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MICHIGAN STATE UNIVERSITY
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This is to certify that the
dissertation entitled

Search for Evidence of Supersymmetry in the Like-Sign
Dimuon Channel at the DE Experiment

presented by

Adam Yurkewicz I

has been accepted towards fulfillment
of the requirements for the

PhD. degree in Physics

 

 

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6/01 cJCIRC/DathuopBS—pJS

 

SEARCH FOR EVIDENCE OF SUPERSYh’IIV’IETRY IN THE
LIKE-SIGN DIMUON CHANNEL AT THE DO EXPERIMENT

B y

Adam Yurkewicz

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

2004

ABSTRACT

SEARCH FOR EVIDENCE OF SUPERSYMMETRY IN THE LIKE-SIGN
DIMUON CHANNEL AT THE DO EXPERIMENT

By

Adam Yurkewicz

Supersymmetry (SUSY) is a pr(_)posed symmetry between fermions and bosons. If
this symmetry does exist. it, is clearly broken since only half of the particle spectrum
is observed. One model which provides a simple breaking mechanism is called minimal
supergravity (mSUGRA) inspired SUSY. One clean final state prmlicted by this model
is a trilepton final state from chargino and neutralino decays.

In this analysis. these events are sought in 23?) i 16 pl)‘1 of DC) Run II data by
requiring like-sign dimuon pairs. Requiring only two muons increases the signal accep-
tance, and adding the like—sign recmirement reduces the Standard Model background
from Drell-Yan dimuon pairs and the various resonances in the dimuon spectrum. The
reach into some parts of mSUGRA parameter space will be greater when searching
with the like-sign dilepton final state than the trilepton final state.

Combining results from a search in the like-sign dilepton channels with searches
in the trilepton channels provides increased sensitivity in the search for supersymme-
try. In this dissertation. the best-ever DC? limit on the total cross section for associated

chargino and neutralino production with leptouic final states is presented.

for Kati (3

iii

ACKNOWLEDGMENTS

First, I’d like to thank my thesis advisor. Jim Linnemann, who helped me from
my recruitment visit to MSU to the final days of writing this dissertation. During our
time working together on the L2 trigger and this analysis, he taught me an immense
amount, while convincing me that: I still have a lot to learn.

I’d like to thank professors Brock, \N’eerts, Abolins, and Pope for being the rest of
the core of the excellent MSU D0 group. and allowing me to be a part of it. Thanks
to Dan Edmunds for helping me with my paddle board project. I’d also like to thank
the other members of my thesis committee: professors Repko. h‘lahanti, and Sherrill.

This analysis was a collaboration with Reiner, Roger, and Jim, with early help
from Serban. I owe them gratitude for their technical help with the analysis as well
as their advice and wisdom. 1.\=‘Iany others in the New Phenomena group helped me
as well, including Volker, Custaaf, Greg. U lla. Ryan, hr-‘Iarc, and Meta.

I was lucky to work alongside Reiner, Reinhard, Roger, Dugan, Bob, Dylan, Josh
K., Joe, and Josh D. from MSU. and Christos. Marc. .\'Iiroslav. Jodi, and James from
L2. It was great working with all of you!

Thanks to everyone else in the DO collaboration that I didn’t mention here by
name. This dissertation wouldn’t. be possible without your years of hard work.

While at MSU, I studied (and didn’t study) with Josh, Joy, Dan, Cluze, and C—A.
Thanks for your friendship, knowledge, jokes. company, and weekly dinners.

Thanks, Mom and Dad, for a. lifetime of unconditional love. Knowing I can always
count on it has helped me immeasurably in my life.

Thanks to Charlie for being a great brother, my lifelong friends Dave and Mansoor
for being my lifelong friends, and all three for the Turkey Bowl.

And finally, thanks to Katie for her love, support, and encouragement over the

past five years, and for being my friend and companion in life.

iv

Contents

1 The
1.1

1.2
1.3
1.4

1.5

1.6
1.7

2 The
2.1

2.2

2.3

Standard Model and Supersymmetry

The Standard Model ...........................
1.1.1 Gauge Symmetries ........................
Limitations of the Standard Model ...................
Supersymmetry as an Extension to the Standard Model ........
Sparticle Spectrum ............................
mSUGRA .................................
The Trilepton Final State ........................
Like-Sign Dimuon Channel ........................
Fermilab Accelerators and the D0 Detector

The Fermilab Accelerators ........................
2.1.1 The Preaccelerator ........................
2.1.2 The Linac .............................
2.1.3 The Booster ............................
2.1.4 The Main Injector ........................
2.1.5 The Antiproton Source ......................
2.1.6 The Tevatron ...........................
2.1.7 The Recycler ...........................
The DC Detector .............................
2.2.1 Coordinate System ........................
2.2.2 Luminosity ............................
2.2.3 Silicon Microstrip Tracker ....................
2.2.4 The Scintillating Fiber Tracker .................
2.2.5 Preshower Detectors .......................
2.2.6 Calorimeter ............................
2.2.7 Muon System ...........................
The DC Trigger and Data Acquisition Systems ............
2.3.1 The Level I Trigger ........................
2.3.2 The Level II Trigger .......................
2.3.3 The Level III Trigger and Data Acquisition ...........

\IU‘MH

.9
10
11
13
14

15
15
16
17
17
18
18

30
37
41
42
45
48

3 Offline Event Reconstruction 50

3.1 Track and Vertex Reconstruction .................... 51
3.1.1 Track Algorithm ......................... 51
3.1.2 Selecting the Primary \I’ertex .................. 53
3.1.3 Bottom-Quark Jet Identification ................. 53

3.2 Muon Reconstruction ........................... 54
3.2.1 Muon Types and Qualities .................... 55
3.2.2 Muon Isolation .......................... 57

3.3 Jet Reconstruction ............................ 58
3.3.1 Jet Cone Algorithm ........................ 58
3.3.2 Jet Energy Scale ......................... 59

3.4 Electromagnetic Object Reconstruction ................. 60

3.5 Missing Transverse Energy Reconstruction ............... 61

4 Analysis 63

4.1 Data Set .................................. 63
4.1.1 l\~‘1t10n Selection Criteria ..................... 64

4.2 Trigger Efficiency ............................. 65
4.2.1 L1 Muon Trigger Efficiency ................... 66
4.2.2 L2 Muon Trigger Efficiency ................... 69
4.2.3 L3 Muon Trigger Efficiency ................... 69
4.2.4 Total Trigger Efficiency ...................... 69

4.3 Reconstruction Efficiencies and Smearing in Data and Monte Carlo . 70
4.3.1 Monte Carlo .\-‘Iomeutum Si'nearing ............... 70
4.3.2 Tracking Efficiency ........................ 71
4.3.3 Local Muon Efficiency ...................... 71
4.3.4 Muon Reconstruction Efficiency ................. 71

4.4 Backgrounds ................................ 73
4.4.1 Background From bb/CE Production .............. 76
4.4.2 Sign Misidentification Background ................ 83

4.5 Signal Monte Carlo ............................ 84

4.6 Analysis Cuts ............................... 87
4.6.1 Summary of Analysis Cuts .................... 92

4.7 Comparison of Expected Background to Data ............. 93

4.8 Combining Results with Other Channels ................ 98
4.8.1 CLS Method ........................... 100

4.9 Cross Section Limit ............................ 102

5 Conclusions 106

5.1 The Future of the Analysis at DC) ................... 106

5.2 The Future Beyond DO ......................... 109

vi

A L2 Global Worker

A.1 Input ....................................
A.2 Trigger Bits and Scripts .........................
A.3 Tools and Filters .............................

A.3.1 Tools and Filters Currently Available ..............

A.3.2 Tools and Filters Used in this Analysis .............
A.4 Output ...................................
A.5 Code Design and Structure ........................

B L2 Error Logger
B. 1 Motivation .................................
82 Architecture ................................
8.3 User Interface ...............................

C Paddle Board for Hardware Sealers
Bibliography ...................................

vii

110
111
111
113
114
114
119
119

121
122
123
124

126
131

List of Figures

1.1

1.2

1.3

1.4

2.1
2.2

2.3

2.4
2.5

2.6

2.7

Feynman diagram showing the electromagnetic interaction between
two electrons mediated by the exchange of a photon. .........

Evolution of the coupling strengths as a function of energy in the Stan-
dard Model, where on corresponds to U(1) (electromagnetic force), 02
corresponds to SU(2) (electroweak force). and 03 corresponds to SU (3)
(strong force). Diagram from [6] ......................

The evolution of the coupling strengths as a function of energy in
supersymmetry, where (11 corresponds to U(1) (electromagnetic force),
a2 corresponds to SU(2) (electroweak force), and (13 corresponds to
SU(3) (strong force). Diagram from [6]. ................

Feynman diagrams showing chargino (\f) and neutralino ({3) pro-
duction and decay to three leptons and other particles including neu-
tralinos ()2?) through a) intermediate smuons ([1) and b) intermediate
virtual gauge bosons ...........................

Schematic diagram of the Fermilalg) accelerator chain. .........

The DC detector, including the tracking system, calorimeter, and muon
system ....................................

The DO tracking system surrounding the beam pipe. including the
silicon barrels and disks and the fiber tracking ..............

Diagram of the DO) silicon barrel detector. ...............

An F disk, part of the DO silicon detector. Each of the 12 individual
wedges is approximately 7.5 cm in length. ...............

Photograph of wedge used in F disk in the DO silicon detector. The
wedge is approximately 7.5 cm in length. Also visible are the SVX II
chips used to read out the detector. ...................

a) Diagram showing the location of the DO central fiber tracker. b)
Closeup view showing the axial and stereo layers of scintillating fibers
attached to detector barrels ........................

viii

10

13
16

20

24
25

26

27

2.8

2.9

2.10

2.11

2.12

2.13

2.14

2.15

2.16

2.17

2.18

2.19

2.20
2.21
2.22

Simulation of the transverse momentum (pT) resolution of the tracking
system as a function of pseudorapidity for tracks with pT : 1.10,
and 100 GeV/c ...............................

End view of the DC?) central fiber tracker .................

Insertion of the central fiber tracker into the DO (’letector. inside the
calorimeter. ................................

a) Diagram showing the locations of the central (CPS) and forward
(FPS) preshower detectors, outside the central fiber tracker (CF T).
b) End view of the CPS, including a closeup view of the three layers
of scintillator strips. Not drawn is the tapered lead radiator, which is
between the solenoid and the preshower detector. ...........

The solenoid’s radiation and nuclear interaction lengths as functions
of pseudorapidity. Diagram from [22] ...................

Thickness of lead needed to yield a constant 2X0 (2 radiation lengths)
for all particle trajectories. Diagram from [22] ..............

A portion of the DO central preshower detector, a thin cylindrical
detector mainly consisting of scintillating fibers. ............

The DC calorimeter. composed of layers of heavy metals and liquid
argon. ...................................

The DO calorimeter sitting inside the DO detector outside of the col—
lision hall during the period between Run I and Run II .........

A DC calorimeter cell with alternating layers of absorber plates, liquid
argon, and signal boards. Many cells form the layers of the calorimeter.
Absorber plates can vary in size, but the gap between the absorber
plate and the signal board is always 2.3 mm ...............

The DC muon system. including scintillator (scint) and proportional
and mini-drift tube chamber layers (PDT and MDT) ..........

A muon proportional drift tube unit cell consisting of an anode sense
signal wire in a gas-filled chamber and two sets of cathode pads. . . .

A proportional drift tube unit cell viewed from above ..........
Part of the C layer of the DO forward muon system. .........

A single 4.5 degree central fiber tracker (CFT) sector along with a
hypothetical track and hits in all eight CFT layers and the central
preshower (CPS) axial layer ........................

28

29

30

31

32

33

34

35

36‘

37

38

39
39
40

4.1

3.1

3.2

4.1

4.2

4.3

4.4

4.5

4.6

4.7
4.8

4.9

The muon isolation variable in the calorimeter. The energy contained
in a cone of radius 0.1 around a muon is subtracted from the energy
contained in a cone of radius 0.4. ....................

The electromagnetic (EM) isolation variable (iso) in the calorimeter.
The energy measured in the central preshower (CPS) detector is not
used in the calculation. Energy measured in the EM, fine hadronic
(FH), and coarse hadronic (CH) layers are used in the calculation.
Diagram from [41]. ............................

a) The L1 trigger efficiency as a function of pT with respect to loose,
'nscg : 3 muons. b) The L1 trigger efficiency as a function of 77 with
respect to loose, nscg 2: 3 muons with pT greater than 5 CeV/c. . . .

a) The L2 trigger efficiency as a function of 7} with respect to loose.
nseg : 3 muons with pT greater than 5 CeV/c. b) The L3 trigger
efficiency as a function of pTwith respect to loose, nseg = 3 muons.

a) Tracking efficiency as a function of 77 with respect to local muons in
the J / ‘11 peak measured in data. b) Tracking efficiency of reconstructed
muons as a function of n with respect to Monte Carlo (MC) muons.

Tracking efficiency measured in data divided by the Monte Carlo (MC)
tracking efficiency as a function of 7) with respect to local muons in the

J/‘Il peak. .................................

a) The loose muon efficiency as a function of 7} with respect to tracks
measured in data. The tracks are from muon-track pairs with an in-
variant mass that lies under the Z peak. b) The loose muon efficiency
as a function of 7} with respect. to Monte Carlo (MC) muons. .....

The loose muon efficiency as measured in data divided by the Monte
Carlo (MC) local muon efficiency, as a function of 7) with respect to
local muons in the Z peak .........................

The total muon reconstruction efficiency as a function of I] .......

The measured Act between muons in like—sign nmon pairs in the data
for the cases where both muons are isolated and only one is isolated. .

R, the ratio of the number of events in the sample with two isolated
muons to the number of events in the sample with one isolated muon, as
a function of the pT of the nearly isolated muon. The line is an exponen-
tial function fit to the data which was used to weight the background
sample in modeling the bb background ..................

61

67

68

72

73

74

77

80

4.10

4.11

4.12

4.13

4.14

4.16

4.17

4.18

4.19

4.20

a) Circles show the invariant mass distribution of opposite—sign muon
pairs. Backgrounds are described by the legend. b) Circles show the
invariant mass distribution of opposite-sign muon pairs after the sub-
traction of Monte Carlo background estimates. The shaded histogram
is the expected remaining background from bb/cE, which is estimated
using like-sign data .............................

Circles show the invariant mass distribution of isolated like-sign muon
pairs in data. The shaded histogram is the expected remaining back-
ground, from bb/CE, which is estimated using the nearly isolated like—
sign data as described in the text .....................

The pT spectrum of opposite-sign muon pairs as measured in data.
These muons could be used to estimate the pool of candidates for sign
mismeasurement. .............................

The cross section times branching ratio into three leptons as a. function
of the m0 parameter. ...........................

The cross section times brancl'iing ratio into three leptons as a function
of the mass of the chargino. .......................

The pT distribution of muons in the bfi background sample and in a
signal Monte Carlo sample (SUSY point 14) ...............

The Adm, ,u) distribution in the b5 background sample and in a signal
Monte Carlo sample (SUSY point 14). .................

The scaled missing transverse energy distribution in the bb background
sample and in a signal Monte Carlo sample (SUSY point 14) ......

The distance in d) (A¢)(MET, Jet)) between the direction of the missing
transverse energy (MET) in the event and the jet furthest away from
the direction of the MET in the bb background sample and in a signal
Monte Carlo sample (SUSY point 14). .................

The distribution of missing_ transverse energy multiplied by the pT of
the lower pT muon in the bb background sample and in a. signal Monte
Carlo sample (SUSY point 14). .....................

Event display of the event passing all cuts in data, event number
44096517 from run 177010. In the middle of the display, reconstructed
charged—particle tracks can be seen. The green lines represent muons
traversing the detector ...........................

xi

81

82

84

86

86

88

88

89

90

91

98

4.21 Event display of the event. passing all cuts in data, event number
44096517 from run 177010. Reconstructed tracks are visible in the cen-
ter of the display. The red, orange and green bars are hits in the A, B,
and C layers of the muon system. ....................

4.22 Event display of the event passing all cuts in data, event number
44096517 from run 177010. Reconstructed tracks are visible in the cen-
ter of the display. The red, orange and green bars on the outer part of
the display are hits in the A, B, and C layers of the muon system. The
red and blue blocks represent energy in the calorimeter and the yellow
block represents missing energy. .....................

4.23 Limit on the total cross section for associated chargino ()2?) and neu-
tralino ()23) production in the like-sign dimuon channel as a function
of the )2]: mass. ..............................

4.24 Limits on the total cross section for associated chargino ()2?) and neu-
tralino ()23) production with leptonic final states set by DC in Run I
(top line) and in this analysis (second from top) in comparison with
the expected limit. (second from bottom) and the signal cross section
predicted for in mSUGRA (bottom line) as a function of the )21i mass.
Chargino masses below 103 GeV/c2 are excluded by direct searches at
LEP. The DC Run I limit was based on searches in the see, ecu, can,
and mm trilepton final states with between 75 pb‘1 and 95 pb‘1 of
integrated luminosity ............................

A.1 Data flow from the detectors to the L2 Global worker ..........

B.1 Simplified Unified Modeling Language (UML) diagram showing the
major classes in the l2errorlogger package and the relationships be-
tween them. ................................

C.1 The paddle board. Picture courtesy of Kathleen 'Yurkewicz. . . . . . .

C.2 Design diagram of the paddle board, showing the connectors and traces
connecting them. .............................

C.3 A pie chart and corresponding legend showing the amount of time spent
in each state for the Global worker. ...................

IMAGES IN THIS DISSERTATION ARE PRESENTED IN COLOR.

xii

99

100

104

105

112

122
127

128

List of Tables

1.1

1.2

1.3

1.4

4.1

4.2

4.3

4.4

4.5

The fundamental forces and the 1i)articles (gauge bosons) mediating
those forces .................................

The fundamental particles of the Standard Model and some of their
properties. Le, Lfl, and L, are the electron, muon, and tau lepton num-
bers. For every particle there is a corresponding antiparticle. .....

The fundamental particles of the Standard Model grouped into gener-
ations. The main difference between the generations is the masses of
their particles ................................

The particles of the Standard Model and their corresponding sparticles
in supersymmetric models .........................

The sizes, calculated cross sections, and integrated luminosities of the
Monte Carlo (MC) samples. .......................

The values for the 20 points in mSUGRA parameter space chosen for
study, the cross section times branching ratio to trileptons for each
point, the masses of the two neutralinos ()23 and )23), chargino (2?),
and slepton (f) for each point, the number of events expected (Nexp) for
239 pb‘”1 of data and the efficiency (E) for each point. The mSUGRA
parameters are defined in Section 1.5. The sign )1 parameter is always

positive. Points in bold are used in setting a limit in Section 4.9. . . .

Number of events after applying each cut to signal Monte Carlo samples
for points 1—12. Total errors (sum of statistical and systematic) are in
parentheses. ................................

Number of events after applying each cut to signal Monte Carlo samples
for points 13-20. Total errors (sum of statistical and systematic) are
in parentheses. ..............................

Number of events remaining in bb, WZ, ZZ, tf, be, W’, \N’jj, Wbb,
Z / 7 background samples after applying each cut to the samples. Total
errors (sum of statistical and systematic) are in parentheses. .....

xiii

94

96

4.6

4.7

4.8

4.9

A1

A2

A3

A4

A5

B.1

Number of events remaining in data and the number expected from
the sum of all backgrounds after applying each cut. Total errors (sum
of statistical and systematic) are in parentheses .............

Table showing the kinematic values for the two muons and MET in
run 177010, event 44096517. .......................

Luminosity, number of observed candidate events, expected number of
background events for each final state used in determining the com—
bined cross section limit, and the excluded number of signal events

(Newuded) ..................................

For the SUSY points, the cross section times branching ratio to trilep-
tons, the mass of the chargino ()23), the number of events expected
(Nexp) and the efficiency (E) for each point for 239 pb‘1 of data, and
the cross section limit in the like—sign dimuon channel (0%,) and overall

(offfif’). Points in bold are used in Figures 4.24 and 4.23 ........

L2 tools currently available. For each tool. the configurable parameters
are listed, along with a brief description [61] ...............

L2 tools currently available. For each tool. the configurable parameters
are listed, along with a brief description [61] ...............

L2 filters currently available. For each filter, the configurable parame-

ters are listed, along with a brief description [61]. ...........

L2 filters currently available. For each filter, the configurable parame-
ters are listed, along with a brief description [61]. ...........

L2 filters currently available. For each filter, the configurable parame-
ters are listed, along with a brief description [61]. ...........

The available severity levels in the l2errorlogger .............

xiv

97

98

99

116

117

118

124

Chapter 1

The Standard Model and

Supersymmetry

The Standard Model of particle physics is a quantum field theory which encapsulates
the knowledge of fundamental particles and forces. It identifies structureless, elemen-
tary particles that constitute all the observed matter in the universe—~these are the
quarks and leptons. The interactions between the quarks and leptons are mediated
by particles called gauge bosons (see Table 1.1). The Standard Model provides the
theoretical framework to calculate physical (measurable) quantities. explain observed
phenomena, and make predictions that can be checked experimentally. Most of these
predictions have been confirmed to spectacular precision (many at Fermilab), which
has given the Standard Model its name and made it the theoretical framework in
which particle physics currently resides.

Despite its many successes. there is consensus among particle physicists that the
Standard Model is not the final theory of particle physics. This dissertation is con-
cerned with the search for evidence of supersymn‘ietry, one of the proposed extensions
to the Standard Model.

Much of the description of the Standard Model in this chapter draws heavily

 

 

Force Particles Mediating Particles Experiencing
strong gluons (g) quarks, gluons
electromagnetic photon (q) electrically charged
weak W +, W'", Z0 quarks, leptons
gravitation graviton (unobserved) all

 

 

 

 

 

Table 1.1: The fundamental forces and the particles (gauge bosons) mediating those
forces.
from references [1—3]. These excellent texts should be consulted for a more thorough

introduction to the Standard Model.

1.1 The Standard Model

The familiar matter of everyday life is made of molecules. These molecules are built
from atoms, which in turn are built from protons, neutrons. and electrons. Protons
and neutrons are made of quarks. Electrons and neutrinos are examples of leptons.
Quarks and leptons are spin 1 / 2 fermions. Spin 1 gauge bosons are responsible for the
exchange of forces between quarks and leptons. Quarks, leptons, and gauge bosons
(and their antiparticles) are the particles of the Standard Model.

The Standard Model is a quantum field theory. It postulates that several fields,
one for each type (also called flavor) of particle. permeate all space and interact with
each other. Excitations in these fields are observed as particles.

The flavors and properties of the Standard Model particles are summarized in
Table 1.2. The quarks and leptons can be arranged in generations (see Table 1.3).
The grouping of Table 1.3 highlights the sin'iilarities between these gei'ierations.

Different combinations of quarks form the spectrum of particles called hadrons.
The hadrons are divided into baryons (three quark fermion states) and mesons (two
quark boson states). One baryon, the proton, is made from the combination {uud}.

The charge of the proton (in units of the electron charge) is the sum of the charges

 

 

 

 

 

 

 

 

 

Flavor Electric Spin Mass (GeV) Baryon Le LI, LT
] Charge (e) ] Number ] ]
Quarks
u (up) +2/3 1/2 00015—0004 1/3 0 0 0
d (down) —1/3 1/2 0.004—0008 1/3 0 0 0
c (charm) +2/3 1/2 1.15—1.35 1/3 0 0 0
s (strange) —1/3 1/2 0.08—0.13 1/3 0 0 0
t (top) +2/3 1/2 178 1/3 0 0 0
b (bottom) —1/3 1/2 4.1—4.4 1/3 0 0 0
Leptons
e (electron) -1 1/2 0.511 x 10*3 0 1 0 0
11,, (electron neutrino) 0 1/2 <3 x 10“9 0 1 0 0
u (muon) -1 1/2 0.106 0 0 1 0
14, (muon neutrino) 0 1/2 <1.9 x 10‘4 0 0 1 0
r (tau) —1 1/2 1.78 0 0 0 1
11, (tau neutrino) 0 1/2 <1.8 x 10‘2 0 0 0 1
Gauge Bosons
Wi (charged weak) :l:1 1 80.4 0 0 0 0
Z0 (neutral weak) 0 1 91.2 0 0 0 0
'7 (photon) 0 1 0 0 0 0 0
g, (i:1,...,8 gluons) 0 1 0 0 0 0 0
g (graviton) 0 2 0 0 0 0 0

 

 

 

 

 

 

 

 

 

 

Table 1.2: The fundamental particles of the Standard Model and some of their prop-
erties. Le, L“, and L, are the electron, muon, and tau lepton numbers. For every
particle there is a corresponding antiparticle.

 

 

 

 

 

 

Generation 1 Generation 2 Generation 3
u c t
d s b
e p. T
we 11), 11,

 

Table 1.3: The fundamental particles of the Standard Model grouped into generations.
The main difference between the generations is the masses of their particles.

of its constituent quarks. 2/3 + 2/3 + (—1/3) : +1, its baryon number is 1, and its
lepton number is 0 (baryon number and lepton number are additive quantum numbers.
See Table 1.2). A neutron is made with the combination {udd}. It has electric charge

2/3 + (—l/3) + (—1/3) = 0, baryon number 1, and lepton number 0. The fundamental

 

e- 8"

Figure 1.1: Feynman diagram showing the electromagnetic interaction between two
electrons mediated by the exchange of a. photon.

similarity between neutrons and protons is evident using this scheme. The success of
the quark model in explaining and predicting other experimentally observed states
led to its acceptance.

There are problems with this simplistic view. The conilnnation {uuu} has been
observed as the A++ baryon. The existence of the AH presents a problem because
its spin, J : 3/ 2, is obtained by combining three identical fermions which violates
Fermi statistics. Another problem is that neither combinations of more than three
quarks or single quarks are observed (Recent results have raised the possibility of the
existence of pentaquark states. which were recently predicted to exist [4]).

The solution to these problems is the introduction of another quantum number
called color. It can have one of three values. called red (R), green (G). and blue (B),
with antiquarks having the values R, G, and B (These names have no connection to
the colors of the macroscopic world). In this theory, bound states nmst be colorless,
so mesons are formed from one quark and one antiquark which carry a color and its
anti-color (like RR), while baryons are formed from three quarks, one of each color.
Thus the 13“” baryon consists of one u quark of each color.

Interactions between quarks and leptons are mediated by gauge bosons. Photons

are the mediators of the electromagnetic interaction. Feynman diagrams like the one in

Figure 1.1 show pictorially how electromagnetic interactions between particles occur
through the exchange of photons.

Color is exchanged between quarks and gluons (both of which carry a color charge),
much as electric charge is exchanged between electrically charged particles. Gluons
are colored objects that carry color charge as the mediators of the strong force. Unlike
photons, which mediate a force that gets weaker with distance, gluons are responsible
for a binding force that strengthens with distance. Gluons (and quarks) are colored, so
cannot be observed directly because bound states are formed only as colorless objects.
This behaviour is called color confinement. Eventually, when colored objects are pulled
apart from other colored objects (as occurs in high-energy collisions), the energy
released is converted into new colored objects, and colorless objects are formed from
groups of the colored objects. Only colorless objects are observed in particle detectors,
and they are detected as streams, or jets, of particles. It should be emphasized that
leptons do not carry a color charge, and thus do not. feel the strong force. This is the
main distinction between quarks and leptons.

The weak bosons (“if and Z0) mediate the weak force, which is responsible for
radioactive decay. The fact that weak gauge bosons are massive, unlike photons, limits
the distance over which they are effective. It is currently unknown how the weak gauge

bosons acquire masses. One leading theory is the Higgs mechanism (see Section 1.1.1).

1.1.1 Gauge Symmetries

The strong, weak. and electromagnetic forces can be described as a combination of
three unitary gauge groups, denoted as SU(3) Ci? SU(2) X U(1) [2]. The group SU(3)
is the symmetry group of strong interactions. U( 1) describes electrmnagnetic interac-
tions, and SU(2) X U(1) represents the unified weak and electromagnetic interactions.

The symmetries referred to are gauge (phase) symmetries. These symmetries are of

prime importance in particle physics. To illustrate. consider that (:)l_)servables depend

on the wave function squared (I‘I'lz) and not on the wave function. Therefore, the

transformation

\II —+ \I/ : e‘mflhp (1.1)

where x(f, t) is an arbitrary phase which can depend on space and time coordinates,
should leave the observables unchanged. That is, the theory should be locally gauge
invariant. Physically, since the absolute phase cannot be measured, the choice of phase
should not matter. If one successively inserts \I' and ‘11, into the simple Schrodinger
equation for a matter particle,
21—2, 2 \IJ(.1'7'.t) : z————————, (1.2)
the equation is clearly not invariant under the transformation of Equation 1.1. If \I/
satisfies the equation, ‘11, may not since the derivatives may not. cancel.

One can modify the Schrodinger equation to guarantee gauge invariance. For elec-
trically charged particles, the modified Schrodinger equation is

1 . ,- ‘2 __ .- 0 ,
_ (-'l v +(d4) \Il .-_ (IT)? + Cl/ ) ‘1’, (1.3)

2m ( ,

where e is the electric charge. V is the electric potential, and 2f is the vector poten-
tial. With this change, the Schrodinger equation is invariant under the simultaneous

transformations (1 . 1) and

l 1
A-—>A=A+-V\" (1-4)
6
V V : V— -.—. 1.."
—+ edt ( 3)

Thus, the re uirement that the theory be locally an e invariant leads to the re uired
. . g g (1
presence of a field A“ :(V;A). Further, since particles are viewed as excitations in

fields in this theory, the requirement of gauge invariance also leads to the presence of

gauge bosons.

In the Standard Model, phase symmetries (mathematically, re(’{uirements that the
theory be invariant under gauge transformations) are used to guide the construction
of theories. The gauge fields and particles follow naturally from these symmetries.

The gauge theories introduced above can involve only massless gauge bosons. How-
ever, massive gauge bosons (\VJ‘ . Z”) have been observed experimei‘itally. Evidence of
a. mechanism that causes the gauge bosons to acquire their masses is highly sought
in particle physics. Currently, the leading candidate is the Higgs mechanism.

Peter Higgs conjectured in 1964 that the massless gauge bosons of weak inter-
actions acquire their mass through interaction with a scalar field (the Higgs Field),
resulting in a single massless gauge boson (the photon) and three massive gauge
bosons (Wi and 20) [5]. The assumption is that. the universe is filled with a spin-zero
field, called the Higgs field. The gauge bosons’ and fermions’ interactions with this
field give them their masses. This intm'action, in which the particles gain masses, is an
example of spontaneous symmetry breaking. in which the SU(2) and U(1) symmetries

are broken.

1.2 Limitations of the Standard Model

There are indications that the Standard Model is not. the final theory of particle
physics and that more fundamental physics is left to be discovered. Experiments
in the years ahead will give insight into which, if any. of the proposed theoretical
extensions to the Standard Model is correct.

One reason for the need to extend the Standard Model is that the gauge bosons
are massive. Several theories. including supersymmetry. have been proposed which
include the Higgs mechanism to give the gauge bosons masses.

A second reason arises from the fact that several theoretical unifications of forces

Coupling Constant Evolution
Standard Model
010 , . . . .

 

33‘ 0.05

 

 

 

 

0.00 ‘ ' '

2.0 I 4.0 6.0
t=|og(Q/MZ)/27t

Figure 1.2: Evolution of the coupling strengths as a function of energy in the Standard
Model, where 01 corresponds to U(1) (electromagnetic force). (12 corresponds to SU(2)
(electroweak force), and (13 ccn‘responds to SU(3) (strong force). Diagram from [6].
have already occurred. Electricity and magnetism were once thought of as unrelated,
as were the electromagnetic and weak forces. Thus. many theorists expect that a
theory that unifies all of the forces should be the final theory. The Standard Model
separates the unified electroweak forces from the strong force. and does not include
gravity.

The fundamental forces are each characterized by a coupling strength. The cou—
pling strength appears in all physical calculations. and is indicative of the strength
of the interaction. These coupling strengths have a dependence on the interaction
energy; more precisely, they depend on the momentum transfer between two particles

involved in an interaction. Figure 1.2 shows the values of the coupling strengths as

a function of a parameter that depends on the interaction energy. 'I‘heoretical calcu-
lations in the Standard .\-<lodel predict that the coupling strengths are closer at high
energies than at lower energies. The experimental data taken so far agrees. However,
the coupling strengths will not meet exactly without the existence of some new physics
which affects their dependence on the energy. Supersymmetry is one candidate for
this new physics.

A third reason for introducing an extension to the Standard Model is revealed
when calculations using the Standard Model framework include a Higgs boson. The
inclusion of the Higgs boson leads to unphysical results in some calculations. Pertur—
bative calculations of the mass of the Hi ggs boson squared have quadratic divergences.
Infinite terms appear in the sum. It is theoretically possible to introduce counterterms
in the perturbation series which cancel these divergences. but this has no physical jus-

tification, and has been considered unnatural.

1.3 Supersymmetry as an Extension to the Stan-

dard Model

Supersymmetry is a proposed symmetry which relates fermions to bosons [3,649].
It postulates that for every particle there is a corresponding sparticle, identical to
the particle but with a spin different. by 1/2. If it exists, s1.11.)ersymmetry must be a
broken symmetry because no sparticles have been detected with masses equal to the
Standard Model particles.

Supersymmetry solves the problems raised in Section 1.2. It includes lliggs bosons
to give particles mass. It also modifies the evolution of the coupling constants so that
they unify at a high energy (see Figure 1.3). It introduces new terms into the calcu-
lation of the Higgs mass squared which cancel the terms that lead to the quadratic

divergence.

Coupling Constant Evolution
SUSY Model

 

v ' ' '

 

 

 

 

0.00 - ‘ - . ‘
2.0 4.0
t=|og(Q/MZ)/2rt

6.0

Figure 1.3: The evolution of the coupling strengths as a function of energy in su-
persymmetry, where (11 corresponds to U(1) (electromagnetic force). (12 corresponds
to SU(2) (electroweak force). and 03 corresponds to SU(3) (strong force). Diagram
from [6].

Additionally, the Lightest Supersymmetric Particle (LSP) is stable and is a dark
matter candidate. Heavy. stable. neutral particles that are predicted in supersymme-
try could provide some of the missing mass of the universe which has been inferred to
exist through measurements of large—scale gravitational effects [10]. Supersymmetry

is thus a very intriguing extension to the Standard Model.

1.4 Sparticle Spectrum

The proposed spectrum of supersynnnetric particles (sparticles) in mSUGRA (see

Section 1.5) is shown in Table 1.4. Note that in supersymmetry there are multiple

10

 

 

 

 

 

 

 

Particle Spin Sparticle Spin
lepton 1/ 2 slepton O
neutrino , 1 / 2 sneut riuo 0
quark 1/2 squark O
gluon 1 gluino 1/2
W 1 chargino (1.2) 1/2
charged Higgs 0
Z 1
A] 1
light Higgs 0 neutralino (1.2.34) 1/2
heavy Higgs 0
pseudoscalar lliggs f)

 

 

 

 

 

 

 

Table 1.4: The particles of the Standard Model and their corresponding sparticles in
supersymmetric models.

Higgs bosons (four in two doublets). and that the observable sparticles are formed
as mixtures of the superpartners of the Standard Model particles. The superpart-
ners are technically flavor eigenstates. There is one flavor eigenstate corresponding to
each degree of freedom of the Standard Model particles. The observable spectrum of

sparticles (the mass eigenstates) are linear combinations of the flavor eigenstates.

1.5 mSUGRA

Supersymmetry in its most general form has roughly 370 free paraiméters. The Stan-
dard Model without supersymmetry has about 30 free parameters. The number of
free parameters in supersymmetry makes it impossible to make testable predictions
based on the most general form of the theory. Theorists have worked on reducing the
number of free parameters in supersymmetry by making assun'iptions.

The number of free parameters in supersymmetry can be reduced to about 100 by
introducing a quantity called R.-parit.y, which prevents rapid proton decay. R—parity
is defined as:

R _,___ (_1)3(B—L)+2.S'q (1.6)

11

where B is the baryon number, L is the lepton number, and S is the spin of the
particle.

The Standard Model particles have an R-parity of +1. the sparticles have an R-
parity of —1, and the product of R-parity at all interaction vertices must be +1. As
a result of the introduction of R-parity. sj.)articles are produced in pairs, a Sparticle
decays to another Sparticle plus a Standard Model particle, and the LSP is stable.

Other assumptions can be made to further reduce the dimension of the unknown
parameter space. In the minimal su pergravit y (mSUGRA) framework, supersymmetry
is broken at a very high energy scale. A theory that includes gravity operates at.
very high energies, and the broken supersymmet.ry is only an effective theory at low
energies. The masses of the sparticles are functions of the interaction energy and are
unified at the high energy scale.

In mSUGRA, there are only 5 free parameters which must be specified to make
the theory completely predictable. The free parameters. set at some very high energy

scale MX, are:

a mo : common mass for all of the scalar sparticles at the Mx scale
a ml/g : common mass for all of the gaugino sparticles at the Mx scale

0 A0 : parameter that describes the mixing of the left and right stop quarks at

the Mx scale

tan /3 : ratio of the Higgs doublets’ vacuum expectation values

sign(n) : Higgsino mixing parameter.

The search for evidence of supersymmetry in this dissertation is done within the

InSUG RA framework.

12

 

 

(a)

 

 

-si+

(b)

Figure 1.4: Feynman diagrams showing chargino (\f) and neutralino (\3) production
and decay to three leptons and other particles including neutralinos ((3) through a)
intermediate smuons ([1) and b) intermediate virtual gauge bosons

1.6 The Trilepton Final State

Within the mSUGRA framework. calculations have been performed to predict signals
which may be detectable using the DO detector (see Chapter 2). One such signal
would occur with the associated production of chargino and ruxutralino sparticles (see

Figure 1.4). These unstable sparticles will decay. with only stable LSPs leaving the

13

detector. The decays of the chargino and neutralino can produce three leptons. Thus
the final state would be three leptons plus missing energy from the LSPs. The trilepton
final state has been called the “golden mode" for discovering supersymmetry because

it is an uncommon final state in the Stai'idard Model.

1.7 Like-Sign Dimuon Channel

In this dissertation, trilepton events are searched for by requiring pairs of leptons
with the same sign of electric charge. This serves to increase the signal acceptance by
requiring that only two out of the three leptons be detected. The requirement that
the two leptons have the same sign of electric charge is introduced to remove the
large background from opposite—sign lepton pairs. The background is created in the
Drell-Yan process when a quark and antiquark annihilate through a virtual photon
to produce opposite-sign lepton pairs. Other Standard Model sources of opposite-
sign lepton pairs include the decays of resonances such as the J / \11, T, and 20. This
dissertation is restricted to the study of the like—sign dimuon final state.

A key requirement for muons in this analysis is that they be isolated. Muons
produced in association with jets (quarks) must be rejected. as muons from the signal
should be produced in decays not involving jets. Muons produced with jets constitute
a large background, mainly from the (:lecay of B mesons. More. on this background

and others appears in Chapter 4.

l4

Chapter 2

The Fermilab Accelerators and the

DO Detector

Fermilab operates a series of accelerators in order to collide protons and antiprotons
at a center-of-mass energy of 1.96 TeV [11—13]. The final accelerator in the chain is the
Tevatron, the world’s highest energy particle accelerator. The DO and CDF detectors
surround the interaction regions where the collisions occur. The accelerators and the
DO detector are described in the following sections.

The data used in this thesis were obtained during the data taking period known
as Run II, which officially began in March. 2001. The previous data taking period,

from 1992 to 1996, is known as Run I.

2.1 The Fermilab Accelerators

A chain of accelerators is necessary to produce and collide protons and antiprotons.
The Cockroft-Walton preaccelerator. the linear accelerator (Linac). the Booster syn-
chrotron, the Main Injector, the Antiproton Source. the Tevatron. and the Recycler

work in series, with each using the particles passed to it from the. accelerator preceding

FERMILAB'S ACCELERATOR CHAIN

/ :1 .. \MAIN INJECTOR
A f \

   
 
     
 

TEVATRON

\i;/ TARGET HALL

ANTIPROTON
SOURCE

   

‘ BOOSTER
_ LINAC

\
COCKCROFT-WALTON
PROTON

 

Figure 2.1: Schematic diagram of the Fermilab accelerator chain.

it. Figure 2.1 shows a schematic diagram of the Fermilab accelerator chain.

2.1.1 The Preaccelerator

The preaccelerator consists of an ion source, a Cockroft-Walton generator and ac-
celerator column, and a transport line to the Linac. It is responsible for delivering
negatively charged hydrogen ions with an energy of 18 keV. The source of the hydro—
gen ions is a sample of hydrogen gas.

An oval~shaped cathode surrounded by an anode sits in a magnetic field. Injec—
tion of the hydrogen gas into this environment. creates a plasma. Charged particles

randomly strike the cathode and sputter off hydrogen atoms which have been ab—

sorbed on the surface. These negatively charged ions are accelerated to 750 keV by a
commercial Cockroft-VValton generator and accelerator column.

Once generated, the ions move into a transport line. Inside the transport line. a
single gap radio frequency (RF) cavity bunches the beam at the RF frequency of the

Linac. The ions are then transferred to the Linac.

2.1.2 The Linac

The Linac accelerates the beam of ions to 400 .\[eV using RF cavities. The Linac is
a collection of steel tanks, each filled with a series of drift tubes se1_)arated by small
gaps. The tubes are constructed such that a particle experiences accelerating fields
when it is between drift tubes and is shielded from the decelerating fields while in
the tubes. This requires the particle to pass through progressively longer tubes as
it accelerates in order to maintain a constant phase with respect to the accelerating

field. After acceleration. the ions are debunched and injected into the Booster.

2.1.3 The Booster

The Booster is a synchrotron which accelerates protons to 8 GeV. It consists of a
series of 96 magnets interspersed with 17 RF cavities in a circle with a radius of
75 n1.

Negatively charged hydrogen ions are transfered in bunches from the Linac to the
Booster. The first bunch of ions passes through a thin carbon foil as it enters the
Booster to remove the electrons from the ions. The next bunch of ions from the Linac
can then be merged with the proton. beam using a single magnetic field. The ions
then have their electrons removed using the carbon foil. This is repeated with all of
the ion bunches.

This technique is far better than attempting to accelerate protons in the Linac and

17

consequently be required to add more protons to a proton beam already circulating
in the Booster. That scheme would disturb the proton beam already circulating in
the Booster.

The protons in the Booster are accelerated as the RF frequency of the Booster
is increased. The magnets are ramped up synchronously to keep the particles in an
orbit of constant radius. The protons are again bunched in this process. They are

next passed to the Main Injector synchrotron.

2.1.4 The Main Injector

The Main Injector was built for Run II, to replace the Main Ring. The Main Ring.
which accelerated protons for use in the Tevatron in Run 1, was replaced by the Main
Injector for several reasons.

First, because it was in the same tunnel as the Tevatron, the Main Ring passed
through the region where the detectors were located. This required the construction
of overpasses to carry the Main Ring beam over the experiments. which negatively
affected the beam. Second, beam losses inside the DC) detector compromised detector
data. Third, stray fields from the Tevatron disturbed the beam in the Main Ring.

To alleviate these problems. a new tunnel was built adjacent to the Tevatron
to house the Main Injector. The Main Injector accelerates protons from 8 GeV to
150 GeV for insertion into the Tevatron. and accelerates protons to 120 GeV for use

in the Antiproton Source.

2.1.5 The Antiproton Source

The target used for production of antiprotons is a small nickel disk. Protons with
120 GeV of energy strike the nickel disk target and produce a spray of particles. The

spray contains antiprotons, which are selected using a dipole magnet. The ant iprotons

18

are directed to the Debuncher, where their momentum spread is reduced. They are
then stored in the Accumulator. Once a large enough stack of antiprotons is available,

it is transferred to the Main Injector and accelerated to 120 GeV,

2.1.6 The Tevatron

The Tevatron is the world’s highest energy synchrotron accelerator. It is also the
first large-scale superconducting synchrotron. All of its magnets are superconducting,
cooled by liquid helium to a temperature of 4.6 K. The Tevatron is approximately
one kilometer in radius, and accelerates proton and antiproton beams from 150 GeV
to 980 GeV, for a center-of—mass energy in collisions of 1.96 TeV.

The proton and antiproton beams have a “bunch” structure due to the use of
RF cavities in the acceleration of the particle beams. This means that collisions do
not occur continuously inside the detectors, but at regular intervals. In Run II, the
collisions occur every 396 ns. This collision rate is an important input into the design

of the trigger and readout systems.

2.1.7 The Recycler

The Recycler is new for Run II. It was designed to increase the integrated luminosity
(see Section 2.2.2) by providing for larger antiproton stacks in a shorter time. When
the number of antiprotons in the antiproton beam drops below a usable level, they
are transferred to the Recycler. Its purpose is to store the antiprotons for reuse.

During the data—taking period used for this analysis, the Recycler was not used.

2.2 The DC Detector

The D0 detector [14—18] is comprised of several sulxletectors (see Figure 2.2). Clos-

est to the beamline is the magnetic central-tracking system. It. consists of a silicon

19

m 2032

map—DEED
ZODZ

  
 

kam>m
Ozuxuéh

DHOmOH
ZODZ

  

12::

 

luding the tracking system. calorimeter. and muon

inc

Figure 2.2: The D0 detector.

svst em.

.1

20

microstrip tracker and a. central fiber tracker, both located within a ‘2 T supercondmrt-
ing solenoidal magnet. The central and forward preshower detectors are located just
outside of the superconducting coil (in front of the calorimeter), and are constructed
of three layers of extruded triangular scintillator strips.

The next layer of detection includes three liquid-argon/ uranium calorimeters:
the central calorimeter (CC) and two end calorimeters (EC). all housed in separate
cryostats. In addition to the preshower detectors, scintillators between the CC and
EC cryostats provide sampling of developing showers at 0.8 < |7]| < 1.4.

A muon system resides beyond the calm'imeter, and consists of a layer of tracking
detectors and scintillation trigger counters, a layer of 1.8 T toroids, and two more
layers of detectors after the toroids.

Luminosity is measured using two sets of ‘21 scintillation counters, located between
the CC and the two EC cryostats. A forward-proton detector. situated in the Tevatron

tunnel on either side of the interaction region, consists of a. total of 18 Roman pots.

2.2.1 Coordinate System

The coordinate system for DC is right-handed, with the z-axis aligned along the beam
direction, and y pointing straight up. Positive :3 is in the direction of proton travel.
When spherical (7'. Q5. (9) or cylindrical (7. c7). :5) coordinates are Used, gr) : 7r/2 is along

the positive y-axis, and 9 z 0 is along the positive z-axis. Pseudorapidity 77 is defined

6
7) : —ln (tang) . (2.1)

and approximates the true rapidity

1 E .
y : :- ln (tun—,i—pl) (2.2)

as

2 b—p;

‘21

in the limit that the invariant mass 772. << E (772,2 : E2 —- p2).

Rapidity is a useful variable because Lorentz boosts in the z direction (which are
very common at a hadron collider) add only a constant to the rapidity of every particle
in an event. Differences in rapidity between particles are thus unchanged under these
boosts. Also, Lorentz boosts along the z axis do not change the shape of rapidity

distributions in an event.

2.2.2 Luminosity

Luminosity, a measure of particle flux, is a function of the number of particles passing
through a unit area per unit time [16]. The luminosity determines the rate of inter-
esting interactions, and much effort, has been put. into increasing the luminosity of
the Tevatron.

The luminosity must be known in order to perform any analysis. It is measured
at DC by detecting inelastic collisions, and the total amount. of data collected over
an extended period of time is expressed as the integrated luminosity over the whole
time period. The luminosity group at DQ) provides tools to calculate the integrated
luminosity of any data sample. DQ) data are separated into luminosity blocks, typically
about the amount of data. taken in one minute. The luminosity group calculates the
luminosity for each block. and declares any luminosity block which cannot have its

luminosity calculated as bad. Bad luminosity blocks are not. used in data analysis.

Tevatron Time Structure and the Luminosity Calculation

When determining the luminosity, the luminosity group at DC) must. take into account
the Tevatron time structure [19].

The beams in the Tevatron are divided into bunches. A bunch is a group of
particles revolving together in the Tevatron. Each revolution (also known as a turn)

takes approximately 21 ,us. There are 1113 distinct, RF buckets. Each RF bucket is

22

separated by approximately 18.8 ns. A tick is defined as a grouping of seven RF
buckets, with the bunch located in the first bucket. and the remaining six buckets
empty. Each tick is separated by approximately 132 ns.

There are 159 ticks in one turn. The Tevatron currently runs in a mode where 36
bunches of protons and 36 bunches of antiprotons are in the machine at one time. The
36 bunches are separated into 3 symmetrically spaced superbunches. with 19 empty
ticks between the last bunch in one superbunch, and the first bunch in the next
superbunch. There are two empty ticks between each bunch inside a superbunch. and
therefore collisions occur every 396 ns inside a superbunch.

The luminosity system‘s scintillation counters collect data and increment. sealers
for each tick separately. This is necessary because the cl'iaracteristics of each bunch
may differ, changing the average number of interactions per crossing. The luminosity

calculation includes a sum over all of the ticks.

2.2.3 Silicon Microstrip Tracker

The innermost detector system in the DC) detector is the silicon microstrip tracker
(SMT) [20]. It is part of the inner tracking system (see Figure 2.3), which is designed
to measure momenta of charged particles bending within the magnetic field of a
2 T superconducting solenoidal magnet. The SMT also measures the positions of
primary and secondary vertices, which are the locations of partonic collisions in the
event. The SMT is the high-resolution part of the tracking system. essential in b
quark identification through precise measurement of secondary vertex positions. For
example, b quarks are produced in top quark decays. and give rise to B mesons which
travel a short distance before decaying. The location of this decay is measurable as a.
secondary vertex, and is evidence of the presence of a b quark in the event.

The SMT surrounds the interaction region. Beam collisions are most likely to

occur at the center of the detector, however, the typical width of the. interaction

23

CALORIMETER

 

J

fs\\\l L\\\\ l l'\\\\\ 1 k\ \\\.‘ v L.\\\\\\ l l»: \\\\\\\.
I

   
  

SOLENOID MAGNET

FIBER TRACKER

 
       
  

SILICON BARREL SILICON DISKS

 

H DIS KS |

 

Figure 2.3: The D0) tracking system surrounding the beam pipe, including the silicon
barrels and disks and the fiber tracking.

“point” extends 25 cm in the z direction. To detect charged particles emanating from
a collision not at the center of the detector, the SMT has a hybrid design.

It is difficult to build the SMT such that all particles’ tracks are perpendicular to
the detector, due to the extended interaction point. The solution is to build barrel
detectors to measure primarily the 7‘ — 9b coordinate. and disk detectors to measure
7‘ — 2 as well as r — c5 (see Figure 2.4). At high values of 7), vertices for particles
are reconstructed in three dimensions by the disks, and at small 7] the vertices are
determined by the barrels. The detector has six barrels along the :—axis. with four
detector layers per barrel. There are twelve small diameter double-sided “F" disks
(Figure 2.5), and four large diameter single-sided “H” disks. Four F disks are placed

between barrels, except at 7} = 0. The remaining eight are placed at the ends of the

24

 

 

Figure 2.5: An F disk, part of the D0 silicon detector. Each of the 12 individual
wedges is approximately 7.5 cm in length.

barrels. The H disks sit at the furthest distance from :5 = 0, approximately 1.2 m

away, and allow coverage out to 7] z 3. During the data-taking period used for this

25

 

Figure 2.6: Photograph of wedge used in F disk in the D0 silicon detector. The wedge
is approximately 7.5 cm in length. Also visible are the SVX 11 chips used to read out
the detector.
analysis. the H disks were not used.

The barrels and F disks are composed of 300 yin-thick silicon microst rip detectors
(Figure 2.6). In all. the S.\lT has approximately 800.000 individual strips. This allows
a spatial resolution of approximately 10 inn. and the pattern recognition necessary

to reconstruct tracks inside jets.

2.2.4 The Scintillating Fiber Tracker

The scintillating fiber tracker. or central fiber tracker (see Figures 2.9 and 2.10). is the
next detector that most particles encounter as they move outward from the interaction
point [21]. The detector covers the region [7)I < 2. and is used in conjunction with
the SMT to measure trajectories and momenta of charged particles with excellent
resolution (see Figure 2.8). The tracker also provides information for the triggering
system.

The scintillating fiber tracker consists of approximately 70.000 scintillating fibers

mounted on eight concentric cylinders at radii of 19.5. 23.4. 28.1. 32.8. 37.5. 12.1.

26

  
 
 

b.)

MAGNIFIED

SOL ENOID

  

Figure 2.7: a) Diagram showing the location of the D0 central fiber tracker. b) Closeup
View showing the axial and stereo layers of scintillating fibers attached to detector
barrels.

48.8, and 51.5 cm (Figure 2.7). Each cylinder supports two doublets of overlapping
scintillating fibers of 0.835 mm diameter, one doublet parallel to the collision axis.
and the other alternating by $3" relative to the axis. The clear fibers have an inner
polystyrene core (index of refraction 1.59) surrounded by a thin acrylic cladding (index
of refraction 1.49), and a thin fluoro—acrylic cladding (index of refraction 1.42). The
second cladding exists to increase the light trapping efficiency. The fibers scintillate
in the yellow-green part of the visible light spectrum.

The fibers must be precisely mounted onto the mechanical structure of the fiber
tracker in order to accurately reconstruct tracks. Perhaps more importantly, trig-
gering will be adversely affected by fibers not mounted parallel to the beam axis.
The other important issue entering into the construction of the fiber tracker is the
thickness of the support cylinders. They must be as thin as possible to minimize mul-
tiple scattering. Both of these issues were considered during the design of the fiber
tracker [21].

Scintillation light is transferred via clear multiclad waveguides to solid—state, vis-

27

 

100.0
50.0

 
   

lllllllll

pT : 100 GeV /
VdMA

  

llJllll

V 10.0 E‘

l

lllllll

 

 

 

Pseudorapidity 77

Figure 2.8: Simulation of the transverse momentum (pT) resolution of the tracking
system as a function of pseudorapidity for tracks with pT : 1. 10. and 100 GeV/c.

ible light photon counters (VLPC) that have appi‘tiiximatcly 80% quantum efficiency,
and a gain of at least 20,000. The VLPC operate at around 10 K to reduce the

background from electronic noise, and have a rate capability of at. least 10 MHz.

2.2.5 Preshower Detectors

The central and forward preshower (CPS and FPS) detectors are located just outside
of the superconducting coil and inside of the calorimeter [22.23]. These detectors each
consist of a tapered lead radiator and three (CPS) or four (FPS) layers of triangular
scintillator strips that are read out using wavelength-shifting fibers and VLPCs (see
Figure 2.11). The preshower detectors aid in electron identification and triggering and

correct electromagnetic energy measurements for solenoid effects. The detectors can

28

 

Figure 2.9: End view of the D0 central fiber tracker.

be used to accurately measure positions and sample energies of particles before they
enter the calorimeter.

The CPS detector (see Figure 2.14) fits in the small (51 mm) gap between the
solenoid coil and the central calorimeter cryostat. It. is a cylindrical detector with
a radius of approximately 72 cm. covering the region |1}| < 1.2. Two FPS detectors
cover the regions 1.4 < [7)] < 2.5. The FPS detectors are mounted to the inner faces
of each of the end calorimeter cryostats.

Electrons and photons traversing the detectors will have already passed through
the solenoid and tapered lead radiator. Most of these particles will begin electromag-
netic showers in those materials (discussed in Section 2.2.6). and therefore deposit a
large amount of energy in the preshower detector. Muons and charged pions will leave

only a small amount of energy in the detector through ionization. Charged pions will,

29

 

Figure 2.10: Insertion of the central fiber tracker into the DO detector. inside the
calorimeter.
however, often begin hadronic showers in the solenoid. These showers are the biggest
source of background for electron identification in the preshower detector.

The tapered lead radiator is used to ensure that the total amount of material is
constant at all pseudorapidities. Figures 2.12 and 2.13 show the amount of material

needed to have a constant two radiation lengths of material before the CPS detector.

2.2.6 Calorimeter

DC has three uranium liquid-argon calorimeters—a central calorimeter (CC) and two

end calorimeters (EC)Awhich are usually referred to collectively as the calorimeter

30

      
      
 

 

a.) b-)
,.' [_ - STEREOV
i. . « STEREOU
,Igzpr..—?%.;~,‘.4’__L_¥LT\% “‘ AXIAL
PRESHOWER
CC 7 r , ASSEMBLY
* ’ ' ’ t
CPS”—_:—;§E‘;§ is? z -_ ‘
CC ,.‘;‘;,,;:.:;Lé'#—£!».44%;.
SOLENOID ( ,_,,2~"' ;
42—2} SOLENOID! \
._ _——~r«n/ CPS . fl ,
1 I ,// ‘ \\\\\ \\
, V; (‘1‘ // \ '\ ‘
y m .6 CFT 74.19”
1 ' .; J 1‘ 11;”-.. . '
’ dill *1 1“,, is..- :.;_ 7 , t
t t if ““F- ENDiVIEW

Figure 2.11: a) Diagram showing the locations of the central (CPS) and forward
(FPS) preshower detectors. outside the central fiber tracker (CFT). b) End view of
the CPS, including a closeup view of the three layers of scintillator strips. Not drawn
is the tapered lead radiator, which is between the solenoid and the preshower detector.
(Figures 2.15 and 2.16). The CC covers the |7]| < 1.2 range, while the two EC on
either side cover the regions 1.3 < |7}| < 4.

The calorimeter is used in the identification of electrons, photons, jets, and muons,
and in the measurement of the missing transverse energy in an event. It is responsible
for the energy measurement of electrons. photons. and jets.

The calorimeter is composed of a large number of modules. each of which con-
sists of a stack of interleaved absorber plates and signal boards (cells). The modules
are organized into layers and differ mainly by the type of absorber used. The elec—
tromagnetic modules use depleted uranium, the fine hadronic modules use depleted
uranium with 1.7% niobium, and the coarse hadronic modules use copper or stainless

steel. See Figure 2.17 for a schematic view of a calorimeter cell. Liquid argon fills

31

 

i"
u:

N

N

Ul
l

Constant 2X0

P. -----------------------------------------------------------

N

1.5

Radiation/Interaction Length

 

0.25

 

 

 

i l l
O 0.2 0.4 0.6 0.8 1 1.2 1.4
Pseudorapidity

Figure 2.12: The solenoids radiation and nuclear interaction lengths as functions of
pseudorapidity. Diagram from [22].
the 2.3 mm gap between the absorber plates and signal boards. The calorimeter sits
inside a cryostat in order to keep the argon cold.

Liquid argon is used because it is dense. radiation-hard, and reliable, and provides
a uniform, linear response. It allows for relatively easy calibration and fine segmen-
tation.

Uranium is used because of its high density, allowing a more compact calorimeter.

32

 

0))

Lead Thickness (mm)

 

 

 

l l g

l t
-150 -100 -50 O 50 100 150
Z—Position (cm)

 

0

Figure 2.13: Thickness of lead needed to yield a constant 2X0 (2 radiation lengths)
for all particle trajectories. Diagram from [22].

It also improves the energy measurement because energy losses in the uranium are
compensated by energy released in fission of 238U.

Electrons entering the calorimeter interact with the absorber plates through the
Bremsstrahlung mechanism, in which they emit a photon upon feeling the Coulomb
field of a nucleus in the absorber. Photons interact predominantly via pair 1.)rod1.1ction.
when a photon converts into an elect ron-positrcm pair in the vicinity of a nucleus.

The secondary particles emitted in these interactions can undergo these same in-

33

 

Figure 2.14: A portion of the DO central preshower detector. a thin cylindrical de—
tector mainly consisting of scintillating fibers.

teractions themselves. This process. called an elet‘:t1‘01nagnelic shower. repeats itself
until the energies of all the secondary particles fall below the threshold for pair pro-
duction. The particles will then continue to lose energy. mainly through ionization.
The calorimeter works by measuring the energy released in this shower. which is an
indirect measurement of the energy of the original particle.

Hadronic particles lose energy in the calorimeter mainly through inelastic collisions

34

 
 
 
 
  
 
 
 
 
   
 
  

D¢ LIQUID ARGON CALORIMETER .

END CALORIMETER

Outer Hadronic
(Coarse)

Middle Hadronic
(Fine & Coarse)

CENTRAL
CALORIMETER
Electromagnetic

Inner Hadronic Fine Hadronic

(Fine 8 Coarse) Coarse Hadronic

Electromagnetic

Figure 2.15: The D0 calorimeter, composed of layers of heavy metals and liquid argon.

with atomic nuclei. The secondary particles produced in these collisions can also lose
energy through inelastic collisions. This process is called a hadronic shower. Hadronic
showers are more extended in space than electromagnetic showers.

The DC calorimeter is a sampling calorimeter because it uses layers of absorber
plates to absorb most of the energy of the incident particles while causing them
to shower, and its liquid argon sections to sample the energy of the showers. This
sampling is done by grounding the absorber plates and maintaining the copper pads
on the signal boards at a voltage of approximately 2 kV. Charged particles passing
through the liquid argon ionize electrons in the argon. These ionized electrons are
drawn across the potential difference to the signal boards and they induce a signal
on the copper pad. These signals allow measurement of the energy in the showers.

The final pieces of the calorimeter are between the CC and EC. Particles entering

35

 

Figure 2.16: The D0 calorimeter sitting inside the DC?) detector outside of the collision
hall during the period between Run [ and Run II.

this region may escape detection by traveling through the space between the CC
and EC. To measure energies of particles in this region. massless gaps (MG) and the
intercryostat detector (1CD) are used. The MC are rings of signal boards mounted
on the ends of parts of the CC and EC. The ICD is a ring of scintillation counters

mounted on the exterior of the EC cryostats [16].

36

 

( Absorber Plate Pad Resistive Coat Liquid Argon \
GIO Insulator J] Gap
_ 7 _

 

 

 

 

 

 

 

 

 

 

-J

K‘— Unit Cell —9 J

 

 

\\\‘\

 

 

 

\\\\ I

 

 

 

 

Figure 2.17: A DQ) calorimeter cell with alternating layers of absorber plates. liquid
argon, and signal boards. Many cells form the layers of the calorimeter. Absorber
plates can vary in size, but the gap between the absorber plate and the signal board
is always 2.3 mm.

2.2.7 Muon System

The muon system (Figure 2.18) is the outermost detector system in the D0 detec-
tor [24,25]. It is separated into the central muon detectors and the forward muon
detectors. Muons produced in collisions at D0 are too massive to be stopped in the
calorimeter, and move too fast to decay before leaving the detector. They can be
detected by the tracking system and calorimeter, but the muon system provides the
ultimate confirmation. This is accomplished using the various detectors in the muon
system and the iron toroid magnet. which allows a crude measurement of the muon
momentum independent of the tracking system.

The wide angle muon system (WAMUS) covers the region [7]] < 1 and has three
layers (called A, B, and C). The A layer lies between the calorimeter and the toroid

magnet, and the B and C layers are outside of the magnet. The WAMUS is composed

37

FORWARD [30 T8
TRACKER (MDTS)

  
  
  
  
  

UON
TOR/CID

 

 

 

 

 

 

 

 

 

 

 

 

CENTRAL
F ’TRIG
5 _. scwr
(Av)
F ............... .\
_SHIELDING
_ x
(m) 0 — :
FORWARb' n [r] CKlNG
TRIG : .- SYSTEM
SCINT fl
(PIXEL ts) '
_5 ——

 

 

 

 

 

 

 

 

 

 

BOOTOMB/CSCINT
llllllllllll

—1O -5 O

(m)

 

Figure 2.18: The D0 muon system, including scintillator (scint) and proportional and
mini—drift tube chamber layers (PDT and MDT).

of 94 proportional drift tube chambers (PDTs) in three layers (A. B, and C). There

are scintillators between the A layer and the calorimeter, and an outermost layer of

38

Vernier pads ,.— Signal wire

“ is H as

5.5 cm

 

 

 

 

 

 

i if: ll “fill
]—————— 10.0 cm _———-[

Figure 2.19: A muon proportional drift tube unit cell consisting of an anode sense
signal wire in a gas—filled chamber and two sets of cathode pads.

 

 

Inner and outer Vernier pads

 

 

 

  

 

Anode wires to
channel electronics

Jumper at far end
of cell pair

Figure 2.20: A proportional drift tube unit cell viewed from above.

scintillators is used to reject cosmic rays.

The PDTs have three or four decks of drift cells. The PDTs are rectangular in
shape, approximately 10.1 cm wide and 5.5 cm high. with one anode sense wire and

two sets (inner and outer) of cathode pads per drift cell (see Figures 2.19 and 2.20).

39

 

Figure 2.21: Part of the C layer of the D0 forward muon system.

Adjacent unit cells share anode wires, allowing a time difference measurement be-
tween the arrival of signals from the two wires. The cells are filled with 80% argon,
10% methane, and 10% CF4. The voltage is approximately 2.5 kV for the pads and
5.0 kV for the wires. Muons that traverse the gaseous region ionize electrons that
accumulate on the wires and induce a charge on the pads. The ratio of the charges on
the pads, the drift time, and the time difference between the arrival of charge from
adjacent anode wires allow the determination of the muons position. Subsequent
measurements allow a trajectory calculation. and the bend in the muon’s path due
to the toroid magnet allows a charge and momentum measurement.

The forward angle muon system (FAMUS, see Figure 2.21) covers the region

1 < [n] < 2. It consists of three layers (A, B, and C) of mini—drift tubes (MDTs),

40

three layers of scintillation counters. and the toroidal magnet. There are three or four
planes of tubes in each of the MDT layers, and every tube has eight 1x1 cm2 cells
with a 50 ,um anode wire in the center. MDTs have excellent coordinate resolution,
short electron drift time, and high segmentation. .

The scintillation counters are mounted on the inside (layers A and C) or outside
(layer B) of the FAMUS MDT planes. The counters are made of scintillator plates
cut in a trapezoidal shape. Wavelength shifting bars are attached to the sides of the
plates for light collection. The bars transfer light to the phototubes with a quantum
efficiency of approximately 15%. The scintillators are used for triggering and track

reconstruction.

2.3 The DD Trigger and Data Acquisition Systems

Proton-antiproton collisions occur inside the D0 detector at. a maximum rate of
approximately 2.5 MHz. Most of the collisions are not interesting in the context of the
physics program at DC. This fact, along with the realities of finite storage resources
and limits on the data-transfer rate to the storage facility, lead to the decision to
write events to permanent storage at a. rate of approximately .50 Hz. D93 employs
a three-level trigger system to quickly characterize all of the events and select the
events to be written to permanent storage [15. 18].

The Level 1 (L1) trigger. mainly composed of custom-built electronics, reduces
the event rate to approximately 5 kHz using coarse informatitm from the detector.
Coarse, or lower resolution, data must be used to allow L1 to keep up with the rate
of collisions. The Level 2 (L2) trigger is designed to be able to process data at a
rate of up to 10 kHz, although it is unlikely to ever operate at this rate. It. uses a
combination of custom-built electronics and commodity processors to make trigger

decisions based on more detector information and with more time than the L1 trigger.

41

The L2 trigger reduces the data rate. to approximately 1 kHz for the L3 trigger. The
L3 trigger is the only trigger level that. has the full detector readout available, and

selects approximately 50 events per second to be written to tape.

2.3.1 The Level I Trigger

The L1 trigger is responsible for reducing the data rate from 2.5 MHz to approximately
5 kHz. It uses custom-built electrtmics. and relies on information from the central fiber
tracker, the calorimeter, the preshower system. and the muon system.

Up to 128 different L1 trigger conditions can be required when programming the
L1 trigger. An event that satisfies any of the requirements will cause the event to
pass the trigger. This allows a diverse set of physics conditions to trigger the event '5
passage. The first requirement in most L1 triggers is the presence of an inelastic

collision, which is detected by small-angle counters.

L1 Calorimeter Trigger

The L1 calorimeter (LlCAL) trigger is based on information from the D0 calorin'ieter
system (see Section 2.2.6).

The LlCAL trigger towers are formed by grouping together calorimeter cells in
An x A46 2 0.2 x 0.2 regions. The energies of all the cells in a tower are summed to
calculate the energy of a trigger tower. The use of 1280 trigger towers for triggering
is an example of the way the L] trigger makes use of coarse detector information by
reducing the resolution of the detector data.

The transverse energy in the trigger towers is measured by first summing up all
of the energy in the cells contained in each trigger tower. The energy of each tower
is then multiplied by the sine of the trigger tower polar angle (time is an implicit
assumption that the event vertex is at z :- 0). The transverse energy contained in

the electromagnetic (EM) layers is summed separately from the total (TOT) trans-

42

verse energy for each trigger tower. The total transverse energy sum excludes energy
contained in the coarse hadronic layers of the calorimeter.

L1 trigger conditions are specified by a certain number of trigger towers and a
minimum transverse energy threshold for the towers. At any one time, there are a.
maximum of four different thresholds for the EM and TOT towers separately. An
example L1 trigger condition is two TOT trigger towers, each registering transverse
energy greater than 5 GeV,

The LlCAL trigger system also calculates the sum of all of the transverse energy
in the calorimeter. LlCAL trigger conditions can be based on the total transverse
energy or the imbalance of transverse energy (the missing transverse energy, MET).
Total energy and MET triggers are each specified by a minimum threshold.

The LlCAL trigger passes the trigger tower energies to the L2 trigger to be used

in L2 trigger decisions.

L1 Central Track and Preshower Triggers

The L1 central track trigger (LICTT) uses scintillator information from the CF T
(Section 2.2.4) and the FPS and CPS detectors (Section 2.2.5). The LlCTT makes
trigger decisions and provides the L2 and L3 triggers with sorted lists of tracks and
preshower clusters. In the central detector region. the CFT and only the axial strips
from the CPS detector are used. In the forward region, the FPS detector is used in
conjunction with the CFT.

Every bunch crossing (every 132 ns), discriminator bits are read out from the track-
ing and preshower detectors. These outputs are fed into a. series of field-programmable
gate arrays (FPGAs) which use preloaded logic to compare the bits to various hit pat-
terns. The hit patterns correspond to possible tracks. and a. match to a hit pattern
corresponds to the finding of a track with a momentum in one of four pT bins: 1.5—

3 GeV/c; 3—5 GeV/c; 5—10 GeV/c; or above 10 GeV/c. The trigger is divided into

43

CFT AXIAL LAYERS

       

sessreegl
3' :3 ': if. S: r: a? '-‘ N
@N‘ ,1
I
One 4.5°sector
CPS AXIAL
LAYER

(enlarged view above)

Figure 2.22: A single 4.5 degree central fiber tracker (CFT) sector along with a hypo-
thetical track and hits in all eight CFT layers and the central preshower (CPS) axial

layer.

4.5 degree sectors, and a maximum of six tracks can be found per event per sector.
Figure 2.22 shows the track of a hypothetical particle which deposits energy in all
eight CFT layers and the CPS axial layer. Trigger conditions can be specified by a

certain number of tracks above a pT threshold, with or without the requirement of a
CPS cluster match to the track.

L1 Muon Trigger
The L1 muon trigger relies on information from the muon wire chambers and scin—
tillation counters (Section 2.2.7). and tracks from the LICTT. FPGAs in four crates

on the detector platform are used to combine information from these detectors. The

muon triggers are first separated into central and forward regions. and further divided

into octants. Triggers in each region are built up from octant decisions.
Triggers can require muons in the central ([77] < 1). forward (1 < [77] < 2). wide

44

([77] < 1.2 to match the central tracking coverage). or all regions ([77] < 2). Matches
to tracks can also be required. If a match to a track is required. the four pT bins from

the tracker are used as trigger thresholds.

2.3.2 The Level II Trigger

The L2 trigger was designed to process data at a rate between 5—10 kHz and reduce
it to approximately 1 kHz. In practice. front-end crate readout problems have limited
the input rate to L2 to less than 2 kHz.

The L2 trigger system is divided into six crates. There are five preprocessor crates
that process data from both the L1 trigger system and directly from the detector
through the front-end crates. There is also a Global crate that collects data from
the five preprocessor crates and makes trigger decisions by correlating the data and
imposing trigger requirements.

Each of the six L2 crates contains custom-built electronics. The crates work to
process the data and return a trigger decision. This must happen within approxi-
mately 100 ps at a rate of 10 kHz. but. more time is currently available due to current
L1 accept rates being lower than 10 kHz.

Beta processors [26], running identical executables but configured different 1y, are
installed in each crate. A processor’s configuration specifies which algorithm runs in
the processors executable and corresponds to the type of data being processed in the
crate.

The data processed by L2 is not raw detector data. but is coarse or abbreviated
data that can be processed quickly enough to allow the reduction of the rate to L3,
where the full detector readout is available. L2 exists because the full detector cannot

be read out at a rate much greater than 1 kHz.

L2 Calorimeter Preprocessor

The L2 calorimeter preprocessor [27] crate receives data from the LlCAL system. L2
receives the trigger towers created at L1 and combines them to form electromagnetic
objects (for electron and photon triggering) and jets. Some of the trigger towers from
L1 are marked as seed towers. They have transverse energy above some threshold and
are used as the starting point. in forming L2 electromagnetic objects and jets.

Electromagnetic objects are formed by adding the energies of two trigger towers.
An electromagnetic object is formed from each seed and its highest-energy neighbor.
The algorithm can be configured not to add the neighbor‘s energy under specified con-
ditions. Quantities called isolation and EM fraction measuring the objects’ isolation
from other energy in the calorimeter and the fraction of energy in the calorimeters
electromagnetic layers are calculated for use in the Global processor.

Jets are formed by summing the energy in a five—by-five trigger tower array with
the seed tower at the center. Two seeds that. are very close together will not both be
used to form jets. Only the higher seed will be used.

After the electromagnetic objects and jets are properly formatted they are sent.

to the Global processor.

L2 Muon Preprocessors

There are two preprocessor crates for the L2 muon system. The L2 central muon pre-
processor [28] and the L2 forward muon preprocessor [28] crates process information
from the central and forward muon detectors (see Section 2.2.7).

Inputs to the L2 muon system are first. received by second level input computers
(SLICs), where most of the processing is done. One of several different algorithms,
which differ due to the geometry of the detector, processes the data and forms muon
stubs. These stubs are created for the A, B, and C layers of the muon system and

are the result of the combination of scintillator and drift tube information in each of

46

these layers. The stubs are passed to the Beta processor. which forms muon objects
out of the stubs and sends them to the Global processor. The muon objects include
position, momentum, sign, and timing information.

The muons are assigned a quality by the global processor: tight; medium; or loose.

The definitions are as follows:
0 tight

— at. least two A layer hits and two BC layer hits in the central region

— sum of A layer hits and BC layer hits greater than 3 in the forward region
0 medium

- at least one A layer hit and one BC layer hit
0 loose

— at least one A layer hit or one BC layer hit in the central region

— sum of A layer hits and BC layer hits greater than 1 in the forward region.

L2 Tracking Preprocessor

The L2 tracking preprocessor crate. currently being commissioned. uses tracks from
the LlCTT and from the silicon detector. L2 tracks based solely on the LICTT tracks
are called L2CTT tracks. The tracks based on the LlCTT tracks and extrapolated
into the silicon detector are called L2STT tracks. L2CT T and L2STT tracks share an
identical data format, so they can be used interchangeably by the Global processor.

Information associated with tracks includes position, momentum. and sign. Other
quantities which are measured for L2STT tracks are: the quality of the track using
a X2 parameter; the track fit quality; the impact parameter; and impact parameter
significance. Track objects are filled with this information and sent to the Global

processor, sorted by pT or impact parameter significance.

47

L2 Preshower Preprocessor

The L2 preshower preprocessor crate (L2PS) is responsible for the formation of clus-
ters for the CPS and FPS detectors (see Section 2.2.5). The information received from
the L1 trigger includes one-dimensional clusters of energy deposition. L2PS forms
two-dimensional clusters by checking for overlaps of the one dimensional clusters.

The two-dimensional clusters are sent to the Global processor for use in triggering.

L2 Global Preprocessor

The L2 Global worker makes trigger decisions based on the ob jects created by the L2
preprocessors. L2 trigger decisions are made by first creating Global physics objects.
These objects can be based directly on the objects reported by the preprocessors
or can be created by combining objects from different preprocessors. The L2 Global
worker imposes cuts on the Global physics objects according to configuration informa-
tion it receives from the trigger control computer based on the trigger list. A complete

description of the L2 Global worker is included in Appendix A.

2.3.3 The Level III Trigger and Data Acquisition

The L3 trigger is responsible for reducing the data rate from approximately 1 kHz
to 50 Hz. It uses a Cisco 6509 Ethernet switch. standard PCs, and commodity VME
single-board computers [29].

The L3 data acquisition system receives digitized data from all of the detector
subsystems. It then routes the data. to filter processes running on PCs in the L3
trigger farm. The processes are configured through a supervisor process running on
a dedicated CPU which is the interface between the L3 trigger system and the run
control system, COOR.

The L3 trigger has full access to the D0 data. and so can offer a complete menu

48

of triggering options. It is not restricted to a one—to-one correspondeiice with L1 and
L2 triggers, and so several slightly different conditions can be applied to optimize the
efficiency and rejection of an L3 trigger condition. The L3 trigger is as similar as pos-
sible to the offline reconstruction code. the only restriction being the amount of time
allowed for processing each event. The L3 trigger makes available electromagnetic,
muon, tau, track, and several other triggers.

After an event passes the L3 trigger. it. is transferred over a separate network

connection to the Feynman Com )utincr Center for ermanent storage.
c O C)

49

Chapter 3

Offline Event Reconstruction

The DC detector (described in Chapter 2) is designed to detect and identify the
particle remnants of proton—antiproton collisions. Particles produced in collisions in-
teract with the detector, and records of these interactions are stored as raw data.
To study the physics of particle interactions, it is necessary to reconstruct, from the
raw data, the kinematic properties of the particles that emerged from the original
interaction. This reconstruction is done through the use of a software program called
“ereco” [30], written in the C++ programming language.

The dQDreco program is separated into many software packages, collections of files
containing C++ source code. each responsible for one piece of the total event recon-
struction. There is one dfflreco executable program run on several computer farms,
each containing hundreds of PCs. Each farm is assigned a subset of the total data
recorded by DC. New versions of dC/h‘eco, organized using version numbers, are cre-
ated periodically as updates and improvements become available. The data used in
this analysis were reconstructed using p14.x versions of d®reco. The dQDreco program
is the result of many years of work by many people. and in this section only an

overview of the basic concepts of particle reconstruction is presented.

3.1 Track and Vertex Reconstruction

Charged particles passing through the DQ) SMT and CFT detectors leave energy in
many layers of the detectors through which they pass (see Sections 2.2.3 and 2.2.4).
These localized depositions of energy in each layer of the tracking detectors are called
hits. In addition to the hits from high-momentum charged particles traversing the
detector (which are of primary interest in this analysis), there are also hits from low-
momentum tracks from jets, tracks from secondary collisions in the event, tracks from
particles interacting with the beam pipe, and random electronic noise. For any event,
there are many such hits in the tracking detectors which make the reconstruction of

tracks difficult.

3.1. 1 Track Algorithm

Several different algorithms have been used to reconstruct tracks in the D0 detector.
Algorithms are chosen for each analysis based on the unique requirements for each
analysis. The most common algorithm, used in this analysis, is now a combination of
the AA track algorithm [31] and the Hough transform (HTF) algorithm [32]. Each
runs separately to generate a list of track candidates. Then the two lists are combined,
and duplicates are removed, before final fitting is done.

The AA track algorithm starts by generating a pool of track candidates using the
hits in the SMT. The algorithm selects all sets of three hits which lie along a path
originating from the beam spot. It then extrapolates the path of the track outward to
either the next layer of the SMT or to the CF T, to calculate the location where the
track would have crossed the next layer. The algorithm checks whether there is a hit
near this location, and then extrapolates to the next layer. and repeats the procedure.
At each layer, it calculates a x2 value for the track and associates the hit with the

track if the X2 value is below a configurable value. New tracks can be constructed if

there are multiple hits in a layer that produce acceptable tracks. If there is no hit in
a given layer, the algorithm continues and tallies a miss for that. track. At the end
of this procedure, a list of track candidates is produced along with a number of hits.
misses, and x2 for each track.

A list of vertices is next constructed by following the tracks back to the z-axis.
This list of vertices is used to look for more track candidates that only have hits in the
CFT. The same extrapolation procedure is repeated as above. starting in the CFT,
but with the constraint that the track start. at a primary vertex. CFT-only tracks have
been used in several analyses. and their use can give an increase in efficiency. Each
analysis must decide whether the corresponding increase in background is acceptable.

The trajectory of a particle in the plane per1.)endicular to a magnetic field is a. circle
characterized by three parameters: its curvature; impact parameter; and direction at
the point of closest approach. The HTF algorithm begins by dividing this parameter
space into bins. Each pair of hits in the tracking detector corresponds to a point
in the parameter space. For each point, the algorithm increments a histogram bin
corresponding to the point in the parameter space. All hits from a track correspond
to the same bin, so a peak corresponds to a track. The HTF algorithm uses this
technique to generate a list of tracks.

The separate lists of tracks from the AA Track algoritfu‘n and the HTF algorithm
are combined into one list. Once the complete list of tracks has been generated. it is
sorted by number of hits, fewest misses, and lowest \2. in that, order. The best track is
automatically kept, and the rest of the tracks are examined. The number of hits that
each of the remaining tracks shares with the already-selected tracks is calculated. If
the number of shared hits is less than 2/3 the number of total hits. or the number of

unique hits is greater than three. the track is kept.

3.1.2 Selecting the Primary Vertex

After a list. of tracks and a list. of vertices have been generated, the primary vertex
must be selected [33]. The primary vertex is used by dOreco in the reconstruction
of jets, b-jets, electrons, and missing transverse energy. Other vertices in the event
may be due to minimum-bias interactions. Minimum-bias interactions are proton—
antiproton interactions besides the primary hard scatter, which generally produce
particles with low pT.

The first step in selecting the primary vertex is to group all of the vertices in
clusters. Vertices within 2 cm of each other in the z direction are grouped together.
For every cluster, the highest multiplicity vertex is chosen and added to a new list
of selected vertices. For each of the selected vertices, the probability that each track
comes from a minimum-bias vertex is calculated relative to a pT-dependent function
derived from a minimum-bias Monte Carlo sample. Higher pT tracks are less likely
to come from minimum-bias vertices, and have a. lower minimum-bias probability.
The minimum-bias probabilities are combined to calculate a minimum-bias vertex
probability. The vertex with the smallest minimum—bias vertex probability is chosen

as the primary vertex.

3.1.3 Bottom-Quark Jet Identification

Identification of b-quark jets is extremely important for the DO physics program.
Bottom-quark jets are jets of particles that originate from b quarks. and are important
because b quarks appear in the decay chains of many particles of interest.

Bottom quarks are identified. or tagged. using several different b-tagging algo—

rithms. These include:

0 Secondary vertex tagging algorithm

Reconstructs the decay vertex of long—lived B hadrons within jets. The decay

of a long-lived hadron produces several charged particles emanating from a

secondary vertex, displaced from the primary interaction point [34].

0 Jet lifetime probability algorithm
The impact parameters of all tracks associated with a. calorimeter jet can be
combined into a single variable, the jet lifetime prolmbility. which is used to tag

b jets [35].

0 Counting signed impact parameter algorithm
Relies on the fact. that tracks produced by charged decay products of long-lived
B hadrons have a non—zero impact parameter with respect to the primary vertex.
The sign of the impact parameter is given by the sign of the impact parameter
projection on the jet axis. determined based on calorimeter information. Im-
pact parameter significance is defined as the impact parameter divided by its

uncertainty calculated by the track finding algorithm [36].

0 Soft lepton tagging algorithm
Relies on the fact that B hadrons are more likely to decay to a final state con-

taining a muon than lighter hadrons. This algorithm tags a jet as a b jet if there

 

is a muon around the jet within a cone of AR: \/(A7))2 + (Ac)? < 0.5 [37].

3.2 Muon Reconstruction

The p14.x versions of d®reco rely on muons detected using the forward and cen—
tral muon detectors (see Section 2.2.7), and also makes use of the tracking detectors
and the calorimeter (see Section 2.2.6). Muons reconstructed using only the informa-
tion from the muon detectors are called “local" muons. and those that also have a
matching track are called “central track-matched" muons. Muons can also be recon-

structed using minimum-ionizing particle (.\fIP) signatures in the calorimeter. The

Muon Tracking in the Calorimeter (.\.lT C) algorithm identifies MTC muons using

MIP signatures, although these are not used in this analysis.

3.2.1 Muon Types and Qualities

The dQ’Jreco program classifies muons by type and quality. The types of muons are
differentiated by a parameter nseg. The absolute value of nscg is the number of
segments associated with the reconstructed muon object (this can be between 0 and
3, with a potential segment in each of the A, B, and C layers of the muon system),
and the sign of nseg is determined by whether or not there is a. central track matched
to the muon. Muons with [nscg : 1] have hits only in the A layer of the muon
system, [nseg : 2] muons have hits in the B and/or C layers of the muon system,
and [nseg : 3| muons have hits in the A layer and in the B and/or C layers of the
muon system.

The quality of a reconstructed muon is determined by how many hits it has associ—
ated with it in each layer of the muon system. The possible values of quality are loose,
medium, and tight, with loose having the highest. efficiency and highest background,
and tight having the lowest efficiency and lowest background. The number of hits
required for each value of quality depends on the detector geometry (the bottom of
the detector has less instrumentation due to the presence of detector supports), but
in general more hits are required for a muon to have tighter quality. The requirements

for the various types of muons are [38]:

0 Tight muons
Only [nseg] = 3 muons can be tight. A muon is tight if it has
— at least. two A layer wire hits
— at least one A layer scintillator hit

— at least three BC layer wire hits

CT
CI!

- at. least one BC scintillator hit
- and a converged local fit. (\[3UC > O).
o [nsegl : 3 medium/loose muons
When an [ns.-reg] : 3 muon candidate fails the tight criteria it can still be medium
or loose. An Inseg] : 3 muon is medium if it has
— at least. two A layer wire hits
- at least one layer scintillator hit
-— at least two BC layer wire hits
- and at least one BC scintillator hit (except for central muons with less

than four BC wire hits).

An ['nseg] : 3 loose muon has the same definition as a medium muon, but one
of the above tests is allowed to fail. with the A wire and scintillator requirement

treated as one test, and at least one scintillator is always required.

0 nseg : 2 loose/ medium muons
Muons with [nseg] < 3 can only be loose or medium if they are matched to a
central track, and so have nseg > O. nscg : 2 muons are muons with a BC

segment matched with a central track. An nseg : 2 muon is loose if it has

- at least one BC scintillator hit
- at least two BC layer wire hits.
An nseg : 2 muon is defined as medium if it fulfills the above requirements

and if it is located in the bottom part of the detector (octant 5 and 6 with

[detector 7]] < 1.6).

o nscg = 1 loose/ medium muons
Muons with nseg : 1 are muons with an A segment matched with a. central

track. An 72.569 : 1 muon is loose if it has

— at least one scintillator hit

— at least two A layer wire hits.

An nseg : 1 muon is defined as medium if it fulfills the above requirements
and if it is located in the bottom part of the detector (octant 5 and 6 with

[detector 7)] < 1.6).

Each analysis can choose which type and quality of muon to use based on the needs of
the analysis. Efficiency and background measurements are generally done separately

in each analysis.

3.2.2 Muon Isolation

Muons not produced in association with jets are called isolated muons. To be consid-

ered isolated, a muon must satisfy the following requirements (suggested in [39]):

o The energy measured in the calorimeter in the region defined by a 0.1-radius
cone and 0.4-radius cone in 7) — qt) space centered around the muon (the hollow
cone energy) must be less than 2.5 GeV (see Figure 3.1). The energy that the
muon deposits in the calorimeter should be along the path the muon traveled
in the calorimeter, while significant energy further away from the path is likely

to come from an associated jet.

0 The scalar sum of the transverse momenta of all tracks (except the one matched
to the muon) contained within a cone of radius 0.5 around the muon must be less
than 2.5 GeV/c. Extra tracks around the muon are indicative of the 1.)resence

of a jet, which contains many charged particles.

 

Figure 3.1: The muon isolation variable in the calorimeter. The energy contained in a
cone of radius 0.1 around a muon is subtracted from the energy contained in a cone
of radius 0.4.

3.3 Jet Reconstruction

Partons (quarks and gluons) are detected at DO by the measurement of their hadroniza—
tion products, jets of hadrons which are created due to the color confinement of the
quarks. The d®reco code measures the energies of jets [40]. For use in analysis. an
extrapolation back to the energies of the original partons. which are usually the object

of interest to the analyzer. must be done.

3.3.1 Jet Cone Algorithm

Jet reconstruction starts with the clustering of calorimeter energies into towers with
size A77 x Aqb : 0.1 X 0.1. Towers with ET 2 0.5 GeV are called seeds. and become
the basis for the formation of jets. Next. preclusters are formed by adding all of the

energy within a cone of R : 0.3 around each seed, where R is defined as

R 2 (An)2 + (as)? (3.1)

58

Preclusters with ET 2 1.0 GeV are kept.
Using all the preclusters within Rfmals where anm, is the final size of the jet cone
used (different values of Rfl-nul are used in different analyses), jet 7} and g5 directions

and energies are estimated using

7, : __}:,: E3771. (3.2)
2.1%

, .Ei (bi .

(p _ 21—7; (3.3)

— 21-19%
ET : 2 E} : ZEisinwj), (3.4)

where i is the 'i-th energy deposited in the jet.

All energy deposits within Rfimfl around the axis of a jet are smnmed and a new
direction and energy are calculated. This is repeated until the direction is stable.

If two stable jets are separated by a distance of at least R and at most 2R, a new
jet axis is formed at the midpoint between the two jets and used as a precluster. If
two jets share energy, they are merged if the amount of shared energy is more than

half of the energy of the lower-energy jet. Jets with BT < 8.0 GeV are discarded.

3.3.2 Jet Energy Scale

To determine the parton energy from the jet energy, several effects must be under-
stood [40]. The term “offset. energy” describes energy measured in a jet that does not
come from the original parton. and leads to an offset that must be corrected for in the
energy measurement. Offset energy comes from uranium noise, interactions between
the other partons in the proton and antiproton (known as the underlying event), pre-
vious interactions, and multiple hadron collisions in the event. This may also depend
on the instantaneous luminosity. The calorimeter response. or the relationship be-

tween the energy measured in the calorimeter and the energy of the incident particle,

59

must also be known. Finally. the amount. of energy contained inside the jet cone and
how much energy enters the jet cone from showers of other particles must be known.
The energy of a parton is (.letermined from a jet. using the equation

FJ'jet — huffset
Sjet ° Ps

 

E _
part on —

(3.5)

where Eparmn is the energy of the parton, Ejet is the measured energy of the jet. E0359,
is the offset energy from the sources mentioned above, SM is the response of the
calorimeter to jets, and FS is the fraction of the jet contained within the cone.
These quantities are studied by the jet energy scale group at DC and derived in
various ways. For example, uranium noise is determined and underlying event studies
are conducted using data taken in special runs. SJ-et can be measured as a function
of jet ET with ’7 + jet events. using the energy of the photon as a reference since
photons can be measured more precisely than jets and calibrated more easily. Out-of-
cone showering can be measured using jets in the data, by comparing the energy in
the cone to the energy in a larger cone around the jet axis. The average out-of—cone

energy is estimated as a function of jet ET.

3.4 Electromagnetic Object Reconstruction

Electromagnetic objects are reconstructed using several different algorithms. with
each analysis choosing the one most, suitable for its physics. Here. the simple cone
algorithm is described [41].

First, clusters of adjacent cells with transverse energy greater than 1.5 GeV and a
ratio of energy in the electromagnetic layers to total energy (EM fraction) above 0.9
are identified. Next. the isolation of the cluster is calculated. defined as

EisoTot — EisoCore

isolation :: . . (3.6)
hisoCore

 

60

IQ

0.4 Circle . , Center of Gravity of Initial Cluster
0.2 Circle , ’

   

 

FH+CH

 

EisoTot = '

EiseCore = U

iso: H/U

Figure 3.2: The electromagnetic (E.\l) isolation variable (iso) in the calorimeter. The
energy measured in the central preshower (CPS) detector is not used in the calcu-
lation. Energy measured in the EM. fine hadronic (FH). and coarse hadronic (CH)
layers are used in the calculation. Diagram from [41].

EM
CPS

interaction point

 

 

EisoTot is the total energy in the. cone with radius R : (Al/)2 + (A0)"2 : 0.4 cen-
tered 0n the highest ET tower in the cluster. and EisoCore is the energy in the EM
layers of a cone of radius 0.2 with the same center (see Figure 3.2). The isolation must

be less than 0.2. Clusters which pass these cuts are saved as E.\I clusters.

3.5 Missing Transverse Energy Reconstruction

Missing transverse energy (MET) is a useful tool to select. events containing particles
which will not interact with the detector [412]. Its calculation requires information

from the tracking system. calorimeter, and muon system.

61

MET is calculated by first summing over the i cells in the calorimeter

reg; : 2 Bi”. (3.7)

cells

v is

to determine the x- and y—components of the visible energy. E , in the calorimeter.

The x- and y-projections are METX : —E;i5 and METy : —E;fii"'. The resultant. MET

 

is thus MET: \/(METX)2 + (MISTY)?
The MET can be corrected for muons by subtracting the x— and y-components of
the muon momenta from the x- and y-projections of the MET. The MET corrected

for muons. METCAInLMI ON, is calculated as

 

NIETCAL-PMLON : \/(‘\IETX __ pgmons)2 + (RIETy _ p31u011s)2 (38)
where pgmnb‘ and p‘v‘mo’” are the summed x- and y-components of the muon momenta.

62

Chapter 4

Analysis

Supersymmetry (SUSY) is a proposed syrmnetry between fermions and bosons (see
Chapter 1). In this chapter, the details of the search for evidence of supersymmetry are
presented, including calculations of trigger and reconstruction efficiencies, modeling
of backgrounds, and development of cuts to separate signal from background.

This analysis searches for trilepton events, which may be evidence for supersym-
metry, indirectly by searching for like-sign muon pairs. It has been suggested that the
reach into some parts of SUSY parameter space will be greater when searching with

the like-sign dilepton final state than the trilepton final state [43].

4.1 Data Set

The data used here was recorded between August 2002 and April 2004. It has been
reconstructed with p14.x versions of the ereco package. The data sample used is the
DC New Phenomena group dimuon skim [44]. provided by the DC) common samples
group [45]. The data sample is composed of events with two loose muons and no
trigger requirement.

The quality of the data has been checked by every DC") subdetector group. Each

63

group provides a list of runs which are marked bad due to problems with a par-
ticular subdetector. Events in the sample from runs marked as bad by the muon,
Jet / MET, SMT, or CFT groups are removed. Luminosity blocks marked as bad by
the luminosity group or identified as bad by the calorimeter group are also removed,
as these events may have mismeasured MET and isolation. Up to run 174306, the
trigger 2MU_A.L2MO is required to have fired. From run 174307 to run 184746. the
trigger 2MU_A_L2ETAPHI is required to have fired. For data after run 185746, either
2MU_A-L2MO.TRK5 or 2l\/IU_A_L21\10_L3L6 is required to have fired (see Section 4.2
for trigger definitions). After removing bad runs and luminosity blocks, the total in-
tegrated luminosity of the data. sample that passes one of the selected triggers is

239 i 16 pb-l.

4.1.1 Muon Selection Criteria

Reconstructed muons must satisfy the following criteria (see [38] for more information

about certified muons):

o Satisfy at least the loose muon quality criteria specified by the muon identifi-

cation group.
0 Pass the following cosmic-ray-removal cuts:

1. Time between the expected arrival of a muon and the time measured in
the A-layer scintillator is between -10 and 10 ns (Cosmic-ray muons will
be measured as “out-of—time” with respect to the hard interaction in the

event ) .

2. Time between the expected arrival of a muon and the time measured in

the B- or C-layer scintillator is between —10 and 10 ns.

3. Measured distance of closest approach to the primary vertex is less than

64

0.16 cm. (Cosmic-ray muons can come from any direction, and thus will

not follow paths that point back to the primary vertex.)

0 Parameter 72ch is equal to 3 (the muon has reconstructed segments in the A

and BC layers. plus a match to a central track).

0 Be matched to a three-dimensional central track (two-dimensional tracks based

on only the axial layers of the tracking detectors are also available).

0 Isolated according to the definition in Section 3.2.2. (There is a large dimuon
background from bb production. This cut serves to remove events containing
these muons. Events produced in decays of supersymmetric particles should be

roduced in decays not involvin ' 'ets, and hence be isolated.
. g

4.2 Trigger Efficiency

The triggers used in collecting data. are called 2.\IU_A_L2.\IO, 2.\IU_A_L2ETAPHI,
2.\"1U_A_L21\‘10.TRK5, and 2MU_A-L2I\~IO_L3L6. They have the same requirement at
Ll; at least two muons found in the event using only the scintillatii‘ig tiles.

At L2, the triggers differ. 2.\lU_A_L2.\10 requires one L2 medium muon, while
2.\’lU_A_L2ETAPHI requires two L2 medium muons separated by at least 0.15 in I] or
0.24 in Q5. L2 medium muons are required to have. at least one hit. in the A layer, and
one hit in the B or C layer. The separation requirement is imposed to avoid triggering
on a single muon which the L2 trigger system considers incorrectly to be two muons
very close together.

Only 2MU_A-L21\‘10-TRK5 and 2.\IU_A_L2.\I()_L3L6 have a L3 trigger require-
ment. The L1 and L2 requirement for both is the same as the 2.\1U-A_L2M() trigger. At.
L3, 2MU_A_L2MO-TBK5 requires one track with pT > 5 GeV/c and 2T\lU..’\-L2;\l(§)_L3L6

requires one muon with pT > 6 GeV/c.

The L1, L2, and L3 per-muon trigger efficiencies are calculated with respect to

reconstructed muons, as defined in Section 4.1.1.

4.2.1 L1 Muon Trigger Efficiency

To calculate the L1 muon efficiency with respect to reconstructed muons. events
containing reconstructed muons must be used. Trigger objects stored in the data.
can be checked against the reconstructed muons to calculate the trigger efficiency
However. any event chosen has already fired a trigger in order to be written to tape,
and care must be taken to avoid a bias in calculating the muon trigger efficiency.

To measure the trigger efficiency. dimuon events that fired a single-muon trigger
are selected. At least one of the muons in each dimuon event must have been detected
at the trigger level and caused the trigger to fire. The second muon may or may not
have been detected at the trigger level. and can be used to study the trigger efficiency
without bias.

In each dimuon event. a “control muon" is chosen using a random number gen-
erator. If the control muon is in the same detector octant as a L1 trigger object,
the second muon is used as an unbiased “test muon.” It can be determined whether
the test muon has a matching L1 muon object. The percentage of test muons with
matching L1 objects is the per-muon L1 efficiency. The per-muon L1 efficiency can
be calculated as a function of the reconstructed muon pT, 7], and (,5.

Figure 4.1a shows the L1 muon efficiency as a function of the reconstructed muon
pT measured with respect to loose. nseg : 3 (track—matched) muons. The efficiency

versus 77 is plotted in Figure 4.11) for muons with pT greater than 5 GeV/c.

66

 

 

 

 

 

 

 

 

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.3 E t”
,go.8~—
E I
.. - i
8,0.6—
5.» - f
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50.4——
0.2L
[.
PT(GeV)
(a)
>1_o.o. .0...o‘o ofi—T
‘c’ — o o
.2 “
30.8—
t _
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$0.6r-
.9 j
I: _
50.4:-
0.2—
F
l l l l I l l [#1 I l l l l l l l l
92 -1 o 1 2
11

Figure 4.1: a) The L1 trigger efficiency as a function of pT with respect to loose,
nseg = 3 muons. b) The L1 trigger efficiency as a. function of 7) with respect to loose,
nseg = 3 muons with pT greater than 5 GeV/c.

67

5':

 

 

 

 

 

 

 

1
€9.00... 0. ....oo..
.2 0 o
30.8 o
t .—
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8,015+—
.9 3
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30.4:
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_ L 1 #141 J l 1 l l I l l l I l l l l
92 -1 o 1 :2
n
(a)
1 , ,
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15
PT (GeV)
(b)

Figure 4.2: a) The L2 trigger efficiency as a function of 7; with respect to loose.
nseg 2 3 muons with pT greater than 5 GeV/c. b) The L3 trigger efficiency as a
function of pTwith respect to loose. 'nscg : 3 muons.

68

4.2.2 L2 Muon Trigger Efficiency

The method used to measure the L2 trigger efficiency is similar to the method used to
measure the L1 muon trigger efficiency. Dimuon events that pass the 2l\lU_A._L2.\10
trigger are used to measure the L2 trigger efficiency. Both muons must. be matched
to L1 muons. A control muon is chosen randomly. and is required to be matched to
a L2 muon within AR < 0.5. The other muon becomes the test muon, and can be
checked for a L2 muon match to determine the L2 trigger efficiency. The per-muon
L2 trigger efficiency can be measured with respect to reconstructed muons. The L2

trigger efficiency versus 77 is plotted in Figure 4.2a.

4.2.3 L3 Muon Trigger Efficiency

The method used to measure the L3 trigger efficiency is similar to the method used to
measure the L2 trigger efficiency. Dimuon events that pass the trigger 2l\~*IU_A_L2.\10
are used to measure the L3 trigger efficiency. Both muons must be matched to L1
and L2 muons. A control muon is chosen randomly. The other muon becomes the
test muon, and can be checked for a L3 muon or track match to determine the L3
efficiency. The per-muon L3 efficiency can be measured with respect to reconstructed

muons. The L3 efficiency versus pT is plotted in Figure 4.2b.

4.2.4 Total Trigger Efficiency

The L1, L2, and L3 trigger efficit—mcies are applied to all Monte Carlo samples by
weighting the events by the trigger efficiencies. Since three (.liff(_¥rei'1t. triggers were
used, the total efficiencies are slightly different for the three run ranges. The three

efficiencies are applied in proportion to the amount. of data collected with each trigger.

69

4.3 Reconstruction Efficiencies and Smearing in

Data and Monte Carlo

The measured muon pT resolutions in data and Monte Carlo samples do not agree [46].
The momentum resolution in the Monte Carlo is better than‘in the data. To bring
the Monte Carlo momentum resolution into agreement with the data, the momentum
for each Monte Carlo muon can be randomly altered, or “smeared”, according to a
formula determined by comparing the muon momentum resolution in Monte Carlo
and data samples. Once the smearing is applied, the discrepancy between data and
Monte Carlo reconstruction efficiency must be determined so that the Monte Carlo
can be corrected and used to simulate the data properly.

The muon reconstruction efficiency must also be measured. While the per-muon
trigger efficiency can be determined with respect to reconstructed muons, there is
no analogous reference muon against which the reconstruction efficiency can be mea-
sured. The total muon reconstruction efficiency can be measured, however, by sepa-

rating it into the product of the local muon efficiency and the tracking efficiency.

4.3.1 Monte Carlo Momentum Smearing

In order to correct the difference l.)etween the momentum resolution in Monte Carlo

and data, the Monte Carlo pT is smeared according to the prescription

i—>£+fG. (4.1)
PT PT

where A : 1.0, f : 0.002, and C: is a random number from a Gaussian distribution
with width one and mean zero. The smearing values were determined by comparing

Z bosons in Monte Carlo and data samples [46].

70

4.3.2 Tracking Efficiency

The tracking efficiency for muons is calculated by selecting a high-purity dimuon
sample. Dimuon events that fired one of the dimuon triggers are chosen. One muon,
required to have a matched track. and to be matched to L1 and L2 muons, is chosen
randomly to be the control muon. The other muon is the test muon, and the invariant
mass of the muon pair is then formed using only the local muon system information.
Pairs are chosen whose invariant mass is in the J/\II region (2.0—4.0 GeV/c2), where the
number of real muons should dominate the number of muons from backgrounds. The
frequency with which tracks are matched to the local muons is measured. Figures 4.3a.
and 4.3b show the tracking efficiency as a function of 7] in data and Monte Carlo.

Figure 4.4 shows the ratio of these efficiencies.

4.3.3 Local Muon Efficiency

A sample composed of one track and one muon matched to a track, a L1 muon, and
a L2 muon is selected. The invariant mass of the pair of particles is required to be
in the Z region (70 GeV/c2 < mass < 110 GeV/c2). and the efficiency is measured by
recording how many tracks have matching muons. The single muon skim [45] is used
to avoid a bias from using the dimuon skim. A single muon trigger is required to
have fired. Figures 4.5a and 4.5b show the loose muon efficiency as a function of 7) in
data and Monte Carlo. Figure 4.6 shows the ratio of these efficiencies. A correction

is applied to the Monte Carlo muons to remove the discrepancy.

4.3.4 Muon Reconstruction Efficiency

The muon reconstruction efficiency is obtaiimd by multiplying the reconstruction and
tracking efficiencies. The muon reconstruction efficiency is plotted as a function of 77

in Figure 4.7.

71

"f

 

d

one
o 0...,

P
on

Tracking Efficiency

9

m
lllllillT—f‘l—TIIIT.IIT’

.°
.5

P
N

 

 

 

C)
l
N—
I
_L
c
d
N

 

999
amen-s

.°
N

Tracking Efficiency (MC)
IO
Ntillllillliil
r
L

 

 

(b)

Figure 4.3: a) Tracking efficiency as a function of I] with respect to local muons in
the J / ‘1' peak measured in data. b) Tracking efficiency of reconstructed muons as a
function of 7) with respect to Monte Carlo (MC) muons.

72

 

d
f

iclency

IMCEfl
E;
' l

d
O
O
O
O
O
'0-
.0.
O
O
O
O
O
C

iciency
P
on

[fl T 1

Data Eff

 

 

0.6— I l l l I I l l I I L 1 L 1 I l l l l

-2 -1 0 1 2

 

Figure 4.4: Tracking efficiency measured in data divided by the Monte Carlo (MC)
tracking efficiency as a function of 7) with respect to local muons in the J / ‘11 peak.
There is relatively good agreement between the reconstruction efficiency as mea-
sured in Monte Carlo and data. samples (see Figure 4.7). The small difference is
removed by weighting the Monte Carlo by the ratio of the efficiency in the data to

the efficiency in the Monte Carlo.

4.4 Backgrounds

Not many Standard Model processes are capable of generating a pair of isolated
like-sign muons. The background processes considered are tf, bb/cc. W+jets, and di-
boson (WZ and Z2) production. These backgrounds are modeled with Monte Carlo
samples, with the exception of the bb/CE sample (see Section 4.4.1). The PYTHIA
event generator [47] and the full DQ’) simulation and reconstruction software chain
are used for the Monte Carlo samples with the exception of W+ jets, for which the

ALPGEN event. generator [48] is used. For W+ jets events, the ALPCEN generator

73

 

d

9 9
G on
llllllllllllllill
-.-
.g.
.Q.
.0.
.Q.
.Q.
.0.

Loose Muon Efficiency
9
A

P
N

 

 

 

IO

[.

..

..

..

_

y.

_
Ot—

_.

u
c.

y.

l.

_

_.

N
I
d

 

Loose Efficiency (MC)
P P P
«h m on -t
lilTllillllliIl.llll

.°
N

 

 

 

IO
r
f-
b
h
h-
p—
F
p—
p—
h
b
b

N
.L
O
.5...
[c

(b)

Figure 4.5: a) The loose muon efficiency as a function of I] with respect to tracks
measured in data. The tracks are from muon-track pairs with an invariant mass that
lies under the Z peak. b) The loose muon efficiency as a function of 7) with respect to
Monte Carlo (MC) muons.

 

 

 

 

 

>.m—

o _

C _

.2 _

0

51.2—

n] _

g _

é; — I ‘I I’ f

s: i H H

30.8?

.g _

of
r—riixliiittiiiiliiii
092 -1 o 1

Figure 4.6: The loose muon efficiency as measured in data divided by the Monte Carlo
(MC) local muon efficiency. as a ftmction of 7] with respect to local muons in the Z

peak.

9 .° .° .°
N «5 O on d

Muon Reconstruction Efficiency

IO

 

 

 

 

_:_[]H+"+,++++ WW”

s ] I[f + + [f if

_ i] Mi] [.

£"“-'1"‘6““t ‘2
1]

Figure 4.7: The total muon reconstruction efficiency as a function of I].

 

Sample MC Cross Number of Integrated
Section (pb) MC Events Luminosity (pl) ‘1)

 

tf 0.07 1250 18382

W+1 jet. 757.6 115000 151.8
W+2 jets 222.1 46000 207.1

WZ 3.7 1.6500 4459.4

Z2 1.1 15000 13393

Wbb 1 .54 32000 20779

be 0.2.1 96500 402083
Z M (15-60) 1 13 49000 434
Z/y (60-130) 261 62750 240

Z /7 (130250) 1 22500 22500

 

Table 4.1: The sizes, calculated cross sections, and integrated luminosities of the
Monte Carlo (MC) samples.

is better than the PYTHIA generator. The number of jets can be counted in each
of the W events in data samples. ALPGEN correctly predicts the number of events
with each number of jets, while PYTHIA does not. The CTEQ5L parton distribution
functions (PDFs) are used in generating all the Monte Carlo samples. Table 4.1 lists
the Monte Carlo samples used.

The trigger and reconstruction efficiencies. described in Sections 4.2 and 4.3. are
applied to the Monte Carlo samples. For the bb/cc background, an estimate from the

data is used as described in the following section.

4.4.1 Background From bb/cc‘ Production

The largest source of like-sign muon pairs is expected to be bb and CE production. For
example, like-sign muon pairs can be produced when one B mesons decay produces a
muon, and the other B meson oscillates before decaying. producing a muon with the
same sign. A cascade decay of a b quark (b ——> ccs) from a bb pair can also produce
a like-sign muon pair.

The ideal strategy to model this background would be to generate a Monte Carlo

76

 

 

 

o 1 2 Aq)3

Figure 4.8: The measured Ad) between muons in like-sign muon pairs in the data for
the cases where both muons are isolated and only one is isolated.

sample, as is done with all the other backgrounds. This technique has been tried for
bb/CE, and there are several problems. First. the angular distribution plots made from
the data and Monte Carlo do not agree. There are not enough events produced at low
values of Ad) in the Monte Carlo. This is most likely due to missing bb production
mechanisms such as gluon splitting into bb pairs. Second. the error on the cross section
is large due to a disagreement between the measured and theoretically predicted cross
sections for bb production [49]. Finally. the large bfi cross section and small branching
ratio into like—sign muon pairs makes the production of the desired luminosity difficult.
The number of Monte Carlo events that is needed to simulate the luminosity of
the collected data set is very large. and grows with the size of the data set. The
production of Monte Carlo samples with this many events is very time consuming.
and the computing resources of the experiment are limited. Using a small Monte
Carlo sample would lead to a large error on the background estimate.

In lieu of generating a bfi Monte Carlo sample. data are used to estimate the

77

bb and CE background. The method relies on collecting a set of events that contains
muons similar to those that will be present. in the final data sample. This collection is
formed by looking for like-sign pairs of muons in which one muon passes the isolation
cuts, and one muon fails the isolation cuts by a small margin. The failing muon will
be “nearly” isolated. A nearly isolated muon which fails the isolation criteria by a
small amount will resemble an isolated muon more closely than one that failed the

criteria by a large amount. The following is the definition of “nearly” isolated:
o The muon fails at least one of the isolation criteria defined in Section 3.2.2.
o The muon’s hollow cone energy is less than 7 GeV.
0 The pT sum of all tracks within a cone of radius 0.5 is less than 7 GeV/c.

The number of events in the nearly isolated sample must be scaled to the isolated sam—
ple to accurately predict the number of background events. This is done by defining

the ratio

SN

R: BN

 

(4.2)
A<f>(#~ft)>2.7

where S N is the number of events in the sample containing two isolated muons (signal
sample), and EN is the number of events in the background sample. R is measured in
the region A¢(u, [11) > 2.7 to avoid the bias of normalizing to the signal sample. The
bb/CE background is more peaked in this Act) region than the signal (see Figure 4.8).
The cut A6601, [1) < 2.7 is consequently fixed as one of the final cuts on the data.

R is a function of the momentum of the muons in the like—sign pairs. Since most
of the events in both of the samples used to determine R come from bb decays,
the difference between those measured as isolated or nearly isolated is most likely
due to the momentum kick the muon gets in the decay. Lower-momentum muons

may be kicked away from the b jet and hence measured as isolated more frequently

78

than higher momentum muons. This happens because the lower momentum muons
tend to come from lower momentum B hadrons. The decay products of the lower
momentum B hadrons will naturally be further apart. to conserve momentmn. This
effect is observed when measuring R as a function of pT (see Figure 4.9).

R is measured as a function of the pT of the nearly isolated muon by first calcu-

latin the number of events in each )7 bin in the nearly isolated and in the isolated
r .

sample. R is then calculated in each bin as

SN

1265) : _,, (4.3)

.y
PT Aa(,i.,i)>2.7

 

where SS; is the number of muons in the signal sample at a gIVQI‘l pT, and B]: is the
number of muons in the background sample at. a given Pr

The correct way to measure R would be as a function of the pT of the first and
second muons in the pair. The statistics are not. sufficient to do this. Instead, randomly
choosing a muon from the two muons in the isolated sample has been tried. as well
as using both muons and dividing by two. The results are similar with both methods,
and the second method is used here.

To measure R as a function of pT. an exponential function is fit to the distribution
in Figure 4.9.

The events in the BN sample are then weighted, event-by-event, by the value of
R corresponding to the pT of the nearly isolated muon belonging to the muon pair in
that event. A sample of like-sign pairs remains, composed of muons which represent
the isolated bb/CE muons and scaled correctly to the SN sample. This weighted sample
is denoted here as Bun

Once this weighted sample is in hand, its ability to mimic isolated muons from
bb/CE is tested by looking at the opposite—sign muon pair ii’ivariant mass distribution

(T). The isolated muons from bb/cE contained in the T sample should be similar to

79

 

 

 

 

7? r
N 0.5;-
A _
6- Z
< 04:
h 1—
2 :
E 0.3:— ]
0.2:—
0.13-
W
05 6 7 8 9 10 11 12 13 214
PT(GeV/c )

Figure 4.9: R, the ratio of the number of events in the sample with two isolated muons
to the number of events in the sample with one isolated muon, as a function of the
pT of the nearly isolated muon. The line is an exponential function fit to the data
which was used to weight the background sample in modeling the bb background.
those in the Bw sample, but the normalization will be different.

To make the comparison between the T sample and the BW sample. the Drell—Yan,
Z, and Upsilon backgrounds as predicted by the Monte Carlo are first subtracted from
the T sample. The opposite—sign, isolated muon pairs from bfi/CE remain (T3). The
Bw sample is compared to T3. The two samples are expected to differ only in the
number of events in each sample. The BW sample is scaled by the ratio of the number
of entries remaining in the TB sample to the number of events in the Bw sample, to

get an estimate of the bb/CE background in the opposite—sign distribution:

TN
OS
8“. :BI/V X

_3
3a,. (4.4)

T1; is the number of events in the TB sample, and Ba], is the number of events in the

Bw sample.

80

 

    
 
   
    

 

 

 

A10 DQ Run II Preliminary +039
N % 2/7 mo
3 3 I Y 1s/25 mc OS
> 10 ' scaled bb data(B w )
(3 background sum
n 2
\ 10
a
1:
o
If:
10
1

 

0 20 40 60 80100120 140 1601802
Invariant Mass (GeV/c )

(a)

 

103

.5
O
n

]

Event/3(GeV/c 2)
O

 

15 20 25 30 35 40 45 50
Invariant Mass (GeV/c )

(b)

Figure 4.10: a) Circles show the invariant mass distribution of opposite-sign muon
pairs. Backgrounds are described by the legend. b) Circles show the invariant mass
distribution of opposite—sign muon pairs after the subtraction of Monte Carlo back—
ground estimates. The shaded histogram is the expected remaining background from
bfi/CE. which is estimated using like—sign data.

81

 

Events I 1 GeV
8”

.L
O

 

 

40 sq
Invariant Mass (GeV/c )

Figure 4.11: Circles show the invariant mass distribution of isolated like-sign muon
pairs in data. The shaded histogram is the expected remaining background, from
bb/CE, which is estimated using the nearly isolated like-sign data as described in the
text.

Figure 4.10a shows the opposite—sign, isolated data and the various backgrounds.
Figure 4.10b shows the invariant mass distribution in data after all backgrounds
except bb/CE are subtracted, and the expected distribution from bb/cE background.
The distributions agree well except at low momentum. The difference between the
data and Monte Carlo plots stems from a deficit of Monte Carlo muons just above
the pp cutoff for the plot (5 GeV). Above that, there is good agreement. The search
isn’t badly affected by this region since there is an 11 GeV pT cut on the leading
muon that removes virtually all of these low mass pairs.

Using the nearly isolated sample. the bb/cc background can be modeled in the
signal sample, and the number of bb/CE events can be estimated given any set of cuts.
Figure 4.11 shows the like-sign isolated data, which may contain signal. compared to

the estimation from the scaled nearly isolated sample.

82

4.4.2 Sign Misidentification Background

If the pT of a muon is badly I'nismeasured, the charge assigned to the muon can be
wrong. This can turn a real opposite-sign pair into a II’IQ‘dSUI‘Gd like-sign pair. This sign
misidentification happens because higher momentum tracks bend less in the inner
magnetic field, so it becomes more difficult. to measure their curvature. Straighter
tracks are more likely to have their charge n'iismeasured. Since this analysis depends
upon the proper determination of the sign of each muon, an estimate of the sign
misidentification rate is necessary.

The major source of sign misident ification comes from Z / '7' event s where one muon
has its momentum badly mismeasured. Backgrounds from this source as predicted by
the Monte Carlo simulation are included in the background estimation in Section 4.7.

As a check of the Monte Carlo‘s ability to estimate the rate of sign mismeasure-
ment, like—sign pairs with each muon having a pT greater than 15 GeV/c and with a cf)
difference greater than 2.8 were chosen from the Z Monte Carlo and data. These pairs
should each contain a muon from a Z decay with its charge mismeasured. Although
the statistics are low, there is reasonable agreement with 4 events observe(_l in the

data and 3.4 $1.2 events predicted in Monte Carlo studies.

Sign Misidentification Background Cross-Check

An attempt. to cross-check this estimate using data was made. The spectrum of
opposite-sign pairs that forms the pool of candidates for mismeasurement is plotted
in Figure 4.12. This is a plot of the pT of all muons is opposite-sign pairs contain-
ing at least one muon with a pT greater than 11.0 GeV/c. This spectrum should
be multiplied by the charge misnieasurement rate, if it can be obtained from data.
To determine the mismeasurement rate, opposite-sign pairs of muons are used. One
muon is first chosen randomly. For this muon. the momentum measured in the muon

system is used. The invariant mass of the pair is then formed. If the. invariant mass

83

 

500

2)

llll—rllTWIIITlllllrlllrl
-o-
-o-

400

(GeV / c
0)
O
O

Events I 4
N
O
O

 

 

 

 

1 1 1 1 14 #1 1 1 1
00 50 10 156* 2 200
PT (GeV/c )

Figure 4.12: The pT spectrum of opposite—sign muon pairs as measured in data. These
muons could be used to estimate the pool of C21I'I(.li(l‘di€S for sign mismeasurement.
is in the Z peak. the sign measured by the nmon system is compared to the sign
measured by the tracking system. The rate of sign mismeasurement is extracted as a
function of pT.

Unfortunately, the invariant mass distribution did not show a clear Z peak. This
is likely due to the poor momentum resolution of the muon system at high pT. This

cross-check method is therefore not reliable. and thus was not used.

4.5 Signal Monte Carlo

Signal Monte Carlo samples are generated for several sets of values of the input
parameters described in Section 1.5. The points in mSUGRA parameter space for
which Monte Carlo samples were generated are summarized in Table 4.2. The cross
sections generated by PYTHIA are based on leading order calculations in perturbation

theory. and have been multiplied by a k-factor of 1.25 to correct them based on other

84

 

SUSY ax BR
Point mo 7721/2 tan 1'3 .41, (pb) New B i? {'2 if I

 

1 68 182 3 (1 .59 .45 .0031 63 115 112 104
2 90 180 3 f) .20 .41 .0085 62 114 110 119
3 85 190 5 (1 .40 .20 .0020 68 123 120 118
4 108 220 5 () .15 .10 .0027 82 147 145 142
5 65 170 5 0 .83 .28 .0014 59 107 103 100
6 70 175 3 300 :15 .55 .0051 58 107 101 103
7 75 180 3 300 .38 J“; .0050 60 111 105 108
8 80 185 3 :MX) .33 .45 .0057 63 115 110 112
9 85 190 3 INN) .28 .45 .0067 65 119 114 117
10 85 195 3 IMM) .24 .18 .0031 67 123 118 118
11 90 200 3 300 .20 .31 .0064 70 127 123 123
12 76 170 3 0 .32 .72 .0094 57 106 101 106
13 80 175 3 0 .25 .67 .0112 60 110 106 110
14 84 180 3 () .21 .53 .0105 62 114 110 114
15 65 180 3 300 .58 .52 .0037 60 111 105 101
16 70 185 3 300 .48 .55 .0047 63 115 110 105
17 75 190 3 300 .37 .39 .0044 65 118 114 110
18 72 165 3 0 .39 .82 .0087 55 102 ST? 102
19 74 168 3 0 .35 .79 .0094 56 104 100 104
20 88 185 3 () .18 .47 .0109 64 118 114 118

 

Table 4.2: The values for the 20 points in mSUGRA parameter space chosen for study.
the cross section times branching ratio to trileptons for each point, the masses of the
two neutralinos ()2? and fig), chargino (if) and slepton (l) for each point, the number
of events expected (New) for 239 pl)‘1 of data and the efficiency (E) for each point.
The mSUGRA parameters are defined in Section 1.5. The sign 11 parameter is always
positive. Points in bold are used in setting a limit. in Section 4.9.
next-to-leading order calculations [50]. The CTEQ5L parton distribution functions
and PYTHIA version 6.202 are used in generating the signal Monte Carlo samples.
The same information is presented graphically in figures 4.13 and 4.14. In F ig-
ure 4.13. the points are separated into those with tand : 5, those with tan ,3 2 3
and A0 : 0, and those with tan} : 3 and .40 : 300. The points which are used in
setting a cross section limit in Section 4.9 are marked in Figure 4.13.

These points are chosen for a few reasons. They all have chargino masses near and

above the mass limit set by the LEI) experiment.

 

 

 

 

 

 

 

 

0'9:
C : . +tanBeta=5
20.8?
.5 _ +A0=300
$0.7;— —e—AO=0
$0.6;— , o
2 a
00'55 ,v
m .—
—0.4_— ‘
:9 E 000 v
.20.3:' v
> : ° ,
0.2;— 0 0°
0.13—
:IlllIlllllllllllIllllllllllllllllllllllll‘lllllll
60 65 70 75 80 85 90 95 100 105 0110
m

Figure 4.13: The cross section times branching ratio into three leptons as a function
of the mo parameter.

 

 

C

,9 0.9

8 0.8

u, 0.7

(D

e 0.6
0.5

:73 0.4

.2

> 0.3
0.2
0.1

—-— Points Used for Limit Plot

 

 

 

'11!llllllIIllllllllllllllllIllllllIllll

 

llillLlJl 111

1 l I l 1 l 1 I l J l A 1 L41
100 110 120 130 140 150
Chargino Mass

 

 

{‘3
0111111111

Figure 4.14: The cross section times branching ratio into three leptons as a function
of the mass of the chargino.

For this study. a small number of points is chosen. with the knowledge that a more

complete scan of the SUSY parameter space will follow. The choice of points is based

86

on the masses of the chargino. neutralino. and slepton. If the slepton is lighter than
the chargino and neutralino, the chargino and neutralino will decay into the slepton.
In this case, the event topology is very dependent on the neutrali1‘1o-cl’1argino mass
difference. The study of this case is postponed due to this complexity.

The case where the slepton is heavier than the neutralino and chargino is chosen.
Since the chargino and neutralino decay via virtual gauge bosons, the leptons tend
to have larger momenta. This leads to higher efficiencies for these initial studies.

The sign of 11 is taken as positive because this is favored by measurements made
by the g—2 experiment [51]. Further studies will include points with the sign of /.1.
taken as negative.

The points studied here are used to guide the development of analysis cuts. They

can be fine-tuned on the fuller scan of SUSY space that will follow.

4.6 Analysis Cuts

The final analysis cuts are determined by studying the background and signal Monte
Carlo samples. The goal is to minimize the background efficiency while maximizing
the signal efficiency.

As a starting point, events must have two loose. nscg : 3 (track-matchml), iso-
lated, like-sign muons with pT > 5 GeV/c. This defines the initial data set. part of
which is used to predict the background as described in Section 4.4.1. The pT dist ri-
butions of muons in the bb background sample and in a signal Monte Carlo sample
(SUSY point 14) are shown in Figure 4.15.

To further reduce the bb background, a cut is made 011 the distance in (b between
the two muons. Muons from bb decays tend to be back-to-back in d), as shown in
Figure 4.8. Figure 4.16 shows the A¢6(11.. 11) distribution for the b5 background and

for a signal Monte Carlo sample (SUSY point 14) In addition. the leading muon pf

87

h
0
O

Evenatos l 2 GeV/c

N

100

 

 

O 10 20 30

. SUSY MC
— bb Bgd

 

40 50 60 70 80
PT (GeV/c)

Figure 4.15: The pT distribution of muons in the bb background sample and in a
signal Monte Carlo sample (SUSY point 14).

Events / 0.125
8 ‘3
O O

:10
O
O

IIIIIIIIIIIIIIIIIIIUITIT

200

100

 

 

E} susv MC

._. Background

 

 

 

 

   

Figure 4.16: The Aq5(;1.p) distribution in the bb background sample and in a signal
Monte Carlo sample (SUSY point 14).

88

 

g 2506

3 D9 Run II Preliminary
02000

m 0

ti 0 0 ,

7, . SUSY MC
2

1n

8
8

‘s”

 

    

60 7O 80
1/2

Scaled Missing E 1 (GeV )

Figure 4.17: The scaled missing transverse energy distribution in the bb background
sample and in a signal Monte Carlo sample (SUSY point 14).

must be greater than 11 GeV/c. This greatly reduces the background from these
low-momentum muons.

Mismeasurements in the calorimeter can lead to artificial MET. To remove this
background, a variable called the scaled MET has been developed [52]. It is computed
as the MET divided by an estimate of the jet resolution projected onto the direction
of the MET. This variable can be used to measure the significance of the .\'IET and
to remove events with large MET due to the mismeasurement of the energy of a jet.

This variable is defined as:

MET
\/2(. ET... xsin(01-..t) >< |cos(A(p(jet.I\1ET))I)2

scaled MET = (4.5)

The distributions of scaled MET in the bb background sample and in a signal Monte

Carlo sample (SUSY point 14) are shown in Figure 4.17. A requirement that the

89

 

600

— . SUSYMC
_ — bngd

400

Events I 0.1

 

200

 

 

0.5 1 1.5 2 2.5 3
A¢(MET-Jet)

Figure 4.18: The distance in <15 (AMMET. Jet)) between the direction of the missing
transverse energy (_MET) in the event and the jet furthest away from the direction of
the MET in the bb background sample and in a signal Monte Carlo sample (SUSY
point 14).

scaled MET must be greater than 8 GeVl/2 is introduced.

In addition, the separation in at between the MET direction and the direction of
jets in the event is examined. Events containing bb pairs may have jets aligned with
the direction of MET from the neutrino produced in the b decay (see Figure 4.18).
Also. a jet’s energy can be mismeasured, creating artificial MET. A requirement that
(A¢(Jet, A«[ET)) must be less than 2.7 is introduced to remove these events.

Another variable used to discriminate between signal and background is the prod-
uct of the MET and the pT of the lower pT muon in the event. It. effectively raises the
MET requirement when one muon has a low momentum. when there is more back—
ground from b5 production. The distributions of this variable in the bb background
sample and in a signal Monte Carlo sample (SUSY point 14) are shown in Figure 4.19.

A requirement that the product of the MET and the pT of the lower pT muon in the

90

 

    
 

 

 

 

% f; 0’ D9 Run II Preliminary
02000
s
19 i 0 -— bb Bgd
r o
15 .- . ' .
1000 p
. o.
o
'0‘...
”a... o.
‘-1114411111”1..Q-:.W
0 500 1 000 1 500 2000 2500 3000

Missing ET x PT Second Muon ( GeV 2I c)

Figure 4.19: The distribution of missing transverse energy multiplied by the pT of
the lower pT muon in the bb background sample and in a signal Monte Carlo sample
(SUSY point 14).

event must be greater than 300 GeV2/c is introduced. This implies a cut of 60 GeV
on the MET when the pT of the lower pT muon is 5 GeV/c and a cut of 30 GeV 011
the MET when the pp of the lower pT muon is 10 GeV/c.

To remove background events containing Z bosons. coming from WZ, ZZ and Z/e/
production, a requirement that the invariant mass of opposite-sign muon pairs must
be less than 70 GeV/c2 or greater than 110 GeV/c2 is placed on opposite-sign muon
pairs in trimuon events.

An invariant mass cut can also be used to reject background events containing a
Z boson where one muon’s charge was misidentified. In this case, the momentum of
the misidentified muon tends to be very high. leading to a large invariant mass. A
requirement that the mass of like-sign muon pairs must be less than 80 GeV/c2 is
introduced.

Cuts to remove muons from cosmic rays were applied as suggested by the DO muon

91

identification group (see Section 4.1.1). Further studies indicated that the A4601. 11,) <
2.7 cut actually removes most of these muons. but no additional significant loss is
added by using the muon id cuts. and they remove the few remaining muons from
cosmic rays.

In addition to comparing signal and background samples to determine each cut
to be used, a permutation study was done to check the relative effect of each cut
and to attempt to increase the overall signal efficiency. The permutation study was
done using signal Monte Carlo samples. The number of events remaining after all
cuts was determined and then checked against the number of events remaining after
removing one of the cuts. This was repeated for each cut to check for inefficiencies.
The inefficient cuts were then re-examined. This was useful in focusing attention on
inefficient cuts in need of further study. as well as in uncovering technical mistakes

that were inefficient due to coding errors.

4.6.1 Summary of Analysis Cuts

The final analysis cuts are sumn’iarized here for clarity:
0 Events must have two loose. nseg : 3 (track-matched), like-sign muons.

Both muons must be isolated.

Both muons must have pT greater than 5 GeV/c.

The distance in (15 between the two muons must be less than 2.7.

The leading muon pT must. be greater than 11 GeV/c.

The product of the MET and the pT of the lower Pr muon in the event must

be greater than 300 GeV2/1:.

The scaled MET must be greater than 8 GeV 1/ 2.

92

o If there is a third muon in the event. the invariant mass of opposite-sign muon

pairs must be less than 70 GeV/c or greater than 110 CeV/c.
0 The invariant mass of like-sign muon pairs nmst be less than 80 GeV/c.

o The distance in (.0 between the MET directimi and the direction of any jet in

the event (Ad)(Jct. 111ET)) must be less than 2.7.

The effect of these cuts on the signal Monte Carlo samples is shown in Tables 4.3
and 4.4. It is clear from these tables that. the sensitivity to this new physics varies
depending on the values of the unknown parameters in the theory. This occurs because
the masses of the supersymmetric particles and cross sections vary as these values are

changed.

4.7 Comparison of Expected Background to Data

The effect. of the analysis cuts on the background and data samples is shown in
Tables 4.5 and 4.6. One event passes the cuts in the data and 0.37i0.16 events
are expected from the background. The largest remaining backgrounds are from bb
production and WZ boson production.

Some background from bb production remains due to its large cross section. Es-
pecially at low momentum. it is difficult to remove all muon pairs originating from
this background.

The WZ boson production background is difficult to remove because the W and Z
particles’ superpartners are the chargino and neutralino. Therefore, events from this
background are similar in nature to the events that are being sought.

There are several sources of uncertainty in the background estimation. The uncer-
tainty in the luminosity measurement of the data sample is estimated at 6.5%. The

trigger and reconstruction efficiency measurements have estimated errors of less than

93

 

 

 

 

 

 

 

 

 

 

Sample SUSY l SUSY 2 SUSY 3 SUSY 4
Initial 1.50 (.14) 1.07 (.07) 0.68 (.07) 0.30 (.03)
A69(/1,11) 1.21 (.13) 0.84 (.06) 0.52 (.06) 0.24 (.03)

pT > 7 1.21 (.13) 0.83 (.06) 0.51 (.06) 0.23 (.03)

pT > 9 1.18 (.12) 0.82 (.06) 0.50 (.06) 0.23 (.03)

pT > 11 1.11 (.12) 0.80 (.06) 0.50 (.06) 0.22 (.03)
METXpT > 100 1.06 (.12) 0.73 (.06) 0.45 (.06) 0.21 (.02)
METXpT > 200 0.81 (.10) 0.60 (.05) 0.35 (.05) 0.19 (.02)
METXpT > 300 0.58 (.09) 0.51 (.05) 0.28 (.05) 0.15 (.02)
A6(Jet,MET) 0.53 (.08) 0.49 (.05) 0.26 (.05) 0.14 (.02)
LS InvMass 0.50 (.08) 0.44 (.05) 0.22 (.04) 0.11 (.02)
OS InvMass 0.47 (.08) 0.42 (.05) 0.21 (.04) 0.11 (.02)
scaled MET > 8 0.45 (.08) 0.41 (.05) 0.20 (.04) 0.10 (.02)
Sample SUSY 5 SUSY 6 SUSY 7 SUSY 8
Initial 1.17 (.14) 1.29 (.11) 1.32 (.19) 0.95 (.13)
110501,”) 0.87 (.12) 1.02 (.10) 0.97 (.17) 0.80 (.12)

PT > 7 0.86 (.12) 1.01 (.10) 0.97 (.17) 0.80 (.12)

pT > 9 0.81 (.12) 1.00 (.09) 0.96 (.17) 0.80 (.12)

pT > 11 0.74 (.11) 1.00 (.09) 0.94 (.16) 0.79 (.12)
METXpT > 100 0.66 (.11) 0.94 (.09) 0.91 (.16) 0.75 (.11)
METXpT > 200 0.46 (.09) 0.82 (.09) 0.76 (.15) 0.71 (.11)
METXpT > 300 0.34 (.08) 0.70 (.08) 0.65 (.14) 0.63 (.10)
A¢(Jet,MET) 0.30 (.07) 0.67 (.08) 0.61 (.13) 0.61 (.10)
LS InvMass 0.29 (.07) 0.59 (.07) 0.53 (.12) 0.54 (.10)
OS InvMass 0.29 (.07) 0.59 (.07) 0.53 (.12) 0.54 (.10)
scaled MET > 8 0.28 (.07) 0.55 (.07) 0.46 (.12) 0.45 (.09)
Sample SUSY 9 SUSY 10 SUSY 11 SUSY 12
Initial 0.94 (.13) 0.89 (.16) 0.77 (.14) 2.05 (.09)
A6011, 11) 0.79 (.12) 0.65 (.13) 0.58 (.12) 1.61 (.08)

pT > 7 0.79 (.12) 0.63 (.13) 0.58 (.12) 1.61 (.08)

pT > 9 0.78 (.11) 0.63 (.13) 0.55 (.12) 1.58 (.08)

pT >11 0.78 (.11) 0.61 (.13) 0.55 (.12) 1.54 (.08)
METXpT >100 0.76 (.11) 0.55 (.12) 0.51 (.12) 1.46 (.07)
METXpT > 200 0.70 (.11) 0.45 (.11) 0.45 (.11) 1.23 (.07)
METXpT > 300 0.66 (.11) 0.33 (.10) 0.41 (.10) 1.00 (.06)
A¢(Jet,MET) 0.61 (.10) 0.29 (.09) 0.39 (.10) 0.94 (.06)
LS InvMass 0.49 (.09) 0.23 (.08) 0.35 (.10) 0.84 (.06)
OS InvMass 0.49 (.09) 0.23 (.08) 0.33 (.09) 0.82 (.06)
scaled MET > 8 0.45 (.09) 0.18 (.07) 0.31 (.09) 0.72 (.05)

 

 

 

Table 4.3: Number of events after applying each cut. to signal Monte Carlo samples
for points 1—12. Total errors (sum of statistical and systematic) are in parentheses.

94

 

 

 

 

 

 

 

Sample SUSY 13 SUSY 14 SUSY15 SUSY 16
Initial 1.76 (.08) 1.41 (.06) 1.75 (.17) 1.73 (.15)
A6(11.11) 1.41 (.07) 1.08 (.05) 145(15) 1.34 (.14)
pT>7 1.40 (.07) 1.08 (.05) 1.42 (.15) 1.32 (.14)
pT>9 1.38 (.07) 106(05) 1.35 (.15) 1.29 (.13)
pT>11 1.35 (.07) 1.03 (.05) 1.29 (.14) 123(13)
METXpT>100 1.25 (.07) 0.98 (.05) 1.20 (.14) 1.16 (.13)
METXpT>200 1.08 (.06) 0.85 (.05) 1.20 (.12) 094(11)
METXpT>300 0.88 (.06) 0.70(.04) 0.71(.11) 0.74(.10)
A¢(Jet,MET) 084(05) 066(04) 0.65(.10) 0.71(.10)
LSInvMass 0.76(.05) 059(04) 0.60(.10) 0.65(.09)
OS InvMass 073(05) 0.56 (.04) 0.57 (.10) 0.63(.09)
scaled MET>8 067(05) 053(04) 0.52 (.09) 055(09)
Sample SUSY 17 SUSY 18 susv 19 SUSY 20
Initial 1.33 (.11) 2.60(.14) 2.21(.12) 1.24 (.06)
Arman) 094(10) 2.01 (.12) 1.76 (.11) 0.96(.05)
pT>7 0.92 (.10) 2.00 (.12) 1.75 (.11) 0.96(.05)
pT>9 0.89(.09) 1.93 (.12) 1.72 (.11) 0.95 (.05)
pT>1l 0.85 (.09) 1.84 (.12) 1.62 (.10) 0.92 (.05)
METXpT>100 0.80(.09) 1.74 (.11) 151(10) 0.88 (.05)
METXpT>200 0.68 (.08) 1.49 (.10) 1.26 (.09) 077(05)
METXpT>300 055(07) 1.10 (.09) 1.01(.08) 0.65(.04)
A¢(Jet,MET) 0.52 (.07) 1.03 (.09) 0.95 (.08) 0.61(.04)
LSInvMass 045(07) 0.95 (.08) 0.87 (.08) 0.56 (.04)
OSInvMass 0.43 (.07) 0.93 (.08) 084(07) 0.53(.04)
scaled MET>8 0.39(.06) 0.82(.08) 0.79(.07) 0.47(.04)

 

Table 4.4: Number of events after applying each cut to signal i\"Ionte Carlo samples
for points 13—20. Total errors (sum of statistical and systematic) are in parentheses.

 

 

 

 

 

 

 

 

 

Sample bb WZ ZZ tf
Initial 3961.05 (41.24) 0.53 (.17) 0.08 (.05) 0.01 (01)
A¢(11.11) 2226.71 (31.03) 0.41 (.14) 0.06 (.04) 0.01 (.01)
pT > 7 902.29 (18.00) 0.41 (.14) 0.06 (.04) 0.01 (.01)
pT > 9 269.60 (8.73) 0.41 (.14) 0.06 (.04) 0.01 (.01)
pT > 11 91.85 (4.68) 0.41 (.14) 0.06 (.04) 0.01 (.01)
METxpT > 100 19.83 (2.15) 0.41 (.14) 0.04 (.03) 0.01 (.01)
METxpT > 200 6.88 (1.32) 0.37 (.14) 0.04 (.03) 0.01 (.01)
METxpT > 300 1.42 (.58) 0.37 (.14) 0.04 (.03) 0.01 (.01)
A¢(Jet,MET) 1.012 (.51) 0.37 (.14) 0.04 (.03) 0.01 (.01)
LS InvMass 0.61 (.35) 0.21 (.10) 0.01 (.02) 0 (0)
OS InvMass 0.61 (.35) 0.15 (.09) 0 (0) 0 (0)
scaled MET > 8 0.17 (.12) 0.15 (.09) 0 (0) 0 (0)
Sample be Wj Wjj Wbb
Initial 0.06 (.01) 3.50 (2.73) 0 0.31 (.07)
A¢(,u,/1) 0.04 (.01) 3.50 (2.73) 0 0.26 (.06)
pT > 7 0.04 (.01) 3.50 (2.73) 0 0.25 (.06)
pT > 9 0.04 (.01) 3.50 (2.73) 0 0.25 (.06)
pT > 11 0.04 (.01) 3.50 (2.73) 0 0.25 (.06)
MET><pT > 100 0.02 (.01) 2.38 (2.23) 0 0.23 (.06)
METXpT > 200 0.02 (.01) 2.38 (2.23) 0 0.15 (.05)
MET><pT > 300 0.01 (.01) 1.08 (1.58) 0 0.09 (.04)
A<1>(Jet.MET) 0.01 (.01) 1.08 (1.58) 0 0.06 (.03)
LS InvMass 0.01 (.01) 0 (0) 0 0.06 (.03)
OS InvMass 0.00 (.00) 0 (0) 0 0.06 (.03)
scaled MET > 8 0.00 (.00) 0 (0) 0 0.05 (.03)
Sample Z/7 (15-60) Z/y (60-130) Z/y (130-250)
Initial 1.41 (1.41) 40.59(7.22) 0.52 (.12)
A4501, 11) 1.41 (1.41) 6.43 (2.90) 0.03 (.03)
pT > 7 0 (0) 6.43 (2.90) 0.03 (.03)
pT > 9 0 (0) 6.43 (2.90) 0.03 (.03)
pT > 11 0 (0) 6.43 (2.90) 0.03 (.03)
MET><pT > 100 0 (0) 5.49 (2.73) 0.03 (.03)
METxpT > 200 0 (0) 4.36 (2.41) 0.03 (.03)
METXpT > 300 0 (0) 3.56 (2.23) 0.03 (.03)
A¢(Jet,MET) 0 (0) 3.56 (2.23) 0.03 (.03)
LS InvMass 0 (0) 0 (0) 0 (0)
OS InvMass 0 (0) 0 (0) 0 (0)
scaled MET > 8 0 (0) 0 (0) 0 (0)

 

 

 

Table 4.5: Number of events remaining in b5, WZ, ZZ. tt, be. Wj, Wjj, Wbb. Z/7
background samples after applying each cut to the samples. Total errors (sum of
statistical and systematic) are in parentheses.

96

 

Sample Background Data

 

Initial 4008.06 (42.09) 4223
A¢(11.1i) 2238.85 (31.33) 2417
pT > 7 913.01 (18.45) 966
pT > 9 280.32 (9.62) 285
pT > 11 102.57 (6.19) 95

METXpT>100 28.43 (4.37) 26

 

 

 

 

METxpT > 200 14.22 (3.74) 9
METXpT > 300 3.02 (1.71) 6
A¢(Jet.MET) 1.49 (0.54) 4
LS InvMass 0.90 (0.37) 3
OS InvMass 0.82 (0.37) 2
scaled MET > 8 0.37 (0.16) l

 

Table 4.6: Number of events remaining in data and the number expected from the
sum of all backgrounds after applying each cut. Total errors (sum of statistical and
systematic) are in parentheses.

1%. The systematic errors from the uncertainty on the Monte Carlo cross sections are
estimated at 10%. This estimate is made by comparing the cross sections generated
by PYTHIA with measured cross sections.

There are also systematic errors arising from differences between the Monte Carlo
and data in the METxpT and A¢(MET, Jet) distributions. The differences in these
distributions are checked by comparing Z Monte Carlo and data samples. The percent—
ages of events beyond the cut value in Monte Carlo and data samples are measured
and the difference is used as an estimate of the systematic error on the background.
The errors are estimated at 10% for METXpT and 10% for A¢(MET. Jet).

Three event displays of the event ill the data passing all of the cuts are shown in
Figures 4.20, 4.21, and 4.22. Table 4.7 shows some relevant information about this

event.

97

 

.. 31—- we unnur -:

 

 

Figure 4.20: Event display of the event passing all cuts in data. event number 44096517
from run 177010. In the middle of the display, reconstructed charged-particle tracks
can be seen. The green lines represent muons traversing the detector.

 

Object E pT pI py p; 1] (1) charge

Muon 1 14.1 13.8 12.5 5.8 -2.6 -0.19 0.43 +

Muon 2 62.2 29.1 —10.9 26.9 —55.0 -1.39 1.96 +
MET 33.5 -13.9 -30.4 4.28

Table 4.7: Table showing the kinematic values for the two muons and MET in run
177010, event 44096517.

4.8 Combining Results with Other Channels

Searches for the associated production of chargino and neutralino sparticles have
been conducted using the electron. muon, and track final state. the dielectron and
track final state, and the dimuon and track final state [52—54]. Better limits on the
cross section for associated production of chargino and neutralino sparticles with

leptonic final states are set by combining the results from those searches and the

98

E scale: 3 GeV

35;...2I {L's—.Lv‘

 

Figure 4.21: Event display of the event passing all cuts ill data. event number 44096517
from run 177010. Reconstructed tracks are visible in the center of the display. The
red. orange and green bars are hits in the A. B, and C layers of the muon system.

 

Channel Luminosity (pb‘l) Data Expected Background Neuluded

 

e+e+track 249 1 0.68i0.40 5.0
,u + n+track 221 1 l.83d:0.40 5.7
e+p+track 235 0 0.29:1:033 3.2
LS 1111 239 1 0.37:1:016 4.4
Combined 3 3.17:1:067 4.8

 

Table 4.8: Luminosity, number of observed candidate events, expected number of
background events for each final state used in determining the combined cross section
limit, and the excluded number of signal events (Nemuded).
search described in this analysis [55].

The relevant data from those channels are summarized in Table 4.8. The combina—
tion of results is performed using the LEP CLS method [56]. The number of excluded
signal events is given for each channel separately. and is independent of the SUSY

models used.

99

. q!»
E scale. 3 GeV --.

 

Figure 4.22: Event display of the event passing all cuts in data, event number 44096517
from run 177010. Reconstructed tracks are visible in the center of the display. The
red, orange and green bars on the outer part of the display are hits in the A. B,
and C layers of the muon system. The red and blue blocks represent energy in the
calorimeter and the yellow block represents missing energy.

4.8.1 CLS Method

The LEP CLS method [56] is summarized here for completeness.

The likelihood ratio can be written as
X=H&. mm

with

 

an

‘X’ _ CT<5i+bi)(8i _+_ bi)d,j/€~bib;ii
i — —— .

(iii (11'!

100

where s,- is the estimated signal in the ith channel, I), is the estimated background in
the ith channel, and d, is the number of observed candidates.

The confidence level for excluding the presence of both signal and background is

C7113+b : P3+b(1¥ S Xobs), (4.8)

the probability, assuming the presence of signal and background, that the likelihood

ratio would be less than or equal to that observed in the data. This probability is

 

e (‘2' -+bi)( (s I,er
maxsxobs): 2 H l , (4.9)

{<l}\\{d })i=1

where X ({d,}) is the likelihood computed for the observed set of candidates in each
channel {di}, summed over all outcomes {d;} with likelihoods less than or equal to
the observed one.

The confidence level for the background alone,
C'Lb : Pb(X S X0b3), (4.10)

can also be computed.

The confidence level C L3 is then computed as the ratio
CLS : CL3+b/CL(,. (4.11)

To derive a limit on the cross section for a given SUSY point, the cross section
corresponding to that point is disregarded, and the cross section is treated as a free
parameter. The efficiency and uncertainty for the SUSY point are used. The con-
fidence level is then calculated as a function of the cross section. The value of the

cross section that corresponds to a confidence level of 95% is interpreted as the cross

101

section limit for the SUSY point. This can be repeated at several SUSY points to
obtain a cross section limit for each point. Since each point corresponds to a chargino

mass, a cross section limit as a function of the chargino mass is obtained.

4.9 Cross Section Limit

A 95% confidence level limit on the total cross section for associated chargino and
neutralino production with leptonic final states has been set. The limit is presented
as a function of the if mass (see Figure 4.24 and Table 4.9). SUSY points 12, 13, 14,
18, and 20 are used in setting the limit. These points are chosen because they have
slepton masses equal to or just above the chargino and neutralino masses. These were
chosen to force the decays of the chargino and neutralino via virtual gauge bosons,
which results in higher pT leptons in the final state.

Chargino masses below 103 GeV/c“Z are excluded by direct searches at LEP, while
this search nearly excludes masses above this threshold. Masses below 97 GeV/c2 are
excluded by the present search. For comparison, the limit in the like-sign dimuon final
state alone is shown in Figure 4.23.

This result improves on the D0 and CDF Run I results [57,58] for the regions of
SUSY space it explores. For the D0 Run I result, searches were done in the eee, een,
can, and min final states with between 75 pb‘1 and 95 pb‘1 of data, and limits were
set at the 95% confidence level. Data. currently being collected will permit further

improvement, including the capability to exclude {It masses above the LEP limit.

102

 

SUSY a x B R NW, E )1 1+ affiffl (Iffjffl
1 .59 .45 .0031 112
.20 .41 .0085 110

 

3 .40 .20 .0020 120
4 .15 .10 .0027 145
5 .83 .28 .0014 103
6 .45 .55 .0051 101
7 .38 .46 .0050 105
8 .33 .45 .0057 110
9 .28 .45 .0067 114
10 .24 .18 .0031 118
11 .20 .31 .0064 123
'12 .32 .72 .0094 101 1198 (138
'13 .25 .67 .0112 106 1179 (135
14 .21 .53 .0105 110 176 (133
15 .58 .52 .0037 105
16 .48 .55 .0047 110
17 .37 .39 .0044 114
18 .39 .82 .0087 97 2111 (140
19 .35 .79 .0094 100
20 .18 .47 .0109 1L4 iL70 (130

 

Table 4.9: For the SUSY points, the cross section times branching ratio to trileptons,
the mass of the chargino (if) the number of events expected (Nexp) and the efficiency
(E) for each point for 239 pb‘1 of data, and the cross section limit in the like-sign
dimuon channel (03:2) and overall (0,2231). Points in bold are used in Figures 4.24 and
‘123.

103

 

3.5

2.5

o(xfx§)>< BR<3I> [pr
N
/TTI’I

 

 

-&
lllllllllllllllli

l l l l I l l l i l l l l l l I I

llwl. I
98 100 102 104 106 108 11
Maineew

O

 

l 1 ll
0 112

Figure 4.23: Limit on the total cross section for associated chargino (if) and neu-
tralino (>23) production in the like-sign dimuon channel as a function of the if mass.

104

 

Limit on o x BR(3I)

 

1'4 LEP 00 Run l
Chargino

Searches

c<xfx2>>< BH<3IHpb1
a:

D9 Run II (- - - Expected limit)

 

 

  

O . .mfil’GBA Predktiqn l . . . I . . .
98 100 102 104 106 108 110 112 114
M(xf)[GeV]

 

Figure 4.24: Limits on the total cross section for associated chargino (if) and neu-
tralino (£2) production with leptonic final states set by D0 in Run I (top line) and in
this analysis (second from top) in comparison with the expected limit (second from
bottom) and the signal cross section predicted for in mSUGRA (bottom line) as a
function of the if mass. Chargino masses below 103 GeV/c2 are excluded by direct
searches at LEP. The D?) Run I limit was based on searches in the eee, ecu, can, and
Min trilepton final states with between 75 pb'1 and 95 pb‘1 of integrated luminosity.

105

Chapter 5

Conclusions

The first search for evidence of supersymmetry in the like—sign dimuon channel at DC
has been presented. The analysis began with basic issues of data quality, and culmi-
nated in a new limit on the total cross section for associated chargino and neutralino
production with leptonic final states. This new limit was reached in combination with
other DQ’) analyses which studied the dielectron and electron plus muon final states.

While there has been tremendous progress, D0 is currently taking data that will
allow these results to be extended. This data, along with further refinements to the

analysis, will allow searches beyond existing limits.

5.1 The Future of the Analysis at DC

Future work on this analysis at DC? will consist of examining data currently being
collected at DC, and improving the analysis in several ways.

One area which will benefit from further study is the more complete exploration
of SUSY phase space. The unknown parameters in the theory lead to a wide range of
possible cross sections and differing distributions in several key kinematic variables.

Monte Carlo samples for many SUSY points are being generated for exploring more

106

 

of the phase space. including portions with the sign of p negative, and with differing
mass relations between the sparticles. including regions with the mass of the slepton
greater than the masses of the chargino and neutralino. Detailed studies of this space
will allow increased sensitivity if analysis cuts are fine-tuned in different parts of the
phase space.

Improvements in understanding. modeling, and removing backgrounds should be
focused on the bb background and the “"2 backgromid. as they are currently the
largest source of background. It may be possible to use Monte Carlo samples to
model the bb background.

The error from the choice of the PDF set. used in the production of signal and
background Monte Carlo events needs to be included as well. A procedure is outlined
here. The CTEQ6 distribution includes multiple sets of PDFs to be used to estimate
the errors. One can generate several Monte Carlo samples with the different sets of
PDFs and calculate efficiencies with each. The differences can then be used as an
estimate of the error.

The PDF parameters were diagonalized with respect to their linear fit correlations
about the best fit point to the full input data sets. and the extremes in that space
constitute an uncertainty range for the PDFs. The ranges of uncertainty include the
systematic uncertainties as published by many of the input experiments.

Different groups choose to parameterize PDFs differently, and this will affect the
parameter values and uncertainties. 111 another method, one can compare the effi-
ciencies calculated with Monte Carlo events produced with different versions of the
CTEQ PDFs or using PDFs produced by other groups, and take these differences as
a measure of the systematic error.

Uncertainty at the generator level should be considered as well.

In order to reduce the uncertainty in the background estimation, the Monte Carlo

sample sizes need to be increased. Some of the background samples were not large

107

enough to leave even one event after all cuts.

To illustrate, consider the uncertainty of b, the background estimate in a channel,

l) : O'MC X E X I’dataa (5.1)

where mug is the Monte Carlo cross section of the background process, E is the
efficiency as measured in data, and Ldata is the luminosity of the data sample. B can
be estimated as n/ N , where n is the number of Monte Carlo events observed passing

all cuts, and N is the number of events generated. However.

N 2 0MC X LMC: (53-?)

where LMC is the luminosity of the Monte Carlo sample. Therefore, one can write

n
b : Ldata X (711C X 9
UMC X LMC

OI‘

 

L .
b : n x data, (5.4)
MC

The uncertainty in b is the uncertainty in n scaled up by Ldau, / LMC. It is clear
that one wants LMC >> Ldata. However. when 031(3 is large, it is difficult to produce a
Monte Carlo sample with enough integrated luminosity.

In this analysis, several of the l\r’Ionte Carlo samples have integrated luminosity
less than or comparable to the data sample (see Table 4.1.) The background errors

can be reduced by obtaining much larger samples.

108

5.2 The Future Beyond DC

Whether or not supersyinn‘ietry is discovered at DC), the Large Hadron Collider
(LHC), currently under construction at the CERN laboratory in Geneva. Switzer-
land, will be a necessary tool in the study of supersymmetry. The LHC will be a
proton-proton collider, operating at a center—of—mass energy of 14 TeV. If SUSY is
not discovered at the Tevatron, it may be discovered at this higher energy. Studies
have shown that if supersymmetry is correct. some sign of its existence should be
evident at the LHC. If SUSY is discovered at the Tevatron, detailed studies will only

be possible at the LHC.

In the next several years, it will be known whether this universe is supersymmetric.

109

 

Appendix A

L2 Global Worker

The DQ) L2 trigger, described in Chapter 2.3, is an essential part of the data acqui-
sition system [59]. The L2 trigger system is divided into six crates, each containing
processors running identical executables (but configured differently). A processor's
configuration specifies which worker runs in the processors executable. The workers
correspond to the type of data being processed in the crate.

Five of the L2 crates are preprocessor crates. These crates receive data from the
L1 trigger system and the front-end crates. Each crate has a custom-built Beta pro-
cessor [26] which forms L2 preprocessor objects by running an algorithm tailored to
its data. For example, the L2MUC crate receives information about the central muon
system and forms muon objects. The preprocessor formats the data properly, and
sends the objects to the L2 Global crate.

The L2 Global worker is responsible for making trigger decisions based on the
objects identified by the L2 preprocessors. Trigger decisions are made by creating
Global physics objects. These objects can be based directly on the objects reported
by the preprocessors or can be created by combining objects from different prepro-
cessors. The L2 Global worker imposes cuts on the Global physics objects according

to configuration information it receives from the trigger control computer based on

110

the trigger list.

A. 1 Input

Data flows from the L2 preprocessor crates into the L2 Global crate (see Figure Al).
The format of the data is described elsewhere [60]. The Beta processor in the L2
Global crate runs an executable which contains the L2 Global worker code.

The L2 Global worker code has access to all of the preprocessor objects as well
as information from the L1 framework (Llfwk) for the current event. For each event,
the Global worker uses the Llfwk information to decide which algorithms to run on
the data from the preprocessors. It then makes a. trigger decision, and returns this
decision to the L2 framework code which passes it to the trigger framework. Thus,
each event must either pass or fail the L2 trigger, and this decision is based on the
input data and the information from the trigger list.

The trigger list specifies which trigger conditions L2 will impose for each run.
The trigger list can change as frequently as every run, but attempts are made to
achieve stability in the trigger list to reduce complexity at the analysis level. All of
the possible configuration values are stored in the trigger database, and the trigger
list is formed by choosing particular values for all of the variable parameters. The
trigger list is downloaded to the L2 Global crate by the trigger control computer,
which receives its instructions from COOR, the system responsible for coordinating

the distribution of all the online data. acquisition information to all the online crates.

A.2 Trigger Bits and Scripts

The most critical piece of Llfwk information is the L1 trigger mask. This is the record

of which L1 bits fired (the reason the current event passed the L1 trigger). The L1

111

Detectors L1 Triggers L2 Triggers

mi—it t

7 Cal _
e/j/E

 

 

 

 

('1

>.
1r]

7

CAL
S

P > PS a
' Global
CFT/ —> —>
i

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

cps : L2
I Track
C v _]
MDT Muon : Muon
PDT
L2: Combines
Ll: ET towers, objects into e, u,j
tracks

 

 

 

 

 

consistent with e, u,j

 

Figure A.1: Data flow from the detectors to the L2 Global worker.

112

trigger mask is a collection of 128 bits. one for each LI trigger condition.

At L1, as many as 128 different conditions can be programmed to fire the L1
trigger. For each event that passes. the bits that passed are recorded and sent to L2.
The L2 Global worker begins its work every event by checking which of the L1 trigger
bits fired. The trigger list specifies which L2 script is associated with which L1 bit.

The L2 script is the trigger condition that must be satisfied in order for the L2
trigger to fire for a given L1 bit. There is a one-to-one correspondence between Ll
bits and L2 scripts. The trigger conditions at each level are closely related, and form
a coherent trigger condition. An L2 script is defined, which is related to a L1 bit.
Once the L1 bit fires, the corresponding L2 script runs. For example, events with a
calorimeter energy requirement at Ll may have an electron requirement at L2.

The L2 script is specified by a number of filters and a minimum number of objects
required to pass each filter. The simplest script has one filter and a minimum number
of objects required to pass that filter. An example is a script with an electromag-
netic object filter and a. minimum of two objects. This script passes if there are two
electromagnetic objects in the event. that satisfied the conditions of the EM filter.

If any script passes, the event passes L2. and is processed by the L3 trigger. Events

are only written to tape if they satisfy L1. L2. and L3 trigger conditions.

A.3 Tools and Filters

Tools and filters are the main parts of the L2 Global worker. The filters make up the
scripts described in Section A.2. The filters in turn rely on tools.

Tools are C++ classes which build a specific type of L2 Global object. The elec-
tromagnetic object (EM) tool builds L2 Global EM objects. The muon tool builds L2
Global muon objects. This building of objects is based on the pre1.)rocessor objects.

A tool starts with a list of preprocessor objects. It. can then apply selection criteria

113

to decide which preprocessor objects should be made into Global objects. It can also
correlate information from two preprocessm's by combining two preprocessor objects
to form one Global object. An example of this is the combination of a track object
and an EM object that come from different preprocessors. but refer to the same real
electron that entered the DO detector. The tools are written to be flexible, and are
configurable through the trigger list. For the above example, one trigger list paran‘ieter
specifies whether or not EM objects from the preprocessor should be matched to tracks
from the tracking system.

The tools produce lists of Global objects. The filters then use these lists of Global
objects to make a trigger decision by imposing trigger requirements on the objects.
The requirements are based on the trigger list. For the case of an EM object, the elec—
tromagnetic fraction, transverse momentum. and isolation are examples of variables
that can be required to have values above or below specified thresholds in order to
pass the filter.

The filter generates its own list of objects which have satisfied the trigger criteria.
The script then checks to see if there are at least the minimum number of objects

required to pass the script.

A.3.1 Tools and Filters Currently Available

Tables A.1, A.2, A.3, A4 and A5 summarize the currently available tools and filters

and their parameters.

A.3.2 Tools and Filters Used in this Analysis

In the analysis described in this dissertation. two different L2 trigger requirements
are used. The first is the requirement of one medium L2 muon. This is implemented

by configuring a L2 muon tool which produced L2 muons based on the list of muons

114

 

 

 

 

MIN NEIGHBO R ETACEN ET

MINNEIGHBORPHICENET

MINNEIGHBORETAFWDET

MINNEIG HBORPHIFWDET

MINSING LETOW ER EM FRAG

MINSIN G LET OW ER ET

Tool Parameter Description
Muon LIPTTHRESH Minimum L1 pT
REQUIRETRACK Is match to track required?
TRACKWINDOW’IPHI Maximum distance to
matching track in (f)
EM MIN ET Minimum ET

Threshold for which, if cen—
tral cluster 7} neighbor is be-
low, it will be turned into 2
separate EM tower objects
Same for central cluster cf)
neighbor

Same for forward cluster 7)
neighbor

same for forward cluster 95
neighbor

Value for which if EM frac-
tion is greater, it will turn
that cluster into two EM
tower objects

In ET for single tower EM
object. Overrides MINET if
MINNEIGHBORET is true

 

 

 

 

 

 

REQUIRETRACK 1 = Require a CFT match
found (0 is false)
TRACKFILTER Track filter
TRACKWINDOVVIPHI (j) match window track
REQUIRECPS 1 2 require a CPS match (0
is false)
CPSWINDOWIETA 7] match window with CPS
CPSWINDOWIPHI (f) match window with CPS
MAXEM Maximum number allowed
to pass
Jet MINET h—JIinimum ET
MET
MJT MINET Minimum ET ofjets to be in-

cluded in calculation

 

Table A.1: L2 tools currently available. For each tool. the configurable parameters

are listed, along with a brief description [61].

 

 

 

 

 

 

Tool Parameter Description
Track MINET Minimum ET
TRACKSOURCE Type of input track
REQUIRELlISO Require L1 isolation confir-
mation
REQUIRELIPS Require L1 preshower confir-
mation
L2ISOTYPE Type of L2 isolation re-
quired. 0 = no requirement,
1 or 2 2 require 1— or 3-
prongs, 3 : require 1-prong
MAXCHISQ Maximum X2 allowed
IPSIG Minimum impact parameter
significance
InvMass MININVMASS Minimum mass
N FILTERS Number of input filters
FILTERO First filter
FILTERI Second filter
Commission

 

 

 

 

 

Table A.2: L2 tools currently available. For each tool, the configurable parameters
are listed, along with a brief description [61].
from the two L2 muon preprocessors.

The muon tool makes Global muons based on each of the preprocessor muons it
receives. The muon tool also determines the quality of each muon. A L2 muon filter
is then configured to loop over all of these muons, and pass any that are of medium
quality or better.

The second L2 trigger used in this analysis is similar, except that. it uses a L2
muon filter to require at least- two medium muons in order to pass. In addition, an
7} — <25 separation filter is used to check the separation in 1] and (25 between the muons
passing the muon filter. The separation filter imposes the requirement that for the

event to pass, two L2 muons have to be separated by at least 0.15 in 77 or 0.24 in a").

116

 

 

 

 

 

 

 

 

 

 

 

 

Filter Parameter Description
Muon MINET Minimum ET
QUALITY Minimum quality (based on
number of hits)
PROMPT Minimum timing quality
(based on scintillator times)
SIGN Required sign of muon to
pass
TOOL Input tool
EM EMF RAC Minimum EM fraction
ISOFRAC Maximum isolation fraction
MIN ET Minimum ET
MAXEM Maximum number allowed
to pass
TOOL Input. tool
Jet MINET Minimum ET
MAXJETS Maximum number of jets al-
lowed
TOOL Input tool
Track MIN ET Minimum ET
QUALITY Minimum quality
IP Minimum impact parameter
IPSIG Minimum impact parameter
significance
TOOL Input tool
MET MINMET Minimum ET
TOOL Input tool
MJT MINMJT Minimum ET
TOOL Input tool
Eta IETAMIN Minimum ieta
IETAMAX Maximum iet a
FILTER Input filter
Phi IPHIMIN Minimum iphi
IPHIMAX Maximum iphi
FILTER Input filter

 

Table A.3: L2 filters currently available. For each filter, the configurable parameters

are listed, along with a brief description [61].

117

 

 

 

 

 

 

 

 

 

 

Filter Parameter Description
PhiSep NFILTERS Number of input filters
IPHIMINSEP Minimum (b separation value
IPHIMAXSEP Maximum (15 separation
value
FILTERO First input filter
FILTERI Second input filter
EtaSep NFILTERS Number of input filters
IETAMINSEP Minimum 7] separation value
IETAMAXSEP Maximum 7] separation
value
FILTERO First input filter
FILTERI Second input filter
EtaPhiSep NFILTERS Number of input filters
IETAMINSEP Minimum 1) separation value
IPHIMINSEP Minimum (1) separation value
FILTERO First input filter
FILTERI Second input filter
FILTER2 Third input filter
FILTER3 Fourth input filter
PhiSepVeto IPHIMINVETO Minimum 96 separation for
veto
IPHIMAXVETO Maximum (15 separation for
veto
NFILTERS Number of input filters
FILTERO First input filter
FILTERl Second input filter
RSep NFILTERS Number of input filters
RMINSEP Minimum R separation
value
RMAXSEP Maximum R separation
value
FILTERO First input filter
FILTERI Second input filter

 

 

Table A4: L2 filters currently available. For each filter, the configurable parameters
are listed, along with a brief description [61].

118

 

 

 

 

 

 

Filter Parameter Description
HT HTMIN Minimum HT
NFILTERS Number of input filters
FILTERO First input filter
F ILTERl Second input. filter
FILTER2 Third input filter
InvM ass MININVMASS Minimum invariant mass

MAXINVMASS Maximum invariant mass
TOOL Input tool

TransMass MINTRANSMASS Minimum transverse mass
MAXTRANSMASS Maximum transverse mass
TOOL Input tool

TimeDelay

RandomPass

 

 

 

 

 

Table A5: L2 filters currently available. For each filter, the configurable parameters
are listed, along with a brief description [61].

AA Output

The output of the L2 Global worker is the record of what the worker did for that
event. This consists first of a trigger mask that records which scripts passed L2. The
trigger mask is used by the L3 trigger to decide which L3 scripts it will run on the
event. The output also includes a record of all of the Global objects which caused the

event to pass. The format of the Global objects is specified in [60].

A5 Code Design and Structure

The code for the L2 Global worker is spread over several packages which are part of
both the DO offline release and the DO L2 online release.

The offline release contains the trigger simulation code which uses a different.
framework than the online release. Both frameworks have the same functions; to
receive the data and run the worker. The L2 Global code is identical in the online

and offline release. The L2 Global code is contained in the packages l2gblem, l2gbljet,

119

l2gbltrack, l2gblmuon, l2gbltau, l2gblgeneric, l2gblbase, l2gblworker, and l2io.

The l2gblbase, l2gblworker, and l2io packages contain the code used to contain the
data, pack/ unpack it, and run the tools and filters. The Llfwk bits are interpreted
here. These include special bits that instruct the worker to treat the event as part of an
unbiased sample by passing it regardless of the results of running the L2 scripts. Errors
that have been noted by the L2 framework are also interpreted in these packages. The
trigger mask from the Llfwk is decoded and the list of L2 scripts to run is prepared.
The code runs all the appropriate scripts, gets the L2 decision, fills the output data,
and returns the decision to the L2 framework.

The tool and filter code is contained in the remaining packages. The packages
are divided only for organizational reasons. The tools all have access to all of the L2
Global data. They each have a parser interface so that they can receive L2 parser
configuration data that originates in the trigger list. They use this configuration
information to decide how to produce lists of Global objects.

The tools pass the list of objects to the filters. The filters can then generate lists
of objects that are subsets of their input lists. It is also possible for a filter to filter the
list produced by another filter. Generic filters are stored in the l2gblgeneric package
and do just this. An example is the rj-separation filter, which can take a list of objects

from any filter as input, and filter those objects based on their separation in 7}.

120

 

Appendix B

L2 Error Logger

The DO L2 trigger, described in Chapter 2.3. is an essential part of the data acqui-
sition system. It must be functioning properly in order for the experiment to trigger
on and record data. It is therefore important to monitor it closely to ensure the con-
tinued flow of data and to make sure that the system is functioning properly. Good
monitoring can greatly speed up the diagnosis of and recovery from problems.

L2 is divided into six crates, each containing processors running identical exe-
cutables (but configured differently). which are responsible for processing data. The
code running on these processors is controlled by an executable written in the C++
programming language. When any error or significant event is noted by the software,
it can communicate the event by writing a message via the L2 error logging code.
The error logging code encapsulates the collecting. sorting, and routing of the er—
ror information. The C++ source code is collected in the packages l2errorlogger and

l2moniogen, which are part of the DO L2 online release.

121

 

 

MessageMaker

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘\ ErrorMessage
V
Router
/ \
Destination Counter > LimitSTable
i
MessageBuffer Summary MessageCounts

 

 

 

 

 

 

 

 

 

 

 

 

Figure 8.1: Simplified Unified Modeling Language (UML) diagram showing the major
classes in the l2errorlogger package and the relationships between them.

B. 1 Motivation

There is an offline package called ErrorLogger which is widely used throughout DO
for collecting, sorting, and routing error information. While this contains all the func-
tionality that is needed for the online L2 system, concerns about speed, memory
usage, and code dependencies motivated the decision to create a L2—specific package
which implements only the functionality that is needed at. L2 according to L2 coding
guidelines [62].

The l2errorlogger package has the same interface as the ErrorLogger package.
Thus users can write code without distinguishing between the online 12errorlogger
and offline ErrorLogger. The switching between the use of the online and offline code

is done separately.

122

 

B.2 Architecture

The h’lessageMaker class contains the entire user interface. User code directs data
to the error logging system by calling functions in the Me’essage.\~1ake.r. It is the only
class that users of the package will interface their code to (:lirectly. One instance of
the class, called “errlog” is created by the L2 framework code, and user code must
only include one file, “ErrorLoghpp,” to make use of the l2errorlogger. The names
“errlog” and “ErrorLoghpp” were chosen to agree with the names used by the offline
ErrorLogger.

The l2errorlogger package contains a header file directory that has files that de-
fine the classes used in the 12errorloger. The implementation of the functionality of
the classes is contained in files in the src directory. The container classes for the
l2errorlogger data are in the l2moniogen package. The main classes that are used in
the 12errorlogger package and the relationships between them are shown in a Unified
Modeling Language (UML) diagram in Figure B1.

The MessageMaker receives data from the user code and constructs an error mes-
sage using the ErrorMessage class. This class contains the information specified by
the user: the message name; the messages severity level (Table 8.1); a text message
which describes the error; and the current bunch and rotation number.

The error message produced by the lV‘Iessageh/Iaker is passed to the Router class,
which is responsible for its fate. The Router first sends the message to the Counter
class, which keeps track of how many times each message has been logged. The
Counter stores each message, how many times it has been logged, and constructs
and fills Summary objects. The Counter consults the LimitsTable class which con-
tains configuration information downloaded from the trigger control computer. The
LimitsTable can be configured to limit how often messages are logged, or suppress

messages based on the number of occurrences or their severity level. The LimitsTable

123

 

 

Error Name Error Severity
0 ELunspecified
1 ELzeroSeverity
2 ELincidental
3 ELsuccess
4 ELinfo
5 ELwarnin g
6 ELwarning2
7 ELerror
8 ELerror2
9 ELnextEvent
10 ELsevere
11 ELsevere2
12 ELabort
13 ELfatal
14 ELhighestSeverit y

 

 

 

 

Table B1: The available severity levels in the l2errorlogger.

returns whether the message should be sent on or disregarded. The Counter receives
this decision and returns it to the Router.

The Router, after receiving the decision to send the message on, sends the message
to the Destination class. The Destination is configurable and can be standard out.
a log file, or a MessageBuffer class that writes to a. block of memory that is written
to the dual port memory every few seconds. The trigger control computer pulls the
contents of the buffer periodically. From there, the data can be transferred to the
monitoring system. It also gets written to log files and stored. Clients can request
the monitoring information from the monitoring system. and use it for control-room

displays.

B.3 User Interface

The user interface for the l2errorlogger starts with the requirement that. the file Er-

rorLoghpp be included. Then. anywhere in the code. the user can log a message by

124

typing
errlog(<message name), <message severity>) << <message text> << endmsg;
where

o <message name> is any text string the user uses to name the message. This is

used as a label, and for the summary inforn‘iation.
o <message severity> is a severity level from Table 8.1.

o <message text> is any detailed text string containing the error message. Data

can also be logged by typing “<< data”.
a endmsg is necessary to terminate the message.
An example of usage is

double chargino_mass = 150;
errlog(“Chargino Found!”, ELinfo) << “A chargino with mass ”

<< chargino_mass << “ has been found” << endmsg;

 

Appendix C

Paddle Board for Hardware Sealers

The state of the running executable on the main processor in each L2 crate is mon-
itored by hardware sealers that are controlled from within the running executable.
There are six L2 crates, each containing Beta processors [26] that run identical exe-
cutables (but are configured differently), that are responsible for processing data. The
code running on these processors is controlled by an executable written in the C++
programming language. As the code moves from one state to another, it changes the
output signals to the monitoring system on the Beta. These signals are transmitted
off the board on a 68-pin cable (3M part number 10168-8000EE).

The signals from this board are transmitted to a crate which receives monitoring
information from many crates. The crate keeps track of the information by increment-
ing sealers (counters) based on the signals. F ield-programmable gate arrays (FPGAs)
in the monitoring crate check the values of the signals for each bunch crossing of the
accelerator. If the value of a signal is high, the corresponding scaler is incremented.
The interface to the monitoring crate is through 24—pin connectors (TYCO electronics
part number 501-2407ES). Since the signals coming from the L2 processor are output
on a 68-pin cable, conversion to 24-pin cables must be performed to allow interfac-

ing to the monitoring crate. This conversion is done through a passive circuit board

126

\ km» .3733"

 

Figure CI: The paddle board. Picture courtesy of Kathleen Yurkewicz.

(referred to here as the paddle board).

The paddle board is a. 4—layer printed circuit board (see Figures Cl and C2). It
has five connectors. J1 is the 68—pin connector which receives the data. from the L2
processor. J3, J4. J5. and J6 are the 24—pin connectors which transmit the data to
the monitoring crate.

The 68-pin cable has four ground wires. The remaining 64 wires transmit 32 ECL
signals. Each pair of wires carries the direct and complement signals. The voltage
difference between the pair signify an on or an off bit to the receiving scalers. The 32
pairs are routed to the four connectors J3. J4, J5. and J6 on the circuit board. Eight
pairs go to each connector. which leaves 8 pins unused on each of the four 16-pin
connectors.

The mapping of signals for all the crates to the sealers is kept in a net list. The
net list consists of rows of information. separated into columns. Each row corresponds
to a net, or one wire on a cable. Column 1 always says “NET". Column 2 is a name

ending in DIR or COMP for direct or cmnplement. Column 3 is the origin of the net.

127

 

 

 

I c O o I 9 I Q o O I C
4 I J l I I.~.o - J 6... .3...
W... .w.‘
~‘ 1’n': ': I': -' L‘x'o:
a q.o -0- '-Q -.-.. *
1 ..... r r . 3 3' . "
v . L ‘
n i J .
r S ‘. t
F ..
I
i
p" . .
‘ I V ‘ o ‘
l n . A‘ ". ‘ ‘
A ' I
7.— A —- o —. ,... .... >7 .,' ‘1'?
l ' , . l
l -t . . ]
. V ’ i e“ 1‘
. t, l
\, ~ .
1‘
'L A. ‘. 0K
. g 1.‘
v If ( . ‘.,
, ,r in
..,;~ . .-
l ' ’ .
.2 . . 1
I .‘J ' a
‘.
L J

 

Figure C.2: Design diagram of the paddle board, showing the connectors and traces
connecting them.

a connector, and a pin number. Column 4 is the destination of the net. Column 5 1s
the FPGA that receives this signal. Column 6 is the control signal on that FPGA.

The monitoring data will contain the counts data from all 384 of the L2 scalers.
with 4 sealers per F PGA, 16 F PGAs per sealer card, and 6 sealer cards. The sealers
on each F PGA are numbered 0 to 3. The FPGAs that contain sealers on each scaler
card are numbered 1 to 16.

Part of the net list. looks like:

#
NET ’ALPHA_IN_01_DIR’ J1-03 J4-19 # FPGA #6 CS 3
NET ’ALPHA_IN_01_COMP’ J1-04 J4-20 # FPGA #8 CS 3
#
NET ’ALPHA_IN_02_DIR’ J1-05 J4-17 # FPGA #6 CS 2
NET ’ALPHA_IN_O2_COMP’ J1-06 J4-18 # FPGA #8 CS 2
#

128

NET ’ALPHA_IN_03_DIR’ J1-O7 J4-15 # FPGA #6 CS 1

NET ’ALPHA_IN_03_CDMP’ J1-08 J4-16 # FPGA #8 CS 1
#

NET ’ALPHA_IN_O4_DIR’ J1-09 J4-13 # FPGA #6 CS 0
NET ’ALPHA_IN_04_COMP’ J1-10 J4-14 # FPGA #8 CS 0

The up—to—date full net list and meaning of each bit are documented on the L2
monitoring web page [61].

The monitoring data is automatically collected every five seconds and displayed
in the control room as part of the L2 monitoring display. Pie charts are generated
which show the amount of time spent in each state. A pie chart and the corresponding
legend for the Global worker are shown in Figure C.3. Distributions can also be made

that show how long the processor spends in each state (on an event-by-event basis).

129

wait_event :1
processing I
l2_answer E]
I3_readout
collect_status E]
reply_worker I

interrupt I

 

  
 
 

l2ps central flflfi‘m
lZps forward {magmas

Figure C.3: A pie chart and corresponding legend showing the amount of time spent
in each state for the Global worker.

130

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