z—>1t,type3:17.6%
IE 60_—— Z—>tt,types1,2:44.3%
"5 : +
b
g 404 +
= - i
Z 20:“
Z t
0 1 2
max(ln)
(a)
+ ' . . .1
H» T Run II Prellmlnary (1 fb )
300* 0 D0 Run Ila Data
" Other
3 : TWF’T—"D Z—>up. : 10.2%
g 1 — Multijets : 15%
> 200—— Z —>1:t, type 3: 17.6%
E - F—H z—m, types 1,2 : 44.3%
3
o
.n
E 100
3
Z

 

 

 

° 2 + 2.5 3
A¢(ll ,t') (radians)
(b)

Figure 8.6: All of the histograms plotted for the VISTA state with one muon and one
tau. The maximum 77 of the ,u and 1'.

204

Run II Preliminary (1 fb'1)
5 D0 Run Ila Data
: “‘- ' ' Other
200f ”—— . Z —> up : 10.2%
5 — Multijets : 15%
t— z —>tr, type 3 : 17.6%
150*— 2 an, types 1,2 : 44.3%

 

 

 

100

Number of Events

50

 

 

 

11177le1111er

0 2.5 3 + 3.5 4
AM“ rt")
('4)

Run II Preliminary (1 fb'1)

D0 Run Ila Data

Other

WW" Z —> up : 10.2%
- Z —) rt, type 3: 17.6%
— Z —> 11:, types 1,2 : 44.3%

 

 

 

Number of Events

 

 

 

10 20 30
clusteredObjectsRecoil p1. (GeV)

6))

Figure 8.7: All of the histograms plotted for the VISTA state with one muon and one
tau. The A’R between the II and 7. The clustered object recoil is the vector sum of
the ET and unclustered energy.

205

 

 

 

 

 

 

 

 

 

9+1" Run II Preliminary (1 fb'1)
. DO Run Ila Data
150 _ Other
{0 , Z —> up. : 10.2%
E - - Multijets : 15%
g 7- Z—>tr,type3:17.6%
lu _ — Z —> ‘61:, types 1,2 : 44.3%
... 100‘—
O
h
a)
D
§ 50
Z
0
0 10 _ 20 _ 30
clusteredObjectsRecoil p1. L (GeV)
(21)
Run II Preliminary (1 fb'1)
D0 Run Ila Data
«- Other

m "" ’ Z—auu:10.2%
E L — Multijets:15%
g 200 — Z—>'c~c,type3:17.6%
I.l.l Z —-) 11, types 1 ,2 44. 3%
“5
h
3
E 100 '
3
Z

 

 

 

0 10 20
clusteredObjectsRecoil pT T (GeV)

6))

Figure 8.8: All of the histograms plotted for the VISTA state with one muon and
one tau. A thrust axis is deﬁned as the vector sum of the two objects in the event.
The clustered object recoil is then determined for the transverse and longitudinal
components with respect to the thrust axis.

206

1.1"? Run II Preliminary (1 fb'1)

 

 

 

 

 

 

 

7 0 D0 Run lla Data
‘ — Other
«I 607— Z—>H11510-2%
u 5 — Multijets : 15%
E, _ — Z—>It,type3:17.6%
“>1 _ — Z —> 1:13, types 1,2 : 44.3%
h
o
L.
a:
.3
E
3
z
0
-1 -O.5 0 0.5 1
cos(9*) (radians)
(a)
+ - . . -1
H T Run II Prellmlnary (1 fb )
0 DO Run Ila Data
_ — Other
,0 — Z-éuui10-2%'
E 1005- Multijets:15%
O ”_ Z—art,type3:17.6%
">4 ~_— 2 —> 171:, types 1,2 : 44.3%
i.-
o
h
a:
.3
E
3
Z

 

 

 

° 50 100
Movie (GeV)

6))

Figure 8.9: All of the histograms plotted for the VISTA state with one muon and one
tau. The plot cos(0*) shows the cosine of the angle between the positively—charged
lepton and the reconstructed Z boson in the frame of the Z boson. Also, the invariant
mass of the u and ‘T.

207

Number of Events

100

50

Run II Preliminary (1 fb'1)

 

 

 

  

DO Run Ila Data

Other

Z —> up : 10.2%

Multijets : 15%

Z —> IT, type 3: 17.6%

Z —> 121, types 1,2 : 44.3%

 

 

100 150
2 pT (GeV)

(81)

Figure 8.10: All of the histograms plotted for the VISTA state with one muon and one
tau. The scalar sum of the transverse momenta of all of the objects in the event plus

the missing transverse energy.

8.2.1

SLEUTH Final States

SLEUTH reduces the number of ﬁnal states searched to lower the overall trials factor

that needs to be applied. Four basic principles are applied in the ﬁnal state reduction.

0 Allow global charge conjugation, which means that an event with each of the

object charges ﬂipped, would go into the same ﬁnal state. For example, an

event that contains a positively—charged muon and negatively—charged electron

would go into the same ﬁnal state as a negatively-charged muon and positively-

charged electron. Or, two positively charged electrons would go into the same

ﬁnal state as two negatively—charged electrons.

0 Apply 1“ and 2nd generational equivalence, which means that events where

each electron is switched to a muon and each muon to an electron would belong

208

to the same ﬁnal state. This would mean an event with two oppositely-charged
electrons would go into the same ﬁnal state as two oppositely-charged muons
but would be in a different ﬁnal state than one muon and one electron with

opposite charges.

0 Jets in the hard scatter are produced in pairs. This point assumes that if an
event has an odd number of jets, the unpaired jet is a gluon from initial or ﬁnal
state radiation. The physics involving this extra gluon would not be directly
tied to the new physics process, so it is not used to deﬁne a separate ﬁnal state.
Therefore, an event with a muon and two jets would go into the same ﬁnal state

as a muon with three jets.

o b—quarks are produced in pairs. This assumes that if there are an odd number
of jets that have been b—tagged in an event, then there is probably another jet
that also originated from a Irquark. This would put an event with one b-tagged

jet and one light jet in the same ﬁnal state as an event with two b-tagged jets.

8.2.2 SLEUTH Algorithm

The SLEUTH algorithm starts with the ﬁnal states described above. For each ﬁnal

state, one variable is calculated: 2 PT,

# objs

Zpr = Z lﬁ't'l + [ET] (3.5)

2'
which is determined from the scalar addition of all of the object transverse momenta
in the event plus the missing transverse energy. At each data 2 pp value, SLEUTH
counts the number of data and expected background events with a 219T equal to
or greater than the EFT of the data event. The probability associated with this
comparison is determined in the same way as for the raw event counts in VISTA.

That is, a minimum 217T cut. is chosen which maximizes the excess of data over

209

 

background for each ﬁnal state. The most signiﬁcant difference in those event counts
is chosen for each ﬁnal state. Pseudoexperiments are performed to ﬁnd the overall
probability that the data seen could result from only statistical ﬂuctuations in the
in the standard model background for that ﬁnal state. The number of events in the
fake data sample is determined from a Poisson ﬂuctuation of the total number of
background events, and then the fake data points are distributed by drawing random
numbers between zero and one, sorting these numbers, and then associating them
with a percentage of backgrormd content that falls before each particular fake data
point. With this new fake data sample, the SLEUTH algorithm is run again. The
number of pseudoexperiments needed to see something as interesting as what is seen
in the data is calculated for each ﬁnal state. Finally, the lowest probability ﬁnal state
is chosen, and the signiﬁcance of that state is reduced by the number of ﬁnal states
checked by the same algorithms used for other multiple comparisons.

An example plot for opposite-sign muons or electrons with two or three jets is

shown in Figure 8.11.

8.2.3 tf Sensitivity Test

We now perform a test of the sensitivity of the SLEUTH search, by testing whether tf
would have been discovered in this data sample. For the tf test, the full background
sample except for the tf Monte Carlo was pushed through the analysis. The main
concern would be whether other ﬁnal states would be able to compensate for the
missing Monte Carlo, and SLEUTH would not be sensitive to tf in the data.

From Figure 8.13, one can clearly see the difference between including and remov-
ing the Monte Carlo. With a threshold of 0.001, the SLEUTH test with the tf Monte
Carlo included has a statistical ﬂuctuation probability of 0.69, but the Monte Carlo
without tf has a probability of only < 1.6 10‘7.

The test was repeated using only a randomly selected 10% of the data (100 pb— 1).

210

_ Do Run II Preliminary (1 lb")
2] P = 0.62

 

   
 
 

   
   
    

0 D0 Run Ila data (
_Z—)ee+lp .
E:lZ—>uu+lp 1
_ Z——>ee+cE
-Z—)uu+c6 ‘
_Oth r

SM= 550
d= 580

  
 
 
  
   

Number of Events N
A A —L A
o N a a:
O O O O

00
O
l l | I I l | l | l l l l | I l l l l I l l | I l l I I l

60

40
20

 

 

5o 10 150 zoo 250 300 350 400 450 500
> GeV
109 Zpr( )

0

 

Figure 8.11: An example SLEUTH plot for the opposite—sign light dilepton (dimuon or
dielectron) ﬁnal state with two or three additional jets (not b—tagged). In this ﬁgure,
the EFT cut that maximizes the discrepancy is at 109 GeV. which encompasses
almost the entire distribution. This region is enlarged in the plot in the upper right,
showing 580 data events compared 550 predicted from the standard model backgrormd
providing a probability of a statistical ﬂuctuation of 0.62.

211

_ D0 Runll Preliminary (1 10‘)

 

Wbb_u 5:069
23 O QORunIIadata 8

5 _tHIJ) 514:.”
> 16 mats) 7 M
I" — W—Iev + lb 6

‘5 EjW-iIII/Hb 5

a 14 _Other 4

E 3

a 12 2

z

10

 

     

700 800
211T (Gel)

600
532

Figure 8.12: Sensitivity test for tf. 111 this ﬁgure the tf Monte Carlo is included, and
there are only minor differences between data and standard model background.

“1

100 200 300 400 500

 

212

W b5 11 D0 Run II Prel'minary(1 1b“)

 

   

 

 

 

 

 

 

 

 

   

P<1.68-07

8 :ommmm
5 — -W-)pI/+bb SM=“
> 161' iW-iell+bb d:32
Ill 5 QCD background
.5 “ E: W-illll + cc
5 14: - Other
E I
:I 12:"
z _

101- 0 ll _

81- 0

— (lo 0 II

5.—

4T

2.—

 
 

 

 

  

"o

1002003004T0500500700800
398 25le

Figure 8.13: Sensitivity test for tf. The ﬁgure shows the results of pushing through
the entire analysis procedure without the tf Monte Carlo. In this case, SLEUTH easily
passes the criterion of interest at 0.001 for this common tf ﬁnal state.

213

This test was also shown to be successful, although starting from a low statistics
ﬂuctuation of probability 2 0.12 and a ﬁxed contribution from heavy-ﬂavor (too few

statistics for ﬁtting). The 10% sensitivity test is shown in Figure 8.15.

214

 

-.. DR "1 '
Wbbll ° “" (OOPblP=o.12

 

 

 

 

 

9 — 0 D0 Run Ila data

5 6' - mu_thar:46°/o

> : eLlIbar:37%

E _ eLbckg :4.3%

O 7 [:1 mu_bckg :3.9%

3 : - Other

,9 _

E _

3 _

z 4: .

- 0 500 550 600 650

3; II
2; II
1: ti

    

 

 

 

 

  

"o

100 200 300 400 500 600 700 800 900
L—> 29, (GeV)

465

Figure 8.14: Sensitivity test for tf in 100 pb'l. This ﬁgure includes the tf Monte
Carlo, and the differences between data and standard model background are again
minor.

215

WbBij D0 Run II (100 pb")P

 

 

 

 

 

 

 

 

ll 0 D0 Run Ila data
5, 6- - eLbckg:25°/o
> : - mu_bckg:22%
E - - mu_bb:13%
O 7 n eLbb:11°/o
3 5: - Other
3 _
E _
3 _
z 4_—
3; ti
2; II
1; II 1) II I) ll ‘13 II
E
5
F— I LI | L11 1 l I Lu 1 Id

 

 

 

 

 

 

 

oII100200300400500600700800900
L——> ZPT(GeV)

338

Figure 8.15: Sensitivity test for It? in 100 pl)_1. This ﬁgure shows the results of
running the full analysis procedure using 10% of the Run IIa dataset when the If
Monte Carlo is removed. Even with this smaller sample, the SLEUTH algorithm still
crosses the threshold.

216

Chapter 9

Results

The process of comparing the data to the expected standard model background in
this analysis was done in three steps. First, the data were separated into seven
ﬁnal states, checked for qualitative agreement, and ﬁt for normalization factors using
the MIS analysis packages. All data cuts and correction factors were applied at
this level. The second step involved dividing the seven ﬁnal states into 180 states
deﬁned by the object content using VISTA. VISTA checked the overall event counts in
each ﬁnal state and plotted over 9000 1-D histograms. Each of the histograms was
checked for agreement using Kolmogorov~Smirnov probabilities. VISTA then reported
the agreement of all ﬁnal states and histograms, putting special focus on those with
statistically signiﬁcant differences that disagree at a level of 30, as discussed in Section
8.1.2. The ﬁnal step was to combine some of the VISTA ﬁnal states and check the
tails of ZPT distributions using SLEUTH. SLEUTH checked for discrepancies in the
tails that correspond to probabilities < 0.001 that the standard model background
distributions would ﬂuctuate to a distribution as discrepant as what is seen in data.
The value of 0.001 is equivalent to approximately 30 after incorporation of the trials

factor.

217

 

9.1 Model Independent Search Normalization Fits

The purpose of the MIS analysis packages is to ensure that the primary standard
model processes used for the background estimate are well-modeled. Seven ﬁnal
states were considered, each with one dominant standard model process, and the
overall normalization for these processes was determined from a ﬁt.

All of the processes considered in each of the seven ﬁnal states with the number
of histograms used in the ﬁts, the number of histograms used to check agreement,
the overall normalization scale factors with their uncertainties, the number of events,

and the X2 of the ﬁt are shown in Table 9.1.

9.2 VISTA

In VISTA, the separation of the input dataset into ﬁnal states (completely deﬁned by
the object content of the event) yields a total of 180 unique ﬁnal states. For these 180
ﬁnal states, the probability of the data distribution resulting from a statistical ﬂuctu-
ation of the background sample is determined from p = 1 — (1 — p f s)180 z 180 p f3(for
p f3 small), where p f s is the probability that the number of events predicted in the
standard model background would ﬂuctuate up to or down to what is observed in

data (before applying the correction for the 180 trials). This is then converted into
2

units of standard deviation using L30 ﬁe—gfdx 2 p. This procedure is described
in more detail in Section 8.1.2. The ﬁnal state probabilities converted into standard
deviations before adding the trials factor correction are shown in Figure 9.1. This
distribution shows most ﬁnal states near the center, with some excess at the tails. Of
the 180 distributions, four show signiﬁcant discrepancy. These are the ﬁnal states [t
+ 2 jets + ET with a converted probability of 9.30 after trials correction, p + 7 + 1

jet + ET with 6.60, 17+ p— + ET with a discrepancy of 4.40 and 71,4611“ + 7 at 4.10.

218

 

Table 9.1: The results of the MIS inclusive ﬁts for all inclusive ﬁnal states. Ignoring
k-factors and trigger efficiencies, all Monte Carlo samples should ﬁt to 1.0 for 1.0
fb”1 of data. The dominant standard model process is listed ﬁrst for each ﬁnal state.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MIS , . Uncer- # # Fit #
State Input Sample Weight tainty Fit Check xz/dof Events
Hists Hists
W —> 8V 0.921 0.004
e + jets QCD e fakes 0.266 0.040 19 22 1297/1022 25k
hf/lp ratio“ 1.94 0.121
W —> by 0.712 0.004
u + jets QCD p, fakes 0.684 0.055 19 21 1861/977 39k
hf/lp ratio“ 1.94 0.043
Z —-> 66 + 01p 1.00 0.007
68 lp/01p ratio“ 1.11 0.016 22 18 1243/8533 18k
hf/lp ratio“ 1.94 0.099
Z _7 up + 01p 0.782 0.007
W lp/01p ratio“ 1.11 0.011 22 22 1321/ 987 30k
hf/lp ratio“ 1.94 0.070
Z —> T7' 1.02 0.035
67' W/QCD T fakes 0.185 0.030 13 8 537/497 1.4k
hf/lp ratio“ 1.94 ﬁxed
Z —> 77' 0.686 0.025
pr W/QCD 'r fakes 0.206 0.049 13 8 593/497 1.4k
hf/lp ratio“ 1.94 ﬁxed
Z —> 77' 1.31 0.016
pe W/QCD 7' fakes 0.02 0.285 13 6 436/467 0.74k
hf/lp ratio“ 1.94 ﬁxed

 

a Heavy-ﬂavor quark (c, b) to light parton (g, s, u, d) radiative jet ratio. It is determined by
allowing the heavy-ﬂavor fraction in each of the ﬁnal states to ﬂoat. An average was taken for
the Drell-Yan and the W ﬁnal states. These numbers were found to be very similar, so a ﬁnal
averaging was done incorporating all of the ﬁnal states. This averaged ratio was then ﬁxed in
all of the ﬁnal states, and the other parameters were fmmd from a second ﬁt.

b The zero light parton to greater than zero light parton ratio. This is the ratio of Drell-Yan
production with additional radiative jets to Drell-Yan production without these additional
partons and is determined for the dielectron and dimuon states. Since this factor is expected
to be ﬂavor-independent, an average of the values was determined, and then ﬁxed for each of
the ﬁnal dilepton ﬁts.

219

 

The M + 2 jets + E T ﬁnal state discrepancy shows an excess of events with a
muon at n > 1.0 as seen in Figure 9.2(a). The excess points to an oversimpliﬁcation
in our approach to trigger efﬁciencies. The proportion of events selected by single
muon vs. muon plus jets triggers changes signiﬁcantly as we increase jet multiplicity.
These triggers introduce n-dependent efﬁciencies which are not properly incorporated
into our simple ﬁts. The dimuon with missing transverse energy ﬁnal state shows an
excess of data compared to the standard model Monte Carlo prediction. A study of the
track curvature of data and MC muons, and of the associated resolution, has shown
that an additional smearing should be applied in the Monte Carlo to appropriately
simulate very high PT muons. The prime signature of these muons is an excess of ET
because of the lack of compensation for the mismeasured, unbalanced track. The A05
distribution of the muon and ET can be seen in Figure 9.2(b), where the excess tends
to be with events where the missing transverse energy is pointing opposite to a muon.
The other two states are directly related to an oversimpliﬁed modeling of the photon
misidentiﬁcation rate. This can be seen in Figures 9.3(a) and 9.3(b). There are three
reasons for the discrepancy in the photon states. First, the Monte Carlo generators
are known to poorly reproduce these processes. Second, the rate of jets misidentiﬁed
as photons are not modeled well in the detector simulation. Finally, the Z —-> TT
contribution with an electron misidentiﬁed as a photon overestimates the tracking
efficiency, so that the Monte Carlo will have fewer of these events than the data. All
of these may contribute to these plots. Hard jets are more easily misidentiﬁed as
photons, which may explain part of the reason the data spectrum is harder, but there
could be many contributing factors.

The 180 ﬁnal states contribute a total of 9335 individual l-D histograms in various
variables, and a shape comparison is performed for each. The trials factor adjusted
probability is determined with p z: 1— (1 — p3 (11093351 where p3 hp is the KS probability

to observe an individual shape discrepancy (before applying the correction for 9335

220

 

U'Flﬁ'a lat.llnu

 

 

Entries: 18d

A
O

Visla Final States
M w
a a

10

 

 

Figure 9.1: VISTA ﬁnal state 0 distribution for Run Ila sample before accounting for
the trials factors. The curve represents a Gaussian distribution centered at zero to
guide the eye. The event count distributions are expected to obey Poisson statistics,
which is why the distribution is narrower than the curve.

trials). As with the probability for a ﬁnal state discrepancy, the probability for a shape
discrepancy is converted into units of standard deviation and the discrepancies are
shown. For the histogram shapes, any deviation >30 is considered discrepant. The
distribution of standard deviations before trials correction is shown in Figure 9.4.
This distribution approm'mates a slightly shifted Gaussian of the expected width,
but several distributions appear in the tails. The shift to the right (toward poor
agreement) is expected because we introduce scale factors only for the most important
discrepancies (minor systematic discrepancies are not individually treated, and these
contribute preferentially towards bad agreement).

A total of 23 distributions are found to be discrepant at the 30 level after trials

221

 

u + 2jets + ET ' DO Run Ila Data
400_. - Other

 

 

 

 

  

 

 

        

 

 

 

  

_ n r imin _ - Multijets
‘9 _Ru llPel ary(1fb1)-Z—)HH
g 300j -W—>HV+CE
u>.l : - W —> PW
"E 2005
O _
.n _
g _
2 100j
E
0 -1 +0 1
l1 Tldet
(n)
“I’ll-ET
Run ll Preliminary (1 fb'1)
: 0 DO Run Ila Data
.3 300? Other ,1,
0; Z Z —-> uu + b5
3: GOOF Z —) up + CE
3 t - Z —> Mil + 'P
g 400:— P- 2 —) up
g 200;

 

 

A¢(u+,ET) (radians)
(b)

Figure 9.2: Figure 9.2(a) shows the excess of data in [.L + 2 jets + E T to be focused on
events with muons that have n values > 1.0. Figure 9.2(b) shows the Act distribution
between a muon and the ET, with the E T pointing opposite to a muon.

222

H Y iet
Run II Preliminary (1 fb

j ° D0 Run Ila Data

. Other _
2°f+ W —9 uv + bb
1o:

.1)

 

 

 
 
  
 

-W—>uv+cE
-Z+uu
EW—auv

 

 

  

 

Number of Events

 

 

0 so 100
Y IoT (GeV)

(21)
+ ' 0 DO Run Ila Data
_ _Other
_ ., Z—>uu+b5
_ -Z—>uu+cE
t -Z—>uu+lp
20~ -Z-—>uu

Run II Preliminary (1 fb'1)

 

 

 

   

 

10

Number of Events

 

 

40
v p, (GeV)
(1))

Figure 9.3: Two ﬁgures showing the PT distributions of the photon.

223

DO Run II Prellmlnary (1 fb")

 

Entrles: 9335

 

400
200

 

 

L gr— overflow

 

llllLllllll

-8 -6 -4 -2 0 2 4 6 8 10
O’

O[I'llllllllllllllilIIIIIIITIII1111T]

JP

Figure 9.4: VISTA histogram a distribution for 100% sample before accounting for
the trials factor. Each curve is a Gaussian distribution. The curve that is shifted to
lower values is centered at zero while the second curve is centered at the mean. The
difference between the two curves approximates the average systematic Imcertainty
found in the plots.

correction. The majority of these are related to spatial distributions involving jets,
low ET excesses in dilepton distributions and multijet—background-dominated 7' dis-
tributions. All of these types of discrepancies are related to known oversimplifications
in our modeling assumptions and would not be expected to severely affect the SLEUTH
search for new physics in the high—pT tails. Eight histogram shape discrepancies are
shown in Figures 9.5( a) through 9.8(b). The full list of discrepant histograms is shown
in Table 9.2.

2‘24

1

 

 

u + 2 jets + ET
. DO Run Ila Data

 

 

      

 

    

 

 

 

 

   

- Other
- gllilﬂffs RunllPreliminary(1 fb-1 )
- W (uv) + CE
3 300 - W(uv) +
E . —“~* ++++
LIJ I
"5 200 j
3 -
D Z
E 100 j
Z _
0 i 2 +_ 3 4
(A)
e + 2 jets + ET
I:
Run II Preliminary (1 fb") ° DO Run Ila Data
r - Other
'2 200L - Diboson
g a - Multijets
l” - W —) ev + cE
*
O
3
D 100
E
3
Z

 

 

A . 2.
n01.12)
(b)

Figure 9.5: The plot 9.5(a) shows the AR difference between the [t and trailing pT
jet. Figure 9.5(b) shows the An distribution between the two jets in the c + 2 jets +
ET ﬁnal state.

225

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

n +1 jet+ EL DO Run Ila Data
- - Other
4000Z_Run II Preliminary (1 fb'1) ,. Multijets
.3 : - W —> uv + c6
g : - Z ——> uu
o H
g 2000?
E _
3 e
2 10005
0 100 200
MOVJ) (GeV)
(3)
1500 e + 1 jet + ET ° DO Run Ila Data
Run II Preliminary (1 fb'1) - Other
L - W —> ev + b5
.2 ’ - Multijets
0 L - W —> ev + CE
1000
“>1 r - W —> ev
u- a
o
E
E 500
3
2
° .2 o 2
j «1) (radians)

(b)

Figure 9.6: Figure 9.6(a) shows the invariant mass of the u and the jet in a 11. 7+ jet
+ ET ﬁnal state. Finally, 9.6(b) shows the (1) distribution for the jet in the e + jet +-
ET ﬁnal state. Each of these is tied to difﬁculties in spatial jet modeling.

226

 

+ - 0 DO Run Ila Data
_ Other
~ Run II Preliminary (1 fb'1) . z —-> ee + b5
i Z —> ee + c‘c‘
§“ ¢ - Z ——> ee + lp
‘1’ 1.1L

 

a
O
O
O
I

   
  

 

 

 

Number of Events

 

 

° 10
ET (GeV)

(8)

 

' D0 Run lla Data
- Other
—Run II Preliminary (1 fb'1) - Z —) up, + b3
— - Z —> up + cc
1000— ,9 -Z->W+'P
%

u+lf

 

 

 

500

Number of Events

 

 

0o 5 1o 15
ET (GeV)
(b)

Figure 9.7: Plots 9.7(a) and 9.7(b) show the E T distribution in the opposite sign
dielectron and dimuon ﬁnal states. Both of these point to ET modeling issues in
dilepton states.

227

 

 

  
 
  

 

 

 

 

 

 

 

    
  
 
  

 

 

 

 

MEET 0 DO Run Ila Data
3oo—Run II Preliminary (1 fb'1) - Other
m — - Z —> up + b5
g T - Z —a W + 65
">1 200— - Z —> nu + Ip
“5 — - Z —> PM
E h i
E 100 §++
3 R
2
° -2 o 2
ET (1) (radians)
(a)
ll..- ”5+ ET
80‘ . _ _

~ Run II Prellmlnary (1 fb 1)
3 _ ,3 DO Run Ila Data
5 60‘ Other
“>1 I Z—>ltu.rtype1.2
~05 - - Z —> its, I type 3
.5 4°: - Multijets, r type 1,2
.3 e Multijets, 1: type 3

F
3
z 20

 

 

80

° 20 40 6O
min(l pT) (GeV)

(1))

Figure 9.8: Figure 9.8(a) shows the (1) distribution of the ET in the dimuon state with
large ET, which also points to dilepton ET modeling issues. Finally. Figure 9.8(b)
shows the minimum PT of the p and the 7' for the same-sign pr + E T ﬁnal state
which shows the diﬂieulty in modeling the jet to T misidentiﬁed background using
loosened data cuts.

228

Table 9.2: The full list of VISTA shape discrepant histograms listed by VISTA ﬁnal
state.

 

 

 

 

 

 

 

 

 

 

VISTA FINAL STATE Histogram a
MUM?) 7-0
MUM’i J2) 46'
ARUIJ‘Z) 4-2
n + 2 jets + ET M(W,j2) 4.0
ET a 3.8
13770142) 3-5
MOI J2) 3'5
#i/ITET ET <15 3-1
pi‘ri p pT 3.5
,ui'riET Min(€ pT) 3.2
Hill; ET 3.4
M(W,j) 8.4
9' PT 8-2
M(,u,j) 7.2
W PT 5.7

II + J'Ct + ET
MT(l»ET) 5-3
ET <15 5-3
Muir) 4-8
ZPT 3-3
e + 2 jets + ET An(j,j) 4.9
e + jet. + ET j <25 3.3
eiei: ET 5.6
219T 4-0

 

 

 

 

 

229

 

9.3 SLEUTH

All VISTA ﬁnal states are input to SLEUTH, and the 180 ﬁnal states are folded into 44
ﬁnal states after applying global charge conjugation, rebinning in number of jets and
using light lepton universality as described in Section 8.2.1. The several VISTA ﬁnal
states that Show broad numerical excesses are found again with the SLEUTH algorithm
as would be expected. One additional distribution crosses the discovery threshold of
F < 0.001, where 75 is the probability after all trials factors, described in detail in [91]
and brieﬂy in Appendix C. The ﬁnal state that crosses the discovery threshold is pi
+ e:F + ET as can be seen in. Figure 9.9. Currently the evidence suggests that
the muon tracking resolution is responsible for this discrepancy from the standard
model. A large fraction of the events in the tail of the SLEUTH distribution have a
muon with a very large PT and large missing energy. With the present modeling of
muon resolution, straight track events are underrepresented in the standard model
background estimation. This state has 46 data events in the tail of this distribution
compared to only 17 predicted by the Monte Carlo. A table of the top ﬁve SLEUTH
ﬁnal states that contain only leptons and jets is shown in Table 9.3. The known VISTA
numerical excesses have been removed since this information is already known. All of
these states are subject to the muon resolution issues discussed above. An example of
another distribution expected to Show the same issue is a single lepton with ET. This
is seen in Figure 9.10. A plot including all of the ﬁnal state probabilities converted
to units of a can be seen in Figure 9.11. In this plot, e and it states are combined
according to light lepton universality. However, as we have seen, the systematic errors
of the e and [1. states differ. This distribution would be expected to improve if only
electrons are searched because the electron energies are measured in the calorimeter.
The corresponding electron-only plot is shown ineFigure 9.12.

In the SLEUTH runs performed at CDF using a slightly different analysis strategy,

the four most interesting observed ﬁnal states were at ei, pi 8i + 2 jets + ET,

230

 

 

 

 
    

I

+ ,- DO Runll Prelimina 1fb'

H Ii, M 1) P<2.9o-06
.2 0 D0 Run Ha data

5 120 - Z—r TT SM=”
> - Il'll' 4:45
E - II'/QCD background

0 )3 Z —> up

g IDOL - Other

E

3

2

 
  

ITIITT‘IWITI

 

 

I
Figure 9.9: SLEUTH plot for opposite sign [6 + ET. The ’P value at the top right
corner of the plot is the probability before ﬁnal state trials factor.

231

00 Run II Preliminary (1 lb")

   
 
 

 

   
   
  

  
 
  

 

 

    
   

  

 

W P = 0.074
3 o 00 Run IIa data 6
535000 - W-allv SM=5.4
> - W—)ev 5 0:13
II.I Z—lllll _ 4
“630000 WWW 3
it 3
£25000:
2 :
20000}
15000}
10000:—
5000:—
0.
0 300 1000
035 2 pT (GeV)

Figure 9.10: SLEUTH plot for 6 + ET. The ’P value at the top right. corner of the
plot is the probability before ﬁnal state trials factor. This plot shows the same issue
in the tails of the distribution as Figure 9.9.

232

Table 9.3: The top ﬁve SLEUTH states with only leptons and jets. The value ’P
represents the probability that the standard model background for an individual ﬁnal
state would have a fluctuation at any cut that would be more signiﬁcant than what
is seen in data. The variable ”)5 calculates the probability that one would observe a
ﬁnal state with ’P less than or equal to the one observed in data based on a statistical
ﬂuctuation.

 

Final State 7’ 15a

 

€+€’_ + ET 2.9 36 0.00018

 

6+ ET .00082 0.049

 

€+€’— .0031 0.17

 

€+T_ +591“ 0.006 0.31

 

e+r+ 0.0066 0.33

 

 

 

 

 

a The value of 75 is not necessarily accurate below 0.001. The important check is whether the
value drops below the threshold. Further discussion can be found in Appendix C and [91].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_ w.
8E-
” E
3 7:—
“ :
o- _
m 6:—
a E
,E 5:- 9
‘F :
'6 45- 0 e
h I
3 37 *
3 2:" "
z E
1?
:
obi llLllLllllllAIJLllliJllJJL lll
-4 -3 -2 -1 0 1 2 3 4

P in units of a

Figure 9.11: Distribution of ﬁnal state SLEUTH probabilities converted into units of
a before inclusion of the ﬁnal state trials factor.

233

 

 

 

 

 

 

 

 

 

 

Number of final states
a
illllliilliillljiiiliilijiilllililjii

 

 

 

 

 

 

llllllllllllllllllLLll ll

-1 o 1 2 3 4
P in units of 0

Figure 9.12: Electron-only distribution of ﬁnal state SLEUTH probabilities converted
into units of a before inclusion of the ﬁnal state trials factor. The two points in the
tails show issues with jets misidentiﬁed as T’s.

 

L
«I:

O
r-
”_—

pi 6i + ET and 6i 6; E, + ET with 2.0 fb—1 [28]. These states were also among
the most discrepant observed by CDF for 927 pb‘1 [91]. We show our results for
these states in Figures 9.3, 9.3, 9.3 except for pi ei + 2 jets + ET in which we have
no data events. Figure 9.3 shows the similar ﬁnal state where the muon and electron
are of opposite sign rather than of the same sign where CDF sees the discrepancy.
At DQ) with 1.07 fb-l, the ’P value is fairly low in Figures 9.3 and 9.3, but neither

of these states are among the most discrepant.

234

 

P I” 00 Run II Preliminary(1 fb")

 

    
    

a P = 0.032

.. _ 0 DO Run Ila data

5 14_ Z—W "i 91:83
> _ - Z —+ T7 3 5 d=18
I" — - W/QCD background '3

‘5 12: m WZ 25

3 _ - Other . '2

9 1.5

g 10 1

z 0.5

 

 

 

 

@
ll—YIj—FIIIIIIIIITIIIW

 

 

 

°o

 

20 40 6 80100120140160180200
l———> mew)

63

/
Figure 9.13: Check of most discrepant. CDF plots from [28]. same sign (SS) £8 . The
P values at the top right corner of the plots are the probabilities before ﬁnal state
trials factors.

235

1+ ln- HT 00 Run II Prellmlnary“ fb 1)

 

 

    
 

P=o-074
0 DORunlladata
- W2 1 91:22
16 -Z->mt+lp d=33

- W/QCD background
.' ',";‘ Z —) Ml + 00 6
14 — Other

12

Number of Events

10

 

 

     

   

   

    

  

50‘ 100 150 200 250 300‘
53 , ZmeeV)

 

I
Figure 9.14: Check of most discrepant CDF plots from [28], same sign [II + ET. The
P values at the top right corner of the plots are the probabilities before ﬁnal state
trials factors.

236

m- 1’ HT 00 Run 0 Preliminary“ ill")

 

 

 

 

 

P = 0.59
3 16!: 0 D0 Runlla data 6
5 — -Z ML 5 sum
> 6 WZ d=16
W 14- - W/QCD background
‘6 Z - zz
‘- - - 0th
'8 12: or
E _
3 _
2 1o
0

3_

GE

43

2:-

 

 

  

°o 50100l———>2Xp(GeV)

/

Figure 9.15: Check of most discrepant CDF plots from [28], ﬂiETE + ET. The P
values at the top right corner of the plot is the probability before ﬁnal state trials
factors.

237

, - 00 Run II Preliminary 1 fb'
1*: All ‘ H.034

 

 

 

 

 

 

 

 

 

  

 

 

2 4.5E o 00 Runlladata
5 _ Z —> W
> I - t?
I" 4: - WW
'5 E — Z —+ TT +cc
g 3.5: - Other
5 E
z 3:—
2.5:—
23— 0 0 ti 0 0
1.5:—
12—
0.5

 
 

 

 

210 300 400 500 600
203 2 T
Figure 9.16: Since there are. no data events in the for D0 in the descrepant CDF
state, pi 6:}: + 2 jets + ET, the distribution for pi e; + 2 jets + ET is shown.
The lack of data in 1 fb‘l shows that we do not see the same data excess in that
ﬁnal state.

238

Chapter 10

Conclusions

This analysis was an attempt to answer the basic question, “Do we see what we ex-
pect?”. In our attempt to answer this, we performed a broad search for new physics
over 1.07 fb"1 of data collected in Run II of the Fermilab Tevatron Collider at the DQ)
experiment. A total of 180 exclusive data ﬁnal states and 9,335 relevant kinematic
distributions were compared to the complete standard model background predictions
using the VISTA algorithm. Only four out of 180 exclusive ﬁnal states show a sta—
tistically signiﬁcant discrepancy. Given the known modeling difﬁculties in all four
ﬁnal states, we refrain from attributing the observed discrepancies to new physics. A
quasi-model independent search for new physics was also performed using the algo-
rithm SLEUTH by looking at the regions of excess on the high-Z pT tails of exclusive
ﬁnal states. Only at + e; + ET surpasses the discovery threshold beyond the
obvious excesses noticed in VISTA. This ﬁnal state is potentially interesting for new
physics processes. Several classes of theories, such as supersymmetry, can produce
high momentum leptons with large missing energy, due to a non-interacting massive
particle. The observed discrepancy in this analysis, however, strongly points to dif-
ficulties in modeling the muon pT resolution. It is possible that there is a residual
signal behind the known resolution issues, but we currently have no compelling case

for this possibility. Further analysis of this same data set (subsequent to the work in

239

 

this thesis) also points to the likelihood that this is due to systematic underestimation
of the muon resolution effects by the detector simulation.

While it is disappointing that we were unable to ﬁnd clear signs of new physics in
our data, the search accomplished two important tasks. First, we found that the vast
majority of high-pT data at D0 could be described through physics simulation of
the standard model and the GRANT—based description of the detector. The ability to
describe high-pT standard model physics processes through Monte Carlo event gener—
ation requires a combination of calculations that can only be done with supercomput-
ers, the integration and collation of information from physics experiments throughout
the world, and a deep understanding of nature such that interactions where no calcu-
lation techniques are available can be estimated in exacting detail. This is then tied
to a description of a 5,000 ton, 30’ x 30’ x 50' detector, often requiring accuracy at
the level of microns. The multipurpose detector requires the integration of materials
ranging from silicon to uranium. The tracking system, for instance, has 800,000 in-
dividual silicon strips and 70,000 scintillating ﬁbers. With an average of 1.7 million
proton/antiproton collisions each second, this analysis shows that this complicated
system can provide a good description of the data (with a handful of well-motivated
correction factors). Secondly, on the few areas where the detector description was
less than perfect, such as the modeling of the curvature resolution of very straight
tracks or the generator-level implementation of photonic radiation, this analysis has
shined a strong light. These issues were not simply corrected away by looking at data
outside the region of interest but were highlighted and brought to the attention of the
collaboration. This information will help provide crucial insight as the D0 detector
modeling and Monte Carlo generation is further improved, as well as point to areas
of interest as future detector experiments are brought online.

In conclusion, the search for new physics tests our understanding of nature and

the limits of technology. In searching for the answers to humanity’s most fundamental

240

questions, even a null result provides profound insights.

241

 

Appendix A

Level 2 Global

The Level 2 triggering system was created to bridge the gap between triggering that
could be done strictly with electronics (the Level 1 system) and the more detailed
triggering using the full detector readout (the Level 3 system). Further detailed
information on the Level 2 Global crate and the Level 2 triggering system in general
can be found in [93], [20]. Much of the information in this section is adapted from
these sources. The speed required for this intermediate region necessitates the use of
pared down software combined with some ﬁrmware components. The original design
parameters included a call for an input rate of 10 kHz, an output rate of 1 kHz with
no more than 5% deadtime. As the triggering for Run II came together, it was found
that the Level 1 system would have its output limited by the readout of the central
tracking system. This kept the Level 1 output below a maximum of 2 kHz. This
allowed Level 2 to operate with a rejection rate of around 50%. With a factor of two
rejection rate, Level 2 can maintain a very high efﬁciency for physics objects while
allowing the implementation ()f a more complex triggering scheme than originally
imagined.

The Level 2 system consists of six processing crates that are connected to individ-
ual detector subsystems and the Level 1 trigger. Each of these crates runs an identical

executable on a Beta processor [94] with individual conﬁguration ﬁles designed for

242

each type of processing. The ﬁve preprocessors create basic physics objects from one
particular subsystem. For example, the L2MUC processor (L2 central muon prepro-
cessor) takes inputs from the scintillators and muon PDTs and creates basic muon
objects from this information. Each of these preprocessor objects is formatted in a
manner consistent with a cormnon format for headers and trailers, and sent on to the
central processing crate, L2 Global.

The L2 Global processor is responsible for making the L2 trigger decision. It takes
all of the preprocessor objects, performs further processing, and determines whether
any of the trigger terms included in the trigger list are met. If any of the triggers
pass, the event is passed to L3 for further triggering. If all fail, then the event is

rejected and triggering continues with the next event.

A.1 Data Flow

The ﬂow of data across the Level 2 system can be seen in Figures A.1 and A2.
Deﬁnitions of each individual component can be found in the references. Inputs from
the detector readout boards and Level 1 flow through the preprocessor crates and
into Level 2 Global. The L2 Global crate layout can be seen in Figure A3 The list
of cards in the L2 Global VME crate is shown in Table A.1. Once each preprocessor
crate creates its objects, the object data ﬂows from each of the ﬁve preprocessor
Beta [94] processing cards across the custom 128-bit wide, 100 ns Magic Bus [95] to
the Magic Bus Transceiver [96]. Here the data is converted to a format compatible
with Cypress Hotlinks cables [97] with a throughput of 16 MB/s. It is then sent
to the input of the Magic Bus Transciever in the L2 Global crate. Next, it is sent.
across the Magic Bus in the Global crate to the Global ﬁeta processor where L2
Global reads the lists of preprocessor objects and L1 framework information. The
framework information includes the L1 decision mask: the list of which L1 terms

passed and failed. L2 Global makes its decision based on the downloaded list of Level

243

 

2 triggers corresponding to the L1 terms that passed and using the input preprocessor
objects. The list of preprocessor inputs to the L2 Global crate based on MBT source
IDs is shown in Table A2.

Photographs of the L2 Global crate can be seen in Figures A.4(a) and A.4(b).

Detector L1 Trigger L2 Pre-Processors L2 Global
Muon
D etector

Fiber
Tracker
l
Silicon
Tracker

[ Trigger Framework, coordinates L1 trigger and L2 trigger and detector readout J

 

    
     

 
   

L2 Global
Processor

  

         
 

 

 

 

‘I-I-I-I-I

 

‘II-I-I-
‘I-l .-.-
‘I-I-I-I

 

 

 

Figure A.1: Data ﬂows from the front end detectors through the Level 1 and Level 2
trigger systems. The solid lines show the path of the detector data while the dotted
lines show the path of the Level 1 and Level 2 triggers. The ﬁnal Level 1 decision
is determined by the trigger framework. The Level 2 system also sends the trigger
decisions to the framework, but. the Level 2 Global processor makes the ﬁnal decisions
on Level 2 event acceptance.

In all events, L2 Global prepares a header for L3 readout, but if the decision is to
reject, the event is completely dropped. If L2 Global passes the event, then each of
the Global objects that were used in passing any of the trigger conditions are tagged
to save ofﬂine. This information is sent from the Beta processor across the VME [98]

bus to the readout SBC (single board computer) [99] located in the crate. The Level

3 system uses this to draw events from Level 2 and into the Level 3 system. This

244

 

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245

MBus

 

 

 

 

 

 

 

VME
TCC2 4—*
GBL
S F W S S M M
Bit-3 O
| r F F B B
MPM k
C C e O O T T
L3 = ' <1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T SCL

Inputs from L2

preprocessors

Inputs from LIITFW Beta (Linux)

Figure A.3: Physical setup of the L2 Global cards within its VME crate.

object information is not used directly in the Level 3 trigger decision, but if the event
passes, the objects are stored for possible ofﬂine analysis. A mask of all of the L2

decisions is also stored and used to determine which algorithms to run at Level 3.

A.2 Trigger Conﬁguration

As with the preprocessor crates, the conﬁguration ﬁle that controls how L2 Global
runs is stored on the Windows machine, DO TCC2 (the trigger control computer).
Level 2 Global differs from the preprocessor crates in that it must enter the decision
state of the event loop and determine whether each event is accepted or rejected. The
interpretation of each of the trigger conditions and the relation of each of these to
the Level 1 decisions is a complex job exclusively done in the Global crate.

The trigger list is stored in the trigger database. The data acquisition coordination

246

 

Figure A.4z The Level 2 Global crate, front A.4(a) and back A.4(b) 011 the front, the
Visisble cards from left to right are the Bit 3 card, SBC, FIC, Beta, 2 SFOS and 2
MBTs. On the back, 2 MBUS terminators and the VTM for the L1 trigger framework
input. The white jumpers shown in the photo of the back of the crate are needed for
proper functioning of the readout SBCs. In order to run the L2 event loop at the
teststand, the L3 handshaking must be faked.

247

Table A.1: The contents of the VME crate that houses the
L2 Global processor. Each card is listed by the VME slot

in which it resides.

 

Slot Card

 

1 Bit 3 Multiport Memory

 

2 SBC

 

3—5 Spare

 

6 FIG input from L1 Trigger Framework

 

7—8 L2 Global Processor ﬁeta

 

 

 

 

 

 

9—16 Spare
17 SF O
18 SFO
19 MBT
20 MBT
2 1 Spare

 

 

 

 

system (COOR) [100] retrieves this information from the database and sends it TCC2.
From there, the triggers are sent. to L2 Global. Each of these trigger conditions
are considered only if the relevant Level 1 triggers have ﬁred. There is a direct
correspondence between a single Level 1 trigger and a group of Level 2 triggers. An

example of a trigger used in this analysis is shown in Figure A.5.

A.2.1 Quick Overview of Relation Among Components of

Level 2 Trigger Decision

0 L1 Triggerbit— One of 128 possible trigger conditions at Level 1. Each of these

bits is either 0 or 1 depending on whether the trigger passed.

248

 

 

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249

Table A.2: L2 Global data sources.

 

ID Source

 

0 L1 Serial Command Link

 

1 L1 Hardware Hamework

 

L2 Cal— EM

 

L2 Cal- Jets

 

rD-QDM

L2 Cal- MET

 

CH

L2 CTT- STT pT

 

L2 CTT- STT ip

 

L2 MUC

 

L2 MUF

 

QDOO'NICE

L2 PS— CPS (disabled)

 

10 L2 PS- FPS (disabled)

 

11 Spare

 

12 L2 CTT- CTT pT (empty)

 

13—15 Spare

 

 

 

 

o Superscript- The superscript is a group of Level 2 trigger terms that are associ-
ated with a L1 triggerbit. There are 128 of these, one for each of the incoming
L1 bits. If ANY of the scripts associated with a superscript passes, then the
superscript (and the event) passes. This was used to easily expand the initial
one-to—one correspondence between L1 and L2 triggers to accomodate several

L2 triggers for each Level 1 trigger at the beginning of Run 11b.

0 Script- This is the term that corresponds to a particular Level 2 trigger. Each
script is made up of a ﬁlter and a number of objects that need to pass that

ﬁlter. The parameters used in that ﬁlter are also speciﬁed in the script.

 

o F ilter- The ﬁlter uses objects created by the tools or other ﬁlters to determine if
they match the parameters set in the script. An example would be a minimum
A77 cut between a Global muon object from a muon ﬁlter and a Global jet object
from a jet ﬁlter. The objects passing the muon and jet ﬁlters would have been

determined from muon and jet tools described below.

0 Tool- Level 2 tools are used to create Level 2 Global objects. These may be
preprocessor objects directly, preprocessor objects with more complex preperties
or combinations of preprocessor objects. An example would be a preprocessor
muon matched to an L2CTT (STT) track. Minimum requirements would be
put on the muon pp and a minimum distance would be needed to match the

track to the muon.

0 L2 Global Ob ject- An L2 Global object is any object that is created by a global
tool. For example, if an L2 jet tool is run, all of the preprocessor jet objects are
looped over. Any of the objects that meet the criteria for the jet tool will be
added to the list of global objects. These objects are then in turn used in the

Level 2 ﬁlters.

0 L2 Preprocessor Object- A preprocessor object is an object sent from one of
the Level 2 preprocessors. These objects always contain only information that
comes from a single preprocessor, which reﬂects just one part of the detector.
For example, the calorimeter will send jet and EM preprocessor objects, L2MUC

will send muon objects from the central muon system, etc.

0 Tool Object List- Once a tool is run, it does not need to be run again. A tool
will only be run if a particular ﬁlter requests it. If a different ﬁlter later requests
the same tool, the objects passing that. tool will not need to be recalculated.
They will simply be read off the list of objects passing that particular tool. The

object list is saved for the event and any object that contributed to the passing

 

of a trigger is saved and sent to Level 3.

a Filter Object List— Once one of the global objects that was part of the tool
object list passes a ﬁlter, that object will be added to the ﬁlter object list.
Once a ﬁlter is run one time, all of the objects that pass that particular ﬁlter
are saved. If the ﬁlter were to be used again in a different script or as an input
to a different ﬁlter, it would not need to be run again. The objects that passed
that ﬁlter would simply be checked to see if they satisfy the higher level ﬁlter or
script requirements. In the case of the script, only the number of objects would

be further speciﬁed.

0 Preprocessor Object List- As each stage of the decision is made, the preprocessor
object associated with a particular Global object is saved. If a tool and ﬁlter
pass as part of a passing trigger, all of the objects that could contribute to
passing the trigger requirements are tagged and saved for ofﬂine analysis. When
this happens, the preprocessor objects that are used in the creation of the global
objects are also tagged and saved for ofﬂine analysis. In the end, the Global

object and preprocessor object list are passed to Level 3.

A.3 Triggerbits, Superscripts, and Scripts

Which of the 128 Level 1 triggers that ﬁre, determines which L2 processes will be
run. The Level 1 trigger associated with the trigger above is shown in Figure A.6.
Each of these corresponds to groups of Level 2 processes known as superscripts.
There is an exact one-to-one correspondence between the L1 Trigger Bits and each
L2 superscript. The list of which superscripts have passed is saved and sent to Level 3.
Each superscript passes if ANY of an associated set of scripts passes. The superscript
performs an OR of all of the scripts associated with it. Each of the scripts corresponds

to a set of Level 2 triggers determined to most efﬁciently bring in physics objects while

limiting deadtime. The superscript associated with trigger “l\v‘IUH5_LMl5” is shown
is Figure A.7.

The superscripts were not implemented to run directly as triggers. Their presence
is based purely on the necessity to expand the old 128 possible trigger conditions to
1024 that are currently available [101]. Previously, only a single script could be run
for each L1 trigger that ﬁred. In order to expand this, another layer of complexity
needed to be added, so that the superscripts now play the role that the individual
scripts did previously. The trigger conditions are still applied at the script level,
and the superscripts match individual L1 trigger decisions to the group of L2 trigger
conditions that should be considered. An example script is shown in A8.

Each script is made up of a particular ﬁlter (described in the next section) and
the number of objects that need to pass the ﬁlter. As with the superscripts, the list
of scripts that pass is saved and sent to Level 3 determining which Level 3 algorithms

are run and for eventual offline analysis.

A.4 Filters and Tools

Filters are the conditions necessary for a particular script to pass. Each filter has a
set of conﬁgurable parameters that are deﬁned in the script. A ﬁlter may be used
multiple times in different scripts with different object requirements. The ﬁlters set
conditions on Global physics objects. Each Global physics object comes from pre-
processor objects sent from the other Level 2 ﬁestas, which can then be used directly,
reﬁned, or combined with other preprocessor objects. As an example of Global ob—
ject creation, we can start with a preprocessor central muon. This can be reﬁned
by looking for overlap with a forward muon, and then checked for a match with an
STT track. The new, more complex muon would then be added to the list of Global
objects that can be used in the L2 ﬁlters. Each of these objects is created only when

the need arises. If there are no ﬁlters that need this particular object, then the tool

253

 

 

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256

will never be run, saving processing time.

A full list of tools available to L2 Global is shown in Table A.3.

Table A.3: Full list of tools zvailable to L2 Global with

the conﬁgurable parameters.

 

Tool Parameter Description

 

LIPTTHRESH Minimum L1 PT
REQUIRETRACK IS match to track required?
KINEFROh-"ITRACK Use kinematic track information
Muon

rather than that of local muon stub?

TRACKWINDOW Maximum distance in iphz’ to match

 

 

 

IPHI a track to the muon

 

 

Continued on Next Page. . .

 

Table A3 (cont’d)

 

Tool Parameter

Description

 

 

MINET
MINNEIGHBOR
ETACEN ET

’PHICEN ET
’ETAFWNET
’PHIFWNET
MINSINGLE TOW -
EREMFRAC

MINSINGLE TOW -

EM
ERET

REQUIRETRACK

TRACKFILER

TRACKWIN DOW
IPHI

REQUIRECPS
CPSWIN DOWI ETA
CPSWINDOWIPHI
MAXEM

 

 

Minimum ET

Threshold for which, if central clus-
ter 77 neighbor is below, it will be
turned into 2 separate EM tower ob-
jects

Same for central cluster 0 neighbor
Same for forward cluster 7) neighbor
Same for forward cluster 0 neighbor
Value for which if EM fraction is
greater, it will turn that cluster into
two EM tower objects

In ET for single tower EM object.
Overrides MINET if MINNEIGH—
BORET is true.

If set to 1, require track match to be
found (0 is false).

Filter used to deﬁne track that is to
be used with track match.

0 window to match track with EM
cluster

1 2 require a CPS match (0 is false)
77 match window with CPS

4') match window with CPS

l\«’Ia.xi11'1um number allowed to pass

 

Continued on Next Page...

2

8

 

 

Table A3 (cont’d)

 

 

 

 

 

 

 

 

Tool Parameter Description
Commission
MININVMASS Minimum invariant mass
NFILTERS Number of input ﬁles (1 or 2 depend-
ing on whether we are looking at two
Inv M ass
of the same type of objects)
F ILTERO First ﬁlter
FILTERl Second ﬁlter
REVERTEX Find actual vertex rather than use
MET default of zero
FILTERO Vertex ﬁlter
Jet MINET Minimum ET
MINET Minimum ET of jets to be included
MJ T
in calculation
MIN ET Minimum ET
MAXTAUS Maximum number of taus
MINRATIO Minimum hadronic isolation fraction
Tau REQUIRETRACK Require a track?
TRACKWINDOVV How close in iphz’ to match tan with
IPHI track?
TRACKFILTER Filter used to select track

 

 

 

Continued on Next Page. . .

259

 

 

 

Table A3 (cont’d)

 

 

 

 

 

 

 

Tool Parameter Description
MINET Minimum PT actually of tracks to be
included in event b—tag calculation
BTag MINIPSIG Minimum impact parameter signiﬁ-
cance for track
MAXCHISQ Maximum X2 value for track
MIN ET Minimum PT of track
TRACKSOURCE Type of input track (now just PT or
z'p ordered STT tracks)
REQUIRELlISO Require L1 isolation conﬁrmation
REQUIRELIPS Require L1 preshower conﬁrmation
Track L2ISOTYPE Type of L2 isolation required. 0 =
no requirement, 1 or 2 2 require 1-
or 3-prongs, 3 = require l-prong
MAXCHISQ Maximum x2 allowed
IPSIG Minimum impact parameter signiﬁ-
cance
MINET Minimum pT of tracks used in vertex
ﬁnding
Vtx IxiAXCHIsoFIRsr h’laximunl x2 for tracks in ﬁrst pass
of vertex ﬁnding
MAXCHISQSECOND Maximum X2111 second pass

 

 

 

 

Continuing with the muon example, a ﬁlter may simply add a tighter transverse
momentum cut to the muon object. It could also look at the 17 or 0 separation between

two muons, or a muon and a jet created by a different tool. The script containing

260

 

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261

that ﬁlter then may require at least two of the muons. A total of 1024 total trigger

conditions can be applied in L2 for each trigger list.

A full list of ﬁlters available is shown in Table A4.

Table A.4z Full list of ﬁlters available .to L2 Global with

the conﬁgurable parameters.

 

 

 

 

 

 

 

Filter Parameter Description
MINET Minimum ET
QUALITY Minimum quality (based on number

of hits)
Muon PROMPT Minimum timing quality (based on
scintillator times)
SIGN Required sign of muon to pass
TOOL Input tool
EMFRAC Minimum EM fraction
ISOFRAC Maximum isolation fraction
MINET Minimum ET
EM
M AXEM Maximum number allowed to pass
MINLIKELIHOOD Minimum value of the EM likelihood
TOOL Input tool
REQUIRENORTH Require North ﬁred
REQUIRESOUTH Require South ﬁred
EIVICalib

REQUIRECENT Require Central ﬁred
REQUIREANY Require any ﬁred

 

Continued on Next Page. . .

262

 

 

 

Table A.4 (cont’d)

 

 

 

 

Filter Parameter Description
BJETMIN Sum of Jet st and Track z'phz's
BJet J ETF ILT ER Jet ﬁlter

TRACKFILTER Track ﬁlter

FILTER Filter used to choose object for ieta
cut

IETAMIN Minimum z'eta (for ﬁrst region if
NREGIONS is greater than 1)

IETAMAX Maximum ieta (for ﬁrst region if
N REGIONS is greater than 1)

NREGION S Number of z'eta regions to consider

IETAMIN2 If more than one region, second min

Eta ieta

IETAMAX2 If more than one region, second max
ieta

IETAMIN3 If more than two regions, third min
ieta

IETAMAX3 If more than two regions, third max
ieta

IETAMIN4 If four regions, fourth min ieta

IETAMAX4 If four regions, fourth max z'eta

 

 

 

Continued on Next Page. . .

263

 

 

Table A.4 (cont’d)

 

 

 

 

 

 

 

 

 

Filter Parameter Description
NFILTERS Number of input ﬁlters
IETAMINSEP Minimum 7] separation value
EtaPhiSep IPHIMINSEP Minimum 0 separation value
FILTERO First input ﬁlter
FILTERl Second input ﬁlter
NFILTERS Number of input ﬁlters
IETAMINSEP Minimum 77 separation value
EtaSep IETAMAXSEP Maximum 17 separation value
F ILTERO First input ﬁlter
FILTERl Possible second ﬁlter
FailAll
HTMIN Minimum HT
N FILTERS Number of input ﬁlters
HT FILTERO First input ﬁlter
FILTER] Second input ﬁlter
FILTER2 Third input ﬁlter
MININVMASS Minimum invariant mass
InvMass MAXINVMASS Maximum invariant mass
TOOL Input tool
MINET Minimum ET required
MET
TOOL Input tool
IPHIMIN Minimum éphz'
Phi IPHIMAX Maximmn iphz’
FILTER Input ﬁlter

 

 

 

Continued on Next Page. . .

264

 

 

Table A.4 (cont’d)

 

 

 

 

 

 

 

Filter Parameter Description
NF ILTERS Number of input ﬁlters
IPHIMINSEP Minimum 0 separation value
PhiSep IPHIMAXSEP Maximum 0 separation value
FILTERO First input ﬁlter
FILTERl Second input ﬁlter
N FILTERS Number of input ﬁlters
IPHIMINSEP Minimum 0 separation value for veto
IPHIMAXSEP Maximum 0 separation value for
PhiSepVeto
veto
FILTERO First input ﬁlter
FILTERl Second input ﬁlter
N FILTER Number of input ﬁlters
RMINSEP Minimum A’R separation value
RSep
F ILTERO First input ﬁlter
FILTERl Second input ﬁlter
PASSPERCENT Percent of ﬁlters to pass
RandomPass
TOOL A commissioning tool
SPHERMIN Minimum sphericity
APLANMIN Minimum acoplanarity
NFILTERS Number of ﬁlters
Spher
FILTERO First ﬁlter
F ILTERl Second ﬁlter
FILTER2 Third ﬁlter

 

 

 

Continued on Next Page. . .

 

 

 

Table A.4 (cont’d)

 

 

 

 

 

 

Filter Parameter Description
DISTRIBUTION Type of distribution (Delta,
Gaussian, Exponential, Hyper-
Exponential)
MEANDELAY Mean time delay
MEANDELAY2 Second mean parameter used for
hyper-exponential
TimeDelay WIDTH Width of Gaussian
PROBABILITY Probability of using ﬁrst expo—
nential in hyper-exponential with
time delay, MEANDELAY. 1-
PROBABILITY is probability
of using exponential with mean
MEANDELAY2
TOOL Input commissioning tool
MINTRANSMASS Minimum value of transverse mass
rIraanIass FILTERO First ﬁlter
FILTERl Second ﬁlter
MINET Minimum ET
Jet MAXJETS Maximum number of jets allowed
TOOL Input tool
MINMJT Minimum ET
MJT
TOOL Input tool

 

 

 

Continued on Next Page. . .

266

 

 

Table A.4 (cont’d)

 

 

 

 

 

 

 

 

 

Filter Parameter Description
REQUIRENORTH Require North ﬁred
REQUIRESOUTH Require South ﬁred
CalCalib
REQUIRECENT Require Central ﬁred
REQUIREANY Require any ﬁred
MIN ET Minimum ET
MINRATIO Minimum ratio of two highest energy
Tau hadronic towers to all jet towers
TOOL Input tool
MIN GOOD Minimum value of b-tagging param-
eter when just looking at best track
MIN ALL Minimum value of b—tagging param-
BTag eter when looking at good tracks
MINGOODTRACKS Minimum number of good tracks in
event
MINET Minimum PT of track
QUALITY Minimum quality
IP Minimum impact parameter
Track
IPSIG Minimum impact parameter signiﬁ-
cance
TOOL Input tool
MAXVTXZ Minimum MULM best cut value
Vtx MINTRACKS Minimum number of good tracks
TOOL Input tool

 

In the end, we have a list of tools which contain the Global objects for which

267

 

 

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268

ﬁlters have been run, and a list of ﬁlters that have been run for the scripts. Once
these have been run once, they do not need to be run again for that event. All objects
matching speciﬁc criteria will be saved in a ﬁnal list. All objects that pass individual
ﬁlter conditions will also be saved in a list. After all of those have been run, based
on script requirements, the later scripts simply choose among these objects to see if

they pass the necessary conditions.

A.5 L2 Global Packages

The L2 Global code is stored in several packages in CVS. Several packages are re—
sponsible for controlling input, output and decision making. The rest are used for
ﬁlters and tools.

The code involved in packing and unpacking data, running tools and ﬁlters, read-
ing L1 trigger masks, making decisions, and ﬁlling output is listed below. This also

is where interpretation of possible errors coming from the L2 framework occurs.

0 ngblbase
o 12gblworker

o 1210

The rest of the code is made up of the individual tools and ﬁlters. These packages

are listed below.

l‘2gblem

12gblmuon

ngbltau

ngbUet

269

 

o l2gbltrack

o 12gblgeneric

All of these packages can use all of the input data. The separation by packages is

for convenience rather than signaling partitions within the code.

A.6 Monitoring and Common Problems

The Level 2 Global crate typically runs well without interruption, but several mon-
itoring tools are available to follow data taking and ensure the crate is running as
expected.

A monitoring script called 12mon keeps track of global quantities from the trigger
framework, as can be seen in Figure A.11. The trigger rates of each individual L2
trigger are also monitored as seen in Figure A.12. If the overall trigger rate jumps
unexpectedly, the individual trigger rates can be checked to isolate the problem.
These rates are plotted with a script called trigstripmon shown in Figure A.13. The
L2 buffers are also monitored for each of the processors. The number of events that are
sitting in buffers awaiting a Level 2 decision can also help with debugging a problem.
If L2 Global stops issuing decisions, these buffers will quickly overflow. The part of
the l2df program that shows this information is shown in Figure A.14.

As the Level 2 executable runs, conﬁguration information and unusual running
conditions are stored in a local log ﬁle. Signiﬁcant errors are marked by a searchable
term, “ELerror”. The errors in L2 Global vary considerably from the preprocessors
because of the additional coalescing of information and decision making that is only
done in global.

Over 2008 and 2009, the L2 Global trigger ran into very few serious errors, but
the log ﬁles were still large relative to the preprocessor crates, due to some errors

occurring quite frequently. Four speciﬁc errors were found from 2008-2009 with three

270

 

more] 12mm I 1.2mm | mas] 1.2mm |

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

{L1 Triggc Monitor MonJun 307-3113620091 D

Global I Spec'mggu | GeoSector l

Ll Accept (Hz) 598.406
L2 Accept (Hz) 375.9%
1.2 rejection (Ll/L2) 1.596
L1 [waiting L2 (raw count) 0]
L2 Pvt Cycle: (Hz) 598.172.l
L2 PW Accept (Hz) 375.374
L2 Fw Reject (Hz) 222.797
L2 decisions enabled? 1e:
Beam X: in L2 Cycle: (Hz) 2018484244
Beam X: with L2 Basie: (Hz) 75862859}
BX: waitingto advertize L2 (Hz) 7828.8
luminosity Block Number 67 74568
TRGFR paused by 000R? no
Tot Alloc Sp Try 106
Tot Alloc Exp Grpc 3
Tot Allan Geo Sect: 80}

 

 

 

Figure A.11: Monitoring the global information from the trigger framework. This
includes overall L2 accept rate and L2 rejection fraction.

271

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H80 8980 .808 08. 800808 88 80me 10:03:08 8000 00 0x03 83. .8838 808$ 80¢ 98.800808 0802 ”San. 08me

 

272

 

Figure A.13: The L2 monitoring program trigstripmon. Each trigger can be individ—
ually monitored with this program.

273

 

 

    

L TBSJI=Q 096
L2BSy:0. 0%

 

L1Accept - 294.219Hz _

LZAccept = 198.291 Hz

 

 

L1 Await L2
n I.

 

 

Figure A.14: The most common tool used in L2 monitoring. Shown are the parts of
the GUI relevant to L2 Global.

of them occurring many times each day but without serious consequence, and one

that is rarer but of signiﬁcant interest. These are as follows:
0 Script overﬂow error
0 Undeﬁned script error
0 MBT channel overﬂow error

0 L2 decision error

274

 

A11 example of each of these can be seen in the following messages taken from the

Level 2 Global log ﬁles:

Mon Apr 27 00:12:36 CDT 2009:
Mon Apr 27 00:12:36 CDT 2009:
Mon Apr 27 00:12:36 CDT 2009:
Mon Apr 27 00:12:36 CDT 2009:
Mon Apr 27 00:12:36 CDT 2009:
Mon Apr 27 00:12:36 CDT 2009:

—ERROR LOG—

message severity(Range is 0-14): 7(ELerror)
bunch: 128

rotation: 38008

message name: Script Overflow

message text:

Mon Apr 27 00:12:36 CDT 2009: Script.cpp(194): Object limit of 50 reached for L2

script 42, while in filter TRACKFILTER12

Sun Apr 26 12:21:59 CDT 2009:
Sun Apr 26 12:21:59 CDT 2009:
Sun Apr 26 12:21:59 CDT 2009:
Sun Apr 26 12:21:59 CDT 2009:
Sun Apr 26 12:21:59 CDT 2009:

out of the loop (pass all).

Mon Apr 27 00:12:38 CDT 2009:
Mon Apr 27 00:12:38 CDT 2009:
Mon Apr 27 00:12:38 CDT 2009:
Mon Apr 27 00:12:38 CDT 2009:
Mon Apr 27 00:12:38 CDT 2009:
Mon Apr 27 00:12:38 CDT 2009:

——-ERROR LOG—_-

message severity(Range is 0-14): 7(ELerror)
message name: Configuration

message text:

SuperScript.cpp(51): No subscript is defined. Breaking

—ERROR LOG—

message severity(Range is 0—14): 7(ELerror)
bunch: 37

rotation: 56201

message name: Too many objects

message text:

Mon Apr 27 00:12:38 CDT 2009: FillableMBTChannel.hpp(186): Attempt to put too

many objects into MBT channel with source ID 230 limit is 100 objects.

 

Sat Mar 21 14:59:36 CDT 2009: ——~ERROR LOG—H

Sat Mar 21 14:59:36 CDT 2009: message severity(Range is 0—14): 7(ELerror)

Sat Mar 21 14:59:36 CDT 2009: message name: L2 Decision Error

Sat Mar 21 14:59:36 CDT 2009: message text:

Sat Mar 21 14:59:36 CDT 2009: L2Decision.cpp(137): Buffer marked as pass but reject
received

Sat Mar 21 14:59:36 CDT 2009: requesting SCLJNIT

The most common error found in the log ﬁles is the script overﬂow error. The
maximum number of objects created with the global tools are set to ﬁfty in the
l2gb1worker package. When an individual tool has more than ﬁfty objects that pass
the conditions set in the ﬁlters deﬁned for that trigger list, the remaining objects will
not be tagged to send to Level 3 for eventual offline analysis. After the maximum
count is met, any other ﬁlter that uses these objects will be completely skipped in the
object tagging portion of the code. This error has no effect on triggering. If a script
passes because of an individual trigger, the result of that decision is appropriately
saved. The effect of this error is simply that certain objects associated with one of
the Level 2 triggers may not be available for eventual ofﬂine analysis. The event will
be saved, but not all of the Level 2 objects that were involved in the event passing
Level 2 will be available for further study. The frequency of this error increases with
increasing luminosity as more and more objects satisfy trigger requirements. Two
plots are shown in Figure A.15. The top plot shows the niunber of times the error
occurred vs luminosity from September 2008 to June 2009. The bottom plot shows
the upper plot normalized to one against the luminosity proﬁle from the same time
period.

During conﬁguration, the undeﬁned script error is frequently seen. As mentioned

in Section A.3, each Level 1 trigger that passes is associated with a particular su—

276

 

 

 

I Number of script object overﬂow errors vs. instantaneous luminositn
1’ 35000
o

 

 

t

"J 30000
525000
5020000
,_ 1 5000

m
E 1 0000

 

5000

lIIIIllIlllllllllllllllllllllllllll

 

 

.l.

. . . l . . . . l . . . . I . . . . l . . . L
50 100 150 200 250 300 350
Instantaneous Luminosity (1030 cm'2 5")
Number of script object overﬂow errors vs. instantaneous luminosityj

 

OC)

 

3
h
3
E
3
z
l

 

 

_o _o p o _o
o o o o o
N w a a: or

l[llllllllllllllllllllllllll

P
O
_L

 

 

 

co

50 100 150 200 go 300 350
Instantaneous Luminosity (10 cm'2 5")

Normalized MBT Errors & Lumi Proflie

 

 

 

Figure A.15: The object overlow error shown as a function of luminosity in the top
ﬁgure. The bottom shows the normalized number of occurances with respect to the
overall luminosity proﬁle. All data is from September 2008 - June 2009. The spike in
the errors near [I : 100- 1030 cm_2 3‘1, is due to an error in the luminosity fetching
program.

277

perscript which is in turn associated with a munber of scripts (or subscripts as they
are called in the error message). If there are no subscripts deﬁned for a particular
superscript, then this error message is sent to the log ﬁle, and all events would a11-
tomatically pass that particular trigger. Since any trigger would be sufficient to pass
an event, if there were a condition in which a script was undeﬁned, we would see
no rejection at Level 2. Since this error occurs frequently, and Level 2 continues re-
jecting events, this error seems to be triggered outside of normal running conditions.
Checking the timestamps associated with the errors conﬁrms that this error does not
happen during data taking. The C++ code associated with this error can be seen

below:

// Initializes the SuperScript class using the parser
bool SuperScript::initialize(void) {
doReset(); // New run, reset everything,
including scripts
char 1abe1[20];
// Look for the super script’s L1 bit number
if(!isDefined("L1BIT")) {
errlog(ERROR,"Configuration")
<< "Superscript configuration missing L1 bit number
assignment" << endmsg;
return false;
} else {
_11bit=getInteger("LlBIT");
}
// Loop over all the possible subscripts until an undefined one is
found...

for(int32 i=0;i<SuperScript::MAX_SUBSCRIPTS;++i) {

278

 

// Construct the label that will be used to get the reference to
// the attached subscript
sprintf(label,"SLOTXd",i+1);
// Check that the subscript is defined. If it is not then break
// out of the loop immediately
if(!isDefined(label)) {

errlog(ERRDR,"Configuration")

<< "No subscript is defined. Breaking out of the loop (pass
all)." << endmsg;
break;

// now using default: pass all

One additional overﬂow error is also found frequently in the global log ﬁle. This
one pertains to the number of objects that are to be sent to Level 3. This is also
limited by object type. Even if the individual object count is not exceeded for a
particular tool, each type of global object also has a maximum number that can be
sent to Level 3. In the speciﬁc case that is seen in the log ﬁle, no particular track
tool has more than 50 objects, but the sum of objects coming from all of the track
tools exceeds one hundred. This is the cap for any tagged object to be sent to Level
3. The effects of this are similar to the script overﬂow error. There is no effect on
triggering but a possible problem with offline trigger modeling. The translation of
the MBT channels to L2 Global objects is shown in Table A.5. Two plots are shown
in ﬁgure A.16 just as in the object overﬂow error. The top plot shows the number
of times the error occurred vs lmninosity from September 2008 to June 2009. The
bottom plot shows the upper plot normalized to one against the luminosity proﬁle
from the same period also normalized.

The ﬁnal error that has been observed recently is a potentially serious problem.

279

 

 

Table A5: The translation of MBT channels to global objects sent to Level 3. Here
the channel of interest is 256 which is translated as global track. The MBT channel
overﬂow message is triggered when more than 100 of these objects are found.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Data ID Name
217 Spher
218 Btag
219 TransMass
220 InvMass
221 Ht
222 MJ T
223 MET
224 EMob j
225 Electron
226 Jet
227 Photon
228 Muon
229 Tau
230 Track
253 DFEBOARD
254 CORRUPT
255 UNKNOWN

 

 

 

 

280

 

Number of mbt overflow errors vs. instantaneous luminosity I
90
80
70
60
50
40
30
20
1O

 

 

ll|l||l|lllllllllIIIlllllllllllllllllll'llllll

 

 

. l . . . . l . . l.—l—h . l . . . . l . . . . l . . .

50 100 150 200 250 300 350
Instantaneous Luminosity (1020 cm'2 5")
Number of mbt overﬂow errors vs. instantaneous luminosity I

 

Number of MBT Overflow Errors _
GO

 

 

.099 .6
#C’QNN

 

l|llllIllll|lllIllllllllllllllIllllllllllllll

 

  

Normalized MBT Errors & Lumi Profile

0 50 100 150 200 3250 300 350
Instantaneous Luminosity (10 ° cm'2 s")

Figure A.16: The object overlow error shown as a function of lmni in the top ﬁgure.
The bottom shows the normalized number of occurances with respect to the overall
luminosity proﬁle. All data is from September 2008 - June 2000.

281

It has not been seen since March 2009 but no explicit steps were taken to solve the
problem, so it may come back. The L2 decision that is made in Global is sent to the
trigger framework and returns a different result from what was sent. This decision
error means that there is a problem in the path that the trigger mask travels and
without the consistency check in Global, the wrong Level 2 decision would be issued.
The decision errors cause the trigger system to reinitialize. These often occur in large
bunches causing bad luminosity blocks which can seriously inhibit data taking. The
C++ code where this check is made is shown in the code below. The route of the L2

trigger mask is shown in Figure A.17.

// Check that the L2 decision matches if we did make a decision
// based on this data, but only if the configuration flag is
set to make this check.
if(buf->decision() && _checkDecision) {
//IMPORTANT
if(buf—>pass() && l2scl->12reject()) {
//if(1) {
// pulse bit #8 on ECL outputs if a decision errors is
observed
AlphaNode::tsi()->setScalerBit(8, true);
AlphaNode::tsi()->setSca1erBit(8, false);
errlog(ERROR,"L2 Decision Error")
<< hex << "Buffer marked as pass but reject received \n"
<< "requesting SCL_INIT" << endmsg;
errlog(INFO,"SCL Sync Info") << hex
<< "buf->bunch: " << buf—>bunch()
<< " l2sc1->bunch: " << 123cl->bunch()

<< " buf->rotation: " << buf->rotation()

282

 

<< " l2scl->rotation: " << l2sc1—>rotation()

<< endmsg;

for (int i=0; i<NHISTORY; i++){
errlog(INFO,"Decision History")
<< hex
<< "L1 "
<< _11_history[i][3] << "\t" << _11_history[i][2] <<
"\t" << _11-history[i][1] << "\t"<< _11_history[i][0] << "\n"
<< "L2 "
<< _l2_history[i][3] << "\t" << _l2_history[i][2] <<
"\t" << _12_history[i][1] << "\t"<< _12_history[i][0] << "\n"
<< endmsg;
}
//IMPORTANT

throw RaiseL2Error();

A.7 Main Projects

After taking over the rmming and maintenance of Level 2 Global in late 2005, there

are several projects in which I contributed personally.

A.7 .1 Triggering on Events with b—Jets

The functionality to look for events with b—jets was added in late 2005. This trigger

was developed by Sascha Caron to identify events that were likely to contain b—jets. A

likelihood look-up table was created which took x2 and impact parameter signiﬁcance

to determine the likelihood for an individual track to have come from a b—quark. The

283

 

 

 

 

 

 

 

 

 

 

 

L1 and L2

Figure A.17: The path of the L2 trigger decision through the online system. Thick
lines correspond to full 128—bit triggers. The thin lines represent a single bit ac—
cept / reject decision. The blue lines are L1 trigger bits, red lines are L2 bits, and the
green line is the AND of the L1 and L2 bits.

trigger then set a parameter to look at the maximum likelihood for any jet in the
event or to look at the product of those values to determine if the event crossed a
minimum threshold. The threshold would be set in the trigger along with the number

of tracks that match minimum criteria associated with a secondary vertex.

A.7.2 Implementation of Electron Likelihood, Tau Objects,
Sphericity, and Acoplanarity

The next update came in the sunmier of 2006. As we updated to a new trigger list.

associated with Run IIb, several users created tools that they integrated into the

284

Level 2 system. The electron likelihood was developed by Joseph Haley to better
discriminate among between EM objects and jets. This was determined by looking at
the electron energy deposition in the seed calorimeter cell, the highest neighboring cell,
5 X 5 blocks of cells and the corresponding information in the hadronic calorimeter.

Tau objects were introduced by Marco Verzocchi to distinguish between hadronic
taus and the wider energy depositions typically associated with jets. A tau object was
found by looking at the highest energy and highest neighboring hadronic calorimeter
cells (similar to the electron in the EM calorimeter). These meaures of energy spread
distinguish taus from light jets and comparing the EM and hadronic calorimeter
depositions can distinguish between electrons and taus.

Finally, the sphericity and acoplanarity were introduced to trigger on all—jet and
jet plus missing energy events that have meaningful physics. Many of the high energy
jet events come from noise within the calorimeter. The sphericity and acoplanarity
are measures of the event that can help determine if the energy deposition is spread
through the calorimeter in a distribution that would be unusual to see in calorimeter

noise.

A.7 .3 L2 [feta Multiple Processing Boards Study

In order to reduce processing times, we conducted a study to see how practical it
would be to add a further layer of parallelization in processing. This would allow
the calorimeter preprocessor to have one board to focus on jets, another on EM
objects, and one for the missing transverse energy. In the global crate, this would
allow alternating events to be sent to different processors with the same setup. We
explored the message passing system and modifications that would need to be made
in the event loop to use multiple processors.

After several timing studies, it was determined that the processing time was not

the limiting factor in preparing for an increase of instantaneous luminosity. The

285

processors that were potentially the most signiﬁcant sources of deadtime were the
L2CTT and L2PS. The L2PS is not used in triggering decisions, so if it becomes
a signiﬁcant source of deadtime, it can be turned off. The L2CT T is dominated
by sending tracks to L2GBL. Parallelization of processing does not help with this
process. After determining that this project would not be particularly helpful, it was
decided to discontinue it.

Level 2 Global is the ﬁrst place in the trigger system that each part of the de-
tector can be considered together in making trigger decisions. This allows for more
complex decisions than can be made at Level 1 by using relationships among objects
throughout the detector. Additionally, Level 2 is the ﬁrst part of the trigger that
incorporates information from the silicon tracking detector. The Global processor
drives the Level 2 system, making all of the Level 2 trigger decisions. This layer of
triggering which did not exist during the ﬁrst run of the Tevatron allows for high
efficiency event selection while reducing the rate of incoming events to a level that

can easily be consumed by the Level 3 system.

286

Appendix B

The High-pT Data Format

A condensed data format was created to decrease the amount of time needed to run
the analysis when small changes were made to the analysis strategy. The condensed
format will only save basic object quantities such as object id, pT, 77, and 05. Addi-
tionally, up to four additional parameters are saved for each object depending on the
object type. The information stored for a high-pT object is shown in Figure B.1 and
a summary of the various parameters is shown in Table B.1.

Events are selected to be part of the high—pT skim if they satisfy one of the
following selection criteria. These criteria for the skim are different and looser than

those required for the MIS analysis ﬁts and later VISTA and SLEUTH ﬁnal states.

,upT > 20 GeV

6 ET > 25 GeV

7' ET > 30 GeV

7 ET > 75 GeV

ET > 80 GeV

jet ET > 150 GeV

287

 

 

 

Obj lD- Particle type and charge, sometimes
some additional object speciﬁc information.
Integral (4B)

 

pT- Object transverse momentum
Float (4B)

 

Eta- Object physics pseudorapidity.
Float (4B)

 

Phi- Object azimuthal angle
' Float (4B)

 

Par[Oj- Object-dependent parameter (isolation,
neural net, likelihood)
Float (4B)

 

Par[1]- Object-dependent parameter
Float (4B)

 

Par[2]- Object-dependent parameter
Float (4B)

 

 

Par[3j- Object-dependent parameter
Float(4B)

 

Total Object Size: 32 B
Also save:
Weight infonnatlon (~123Iobject)

Global event Information and weights

Figure Biz The information stored in a high—pT object is shown. Basic information
is the same for all object types but four parameters are dependent upon the object

288

 

 

Table B.1: Additional parameters stored for each object in the
high-pT format.

 

 

 

 

 

 

 

 

 

 

 

Object par[0] par[1] par[2] par[3]

p Calorimeter Track Halo Curvature Track Hits
Halo Error

e EM Frac- Likelihood 8—variable Isolation
tion H-matrix

'7 NN4 NN5 X X

7' Output EM NN or X
NN Tracks PT

jet b—tag NN Negative taggability TRF / tag-

tag NN SF gable RF

 

0 Any two of ,u, e, T, ’7 with PT or ET > 12 GeV

0 7 and ET both with ET > 30 GeV

Since the reason behind the format is to use as little space as possible, additional
threshold cuts are required for an object to be included in the information stored in
the event. The focus of the analysis is on high-pT objects, so basic selection criteria

are also imposed on objects to be stored as part of the event. The following are the

list of criteria for each individual object to be stored as part of the event.

ppT>4GeV

6 ET > 10 GeV
7‘ ET > 10 GeV

7 ET> 15 GeV

289

 

 

e jet ET > 15 GeV

After the high-pT skim the datasets used in the analysis are signiﬁcantly reduced.
This allows all of the data to be stored on local disks. Differences in the event sizes
can be seen in Table B.2.

Table B2: Storage comparison for some of the datasets used in this analysis

comparing the standard D® CAF tree format and the reduced high-pT format
after the high-pT skim.

 

 

 

 

 

 

 

Sample CAF High- CAF High-
Tree Size pT Events pT
Size Events
EMinclusive 10.45 TB 5.5 GB 274M 19.9M
MUinclusive 8.83 TB 1.6 GB 267M 5.2M
W + Olp 499 GB 2.2 GB 12.8M 4.2M
Drell-Yan ,uu + 01p, M=75—130 116 GB 1.1 GB 3.0M 1.7M
Diboson 230 GB 1.6 GB 3.7M 1.2M

 

 

 

 

 

 

 

 

290

 

Appendix C

Calculation of 15

The probability that a discrepancy seen in a given SLEUTH ﬁnal state is due to a
statistical ﬂuctuation in the standard model background has been deﬁned as ’P. Once
the minimum value of this probability ’Pmm over all ﬁnal states is found, an additional
trials factor must be determined to account for the number of states that are checked.
The value 73 represents the probability of seeing a ﬁnal state as unlikely as the value
of Pmin based purely on the standard model background. This is determined by the

formula

I‘-

73: l—Ha(1—]5a), (C-l)

where (1 represents all SLEUTH ﬁnal states. The variable 13a is deﬁned as the minimum
of 77min and the probability of the total number of predicted events in a ﬁnal state
a to ﬂuctuate up to three data events. Three events is found to be the minimum
necessary to reasonably determine a value of 73 on the order of 0.001. A discussion

of the determination of the minimum number of events can be found in [91].

291

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