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A MEASUREMENT OF THE TOP QUARK’S CHARGE

 

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A MEASUREMENT OF THE TOP QUARK’S CHARGE
By

Zeynep Unalan

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics

2008

ABSTRACT

A MEASUREMENT OF THE TOP QUARK’S CHARGE

By

Zeynep Unalan

The top quark was discovered in 1995 at the Fermilab National Accelerator Lab—
oratory (Fermilab). One way to conﬁrm if the observed top quark is really the top
quark posited in the Standard Model (SM) is to measure its electric charge. In the
Standard Model the top quark is the isospin partner of the bottom quark and is ex-
pected to have a charge of +2 / 3. However, an alternative “exotic” model has been
proposed with a fourth generation exotic quark that has the same characteristics,
such as mass, as our observed top but with a charge of -4/ 3. This thesis presents
the ﬁrst CDF measurement of the top quarks charge via its decay products, a W
boson and a bottom quark, using 2 1 f b-1 of data. The data were collected by the
CDF detector from proton anti-proton (pp) collisions at ‘5 = 1.96 TeV at Fermilab.
We classify events depending on the charges of the bottom quark and associated W
boson and count the number of events which appear “SM-like” or “exotic-like” with
a SM-like event decaying as t —+ W+b and an exotic event as t —+ W‘b. We ﬁnd
the p—value under the Standard Model hypothesis to be 0.35 which is consistent with
the Standard Model. We exclude the exotic quark hypothesis at an 81% conﬁdence
level, for which we have chosen a priori that the probability of incorrectly rejecting
the SM would be 1%. The calculated Bayes Factor (BF) is 2an(BF)=8.54 which
is interpreted as the data strongly favors the Standard Model over the exotic quark

hypothesis.

 

© 2008

Zeynep Unalan

All Rights Reserved

To my grandparents
Saziye and Kenan Akpolat

Zehra and Adem Giinay

iv

ACKNOWLEDGMENTS

First of all, I would like to express my gratitude to my advisor Kirsten Tollefson
for her guidance, explaining to me the detector and trigger system and truly helping
me in every possible way. I am sincerely grateful to Veronica Sorin for always an-
swering my questions and reviewing my thesis even if she did not have to. I am also
grateful to Veronique Boisvert for her crystal clear explanations when things looked
so confusing and for getting me involved in the Level-3 validation. I have learned
various things from Kirsten, Veronica and Veronique, especially how to think as an
HEP experimentalist and how to proceed to the next step during the discussions of
the problems we faced throughout the research. I would also like to thank all the
other members of the top charge group, Yen-Chu Chen, Andy Beretvas, J aroslav An-
tos, Stanislav Tokar and Peter Bednar for the fruitful weekly discussions from which
I beneﬁted alot. I would like to express my special thanks to Kevin McFarland for
his valuable input and useful suggestions. There have been other colleagues that gave
many useful comments on our top charge presentations in the Top Properties and
Top Group meetings. Special thanks to Tom Wright, Chris Neu and Ford Garberson
for their help and suggestions on the calibration of the jet charge algorithm using
data; Luc Demortier for his guidance in the statistical issues and Daniel Sherman for
providing me with the numbers needed for the event selection. I also would like to
thank BoYoung Han for his help with the Level-3 validation.

I wish to express my appreciation to Bernard Pope, C.P. Yuan, Lisa Lapidus and
Megan Donahue for being on my guidance committee and reviewing my thesis. I
would like to extend my gratitude to all my professors from whom I have beneﬁted
and the Department of Physics and Astronomy at MSU for supporting me during the
ﬁrst years of my graduate study.

I would like to take this opportunity to also thank my ofﬁce neighbor Jonathan

\f

Lewis for setting an example of an enthusiastic physicist and providing toys that kept
my son busy while I was trying to work from home. I guess I should also thank people
passing by in the corridor and their laughter for reminding me that I should take a
break when most stressed from problematic code and crashing jobs.

Being a part of a huge collaboration was a different and enlightening experience
for me after a master’s thesis on which I worked alone. I feel obliged to thank all
the members of the CDF collaboration who took part in designing and running the
CDF experiment and the people in the accelerator division for maintaining beam in
the Tevatron for long hours.

I am grateful to all my friends at MSU and at Fermilab for being my surrogate
family during the last 5 years. I would like especially thank Selcuk Cigangir who tried
hard (and mostly succeeded) to bring the Turkish community at Fermilab together
that made us breathe the atmosphere away from home and to my beloved friend
Melek Yaylaci in Istanbul for her encouragement through her emails and phone calls.

I wish to express my deepest appreciation to my parents, Yilmaz and T iilin Gunay
for their love, encouragement and for sparking in me the love of knowledge and
science. Finally I wish to thank my C++ expert Dill-husband Rahmi for all his help
and understanding.

This work was supported by the US. Department of Energy, National Science

Foundation and Michigan State University.

vi

TABLE OF CONTENTS

LIST OF TABLES .............................. xi
LIST OF FIGURES ............................. xvii
1 Theory ................................... 1
1.1 Introduction ................................ 1
1.2 The Standard Model ........................... 2
1.3 Top Quark ................................. 6
1.4 Top Quark’s Production and Decay ................... 7

1.5 Possible Techniques for Measuring the Top’s Charge .......... 11

1.6 Overview of the Thesis .......................... 15

2 Experimental Apparatus ........................ 17
2.1 Tevatron .................................. 17
2.1.1 Proton source ........................... 18

2.1.2 Anti-proton Source ........................ 20

2.1.3 Collisions at the Tevatron .................... 20

2.2 The CDF Detector ............................ 22
2.2.1 Basics of Particle Detection at CDF ............... 24

2.2.2 CDF Coordinate System ..................... 26

2.2.3 The 'Itacking Detectors ..................... 27

2.2.3.1 The Silicon Detector .................. 27

2.2.3.2 The Central Outer Tracker .............. 31

2.2.4 Calorimetry ............................ 33

2.2.5 Muon systems ................. . .......... 38

2.2.6 Luminosity Measurement and CLC detector .......... 43

2.2.7 Triggers and Data Acqusition System .............. 45

2.2.8 Monte Carlo Event Generation and Detector Simulation . . . 48

3 Event Selection .............................. 50
3.1 Trigger Requirements ........................... 51
3.1.1 Triggering Electrons ....................... 52

3.1.2 Triggering Muons ......................... 53

3.2 Ofﬂine Reconstruction and Selection of Leptons ............ 54
3.2.1 Electron Reconstruction and Selection ............. 54

3.2.2 Muon Reconstruction and Selection ............... 58

3.3 Jet Reconstruction and Corrections ................... 63
3.3.1 Jet Clustering ........................... 63

vii

3.3.2 Jet Energy Scale (JES) Determination ............. 64

3.4 Missing Energy .............................. 69
3.5 Identifying b quarks ........................... 69
3.5.1 Secondary Vertex Tagger ..................... 70
3.5.2 Finding the Primary Vertex ................... 71
3.5.3 Finding the Secondary Vertex .................. 72
Determining Top’s. Charge via its Decay Products ......... 77
4.1 Introduction ................................ 77
4.2 Deﬁnition of Performance ........................ 79
4.3 W b Pairing ....... _ ......................... 80
4.3.1 Kinematic Fitter Optimization Studies for Wb paring ..... 82
4.4 Flavor Tagging the b Jet at Production ................. 87
4.4.1 Same-Side Tagging (SST) .................... 88
4.4.1.1 Minimum PT,rel Method ................ 91
4.4.1.2 Voting SST Method .................. 92
4.4.2 Opposite Side Tagging (OST) .................. 92
4.4.2.1 Soft Lepton Tagging (SLT) .............. 92
4.4.2.2 Momentum Weighted Jet Charge ........... 94

4.5 Optimization of the Momentum Weighted Jet Charge Algorithm for
the Top Charge Measurement ...................... 95
4.6 b Flavor Tagging Improvements ..................... 100
Calibration of Flavor Tagging in Data ................ 103
5.1 Introduction ................................ 103
5.2 Data and MC Samples .......................... 105
5.3 Event Selection .............................. 107
5.4 Method .................................. 109
5.4.1 Measuring the b6 fraction ..................... 110
5.4.1.1 Fitting procedure .................... 113
5.4.1.2 Mixing and Cascade corrections ............ 117
5.5 Results ................................... 120
5.5.1 Scale Factor ............................ 122
5.5.2 Method checks .......................... 124
5.6 Dependence on ET, 1) and Number of Vertices ............. 128
5.6.1 ET Extrapolation ......................... 128
5.6.2 77 and Number of Vertices .................... 129
5.7 Systematic Uncertainties ......................... 129
5.7.1 PT,re1 Tag Bias .................... . ...... 129
5.7.2 PT,rel non-b Bias ......................... 131
5.7.3 Mm Bias ............................. 133

viii

5.7.4 Alvtx FitS ............................. 133

5.7.5 Summary ............................. 133
5.8 Conclusion ................................. 134
Backgrounds ............................... 135
6.1 Introduction ................................ 135
6.2 W+Heavy Flavor ............................. 138
6.2.1 Production and Estimation ................... 138
6.2.2 Charge Asymmetry ........................ 139
6.3 QCD (non-W) ............................... 141
6.3.1 Production and Estimation ................... 141
6.3.2 Charge Asymmetry .............. - .......... 144
6.4 Mistags (W+Light Flavor) ........................ 146
6.4.1 Production and Estimation ................... 146
6.4.2 Charge Asymmetry ........................ 147
6.5 Diboson .................................. 147
6.5.1 Production and Estimation ................... 147
6.5.2 Charge Asymmetry ........................ 148
6.6 Single Top ................................. 149
6.6.1 Production and Estimation ................... 149
6.6.2 Charge Asymmetry ........................ 150
6.7 Background Summary .......................... 150
Systematic Uncertainties ........................ 152
7.1 Jet Energy Scale ............................. 153
7.2 Initial/ Final State Radiation ....................... 156
7.3 Top Mass Uncertainty .......................... 157
7.4 b—taggin'g .................................. 158
7.5 Parton Distribution Functions (PDFs) ................. 159
7.6 Monte Carlo Modeling .......................... 159
7.7 Systematics Summary .......................... 160
Studies in the Dilepton Channel .................... 162
8.1 Introduction ................................ 162
8.2 Wb Pairing ................................ 163
8.3 b Flavor Tagging ............................. 167
8.4 Backgrounds ................................ 167
8.5 Systematics ................................ 169

ix

9 Signal and Background Estimates ................... 171

9.1 Expected Number of Events ....................... 171
9.2 Calculating Signal Purity ......................... 172
9.3 Calculating Background Purity ..................... 176
9.4 Summary ................................. 177
10 Statistical Treatment .......................... 179
10.1 Proﬁle Likelihood ............................. 180
10.1.1 Nuisance Parameters ....................... 181
10.1.2 Likelihood Expression ...................... 183
10.1.3 Calculation of the Profile. Likelihood .............. 184
10.2 Extracting a Limit ............................ 186
10.2.1 Hypothesis Test .......................... 187

10.2.2 The Null Hypothesis and Test Statistic for the TOp Charge
Analysis: .............................. 191

10.2.3 Choice of a for the Top Charge Analysis and the Calculation
of 1 — ﬁ .............................. 191
10.2.4 p-value‘ ............................... 192
10.2.5 Interpretation of the Possible outcomes ............. 193
10.3 Bayesian Treatment ............................ 193
10.4 Summary ................................. 195
11 Summary and Results .......................... 196
11.1 Results ................................... 197
APPENDICES ................................ 201
A Charge Bias ................................ 201
B Data Yield Details ............................ 206
C Data MC Comparison Plots ...................... 208
BIBLIOGRAPHY .............................. 216

2.1

2.2

2.3

2.4

2.6

3.1

3.2

4.1

4.2

4.3

4.4

LIST OF TABLES

Tevatron parameters during the Run II data taking period ....... 22

Design parameters of the SVXII detector. The numbers in the last
three rows of the second column correspond to each layer from inward
to outward. ................................ 29

The parts of the CDF calorimeter and their acronyms. ........ 37

Properties of the CDF calorimeter systems. The energy resolutions are
for electrons for the electromagnetic calorimeter and for isolated pions
for the hadronic calorimeters.The percentages after 69 are the average
uncertainty due to tower calibrations. A0 implies interaction lengths

and X0 implies radiation lengths. .................... 38
Design parameters of the muon chambers ................ 43
Output rate at each trigger level. .................... 49

Track selection criteria used in the Loose and Tight Sethx algorithms. 74

The b—tag efﬁciency and mistag rate for a central jet with ET = 60
GeV from a top event. .......................... 77

The results of various methods tried in a previous top analysis [30] to
match jets to the correct b parton. The second column represents how
often each method matches a jet to the correct b parton (leptonic b—jet
to the leptonic b parton) .......................... 82

Efﬁciency (fpairing) and purity (Ppairing) of getting the true leptonic b
using the kinematic ﬁtter on double tagged lepton+jets events. The
ﬁrst colurrm shows results using the tight Sethx tagger and the second 1
column shows results using the loose Sethx tagger ........... 85

Performance of the kinematic ﬁtter for single b-tagged events. The 6D2
in the last column is the product of 5pairing and the square of pairing
dilution D (D = 2Ppairing — I). ..................... 86

Comparison of the performance of the W b pairing method using single
tagged events with double tagged events. The tight version of the
Sethx algorithm was used for b—tagging ................. 86

4.5

5.1

5.2

5.3

5.4

6.1

6.2

Performance of the jet charge algorithm on b—jets tagged by the loose
Sethx algorithm in the top MC sample (A'Itop = 175 GeV/cz). em
and P JQ are the efﬁciency and purity for JQ respectively. The ﬁrst
row is for lepton+jets events where we require both b—jets to have
opposite sign. The second row is when we check the J Q performance
for the leptonic and hadronic sides separately. The purity results are
the average of both sides ..........................

100

Data and MC samples used for the calibration of the jet charge algorithm. 106

Classiﬁcation of events in the heavy ﬂavor enriched MC. The muon (it)
and away-jets (AJ) were matched to partons within a cone of 0.4 and
classiﬁed accordingly for different cases. The fakes category includes
those events where the reconstructed muon did not match a generator
level muon or those where, although there is a matched muon, the jet
is not from a b or c quark. The “Pretagged” column corresponds to
the fraction of each case when only the away-jet is b—tagged (loose) and

the “tagged” column to the case where the muon-jet is also b—tagged
(tight) ....................................

The nine different away—jet ET bins used for the PT,rel and 1”th ﬁts

The relative systematic uncertainties on the scale factor from the PT,rel
ﬁt, Alvtx ﬁt and ET extrapolation. The “Mth ﬁt with be” implies the
ﬁt is performed using bottom (b) and charm (c) jet Mvtx distributions.
Similarly the “Mm ﬁt with bl” implies the ﬁt is performed using bot-
tom (b) and light (I) jet Mm distributions. ..............

Table of expected background events (Nb) for the top charge analy-
sis in the lepton+jets (L+J) channel for 695 pb—1 of data. L+J a
prediction is the number of background events from the cross section
analysis. Third column is the total efﬁciency of the top charge selection
requirements. ...............................

The charge asymmetry (Pb) from MC for W+HF background events.
The Ntotal column shows the total number of events left after applying
the lepton+jets and top charge selection cuts on the MC sample. The
N+ and N _ columns show how Ntotal is shared between SM-like events
(N+) and exotic-like (N_) events respectively. .............

xii

109

114

142

6.3

6.4

6.5

6.6

6.7

6.8

6.9

7.1

7.2

7.3

7.4

7.5

The charge asymmetry (Pb) for W + c loose Sethx tagged events
requiring 1 jet in the event. Pb of 0.5 indicates no charge asymmetry.
The ﬁrst row in the table shows the result where we have not done
any parton level check. Once we require the c jet in the event to be
matched to a c quark (second row), the charge asymmetry is slightly
higher. The result in the third row is obtained using only events where
the c jet is not matched to a c quark. ..................

Purity (Pb) of events from dijet data before b-tagging is applied on the
jet that is back-to—back from the jet including the lepton ........

Purity (Pb) of events from dijet data after b—tagging is applied on the
jet that is back-to—back from the jet including the lepton. We use the
purity in region A for the QCD background. ..............

Jet charge purity (Pb) for the mistags background obtained from
W+LF MC .................................

Jet charge purity (Pb) for diboson background obtained from diboson
(WW + WZ + ZZ) MC samples. ....................

Purity for the b—tagged single top MC events. .............

Background Purity Pb (Charge Asymmetry) for each background cal-
culated from the equation Pb = N+ / (N+ +N_). A purity of 0.5 implies
charge symmetry. .............................

Pairing and jet charge efﬁciencies and purities obtained by shifting the
jet energies up and down by 10 ......................

Pairing and jet charge efﬁciencies and purities obtained from top MC
samples that contain more or less ISR (FSR) with respect to the default
sample ....................................

Pairing and jet charge efﬁciencies and purities obtained from top MC
samples where the generated top mass was changed to 170 and 180
GeV/c2 but the kinematic ﬁtter was still constrained to 175 GeV/c2.

Pairing and jet charge efﬁciencies and pairing purity obtained from
PYTHIA (default sample) and HERWIG MC. .............

Summary of the systematic uncertainties in % where pairing and jet
charge efﬁciencies (e) and purities (P) are presented. Because the J Q
is calibrated on data we do not assign a systematic uncertainty on jet
charge purity (P JQ) due to different MC modeling effects. ......

xiii

 

142

146

146

148

150

151

152

155

157

158

161 t

162

8.1 List of various M 12b.max cuts and their performance for dilepton events
with one jet tagged with the tight Sethx algorithm. Higher perfor—
mance is indicated by a high 6D2 where c is the pairing efﬁciency
((pairing) and D (D = 2 X Ppairing -- 1) is the dilution. ........ 166

8.2 Comparison of pretagged dilepton events with events where one of the
b—jets is tagged by the tight Sethx tagger. Higher performance is
indicated by a high eD2 where e is the pairing efﬁciency, (”pairing and
D (D = 2 x Ppairing — 1) is the dilution. The loss of efﬁciency due to
b—tagging is not included in the tagged case. .............. 166

8.3 Purity (PJQ) of the momentum weighted jet charge along with the
efﬁciency (cJQ) using the dilepton events from if MC .......... 167

8.4 Table of expected background events in the dilepton (DIL) channel for
955 pb‘1 of data. The second column gives the prediction for each
background taken from the CDF dilepton cross-section (a) measure—
ment where one of the b—jets is tight Sethx tagged. After the top
charge analysis cuts, the expected number of background events (Nb)

is 0. .................................... 168
8.5 Jet charge purity (P JQ) for dilepton backgrounds and the efficiency

(Etotal = {pairing x CJQ) for accepting each background. ........ 169
8.6 Summary of systematics uncertainties (in %) in Dilepton channel. . . 171

9.1 Table of expected signal and background events. The second column
shows the predicted number of events that are taken from the cross-
section measurements. The lepton+jets predictions include the efﬁ-
ciency of the lepton+jets event selection with both b—jets tagged with
the loose Sethx algorithm. The dilepton predictions include the efﬁ-
ciency of the dilepton event selection with one of the b—jets tagged with
the tight Sethx algorithm. ....................... 173

9.2 All of the ingredients, fraction of pairs with no b—jets (fnonb)i correction
due to the mistag rate difference between MC and data (SFnonb),
purity of pairing (Ppairingla purity of jet charge (P JQ) and its scale
factor (SF JQ), to correct the P JQ obtained from MC for the dilepton
and lepton+jets channels. ........................ 175

9.3 Signal purity for each channel separately and both channels combined
(total) and the number of SM like (N+) and exotic model like (N_)
events. ................................... 176

xiv

 

 

9.4

9.5

10.1

10.2

10.3

11.1

A.1

BI

82

Background purity for each channel separately and both channels com-
bined and the number of SM like (N+) and exotic model like (N_)
events expected ...............................

Expected number of background and signal pairs together with the
corresponding puritiasSince the amount of background is so small and
does not affect the top charge result the effect of systemmatic uncer—
tainties were not checked on backgrounds. The uncertainty on Nb and
Pb are statistical only. ..........................

The four different possible outcomes from a hypothesis test. .....

Different decisions in a hypothesis test and the corresponding case from
Table10.1 in the parenthesis ........... _ .............

Standard scale for the Bayes factor [47]. ................

The observed number of Standard Model like (SM) and Exotic Model
like (XM) Wb pairs for each channel along with the expectations shown
in parenthesis. The second column shows the number of events after
the lepton+jets/dilepton event selection cuts. In the third column are
the number of events left after pairing. The fourth column gives the
number of Wb pairs for which the b—jet charge was calculated using
the momentum weighted jet charge algorithm. Finally the last two
columns show the number of SM and XM-like pairs in our data.

The jet charge purity Pb (PE) for b (b) jet candidates calculated with
offline tracks or with secondary vertex tracks using dijet data. Sethx
tracks have less bias than the ofﬂine tracks ................

The number of lepton+jets (L+J) events after the lepton+jets selection
(column 2), requiring a double b-tag (column 3) and X2 cut(column
4). The last two columns show the number of measurements for the
leptonic side and hadronic side respectively. . . . .‘ ..........

The results from the leptonic b—jet side of the lepton+jets events show—
ing the SM-like or XM—like Wb pairs depending on lepton type (electron
or muon). The positive/ negative signs in the second column indicates
the signs of the charge of the W boson and the associated b—jet. For

177

188

194

197

202

206

example a “+-” implies W boson charge is + and the b—jets charge is -. 207

XV

B3 The results from the hadronic b jet side of the lepton+ jets events show-
ing the SM—like or XM-like Wb pairs depending on lepton type (electron
or muon). The positive/ negative signs in the second column indicates
the signs of the charge of the W boson and the associated b—jet. For
example a “+-” implies W boson charge is + and the b—jets charge is -. 207

B4 Results from the dilepton events showing the W charge (WQ) and b—jet
Charge (JQ). The lst b—jet column is the highest ET b—jet. The 2nd
bjet column is the other b—jet in the event ................ 207

xvi

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

2.10

2.11

LIST OF FIGURES

The three families of fermions, their masses and electric charges. Each
family is designated with a different color. ...............

Force carriers, their masses and electric charges .............
A scale showing the masses of the fermions and bosons .........
The leading order diagrams for tf production at the Tevatron.

Representation of tf decay modes .....................

The tree-level Feynman diagram for top quark production by qr] anni-
hilation and Standard Model top decay to the lepton+jets channel.

Feynman diagrams for tf'y production by gluon-gluon fusion .....
Feynman diagrams for tt—cy production by qij annihilation .......
Feynman diagrams for t ——> Wb’y ....... , ..............
Diagram of the Tevatron accelerator complex. .............
Isometric view of the CDF detector ....................
Basic representation of particle detection ................
A quadrant of the longitudinal cross—section of the CDF detector.

The projection of the particle’s momentum onto the transverse (a: — y)
plane. The beam is in the direction of the z-axis that is out of the

page. The angle 0 is between z-axis and the momentum of the particle.

Portrait of SVX barrels. .........................
The silicon tracking detectors projected on the r — (b plane .......
The silicon tracking detectors projected on the r — z plane. . . . . . .
The cross-section view of the COT cells. ................

A representation of a calorimeter structure where scintillators are sand-
wiched between absorbing calorimeter material. ............

The CDF detector with the calorimeter systems labeled. .......

xvii

10
12
13
13
19
23
24

25

26
29
30
31

32

34

35

2.12

2.13

2.14
2.15

2.16

2.17
2.18

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

3.10

4.1

Diagram of a single calorimeter wedge. .................

Calorimeter towers for an electron and a muon shown in 1) — ()5 space
of the calorimeter, obtained by rolling out the cylindrical calorimeter.

The CDF detector with the muon systems labeled. ..........
CDF muon coverage ............................

The quadrant view of the CDF detector that shows the location of one
of the CLCs. The amplitude of the signal from the PMTs is propor-
tional to the luminosity. .........................

The passage of a particle through a Cherenkov cone. .........
Functional block diagram of the CDF data acqusition system.

The tracks and the calorimeter towers of objects from a lepton+jets
top event. .................................

Impact parameter do is the distance of closest approach of the particle
track to the interaction point. ......................

 

A jet cone of radius AR 2 \/(A1))2 + (Aqﬁ)2 ...............

The initial parton experiences fragmentation leading to the creation of
energetic particles. What we observe in the calorimeter is a shower of
particles, called a “jet”, that is collimated in the direction of the initial
parton ....................................

Absolute J ES correction as a function of jet PT. ............

An underlying event consists of beam—beam remnants plus initial and
ﬁnal state radiation. ...........................

Out-of-cone JES correction as a function of jet PT. ..........

A drawing showing the primary vertex and secondary vertex with its
associated displaced tracks. .......................

The b—tagging efﬁciency using the Tight / Loose Sethx algorithm for
b-jets from top decays as a function of jet ET (left) and |n| (right). . .

Mistag rate in data as a function of jet ET (left) and In) (right). . . .

To establish the charge of the top quark, we must determine which
b—jet is associated with the lepton from the W" decay in the event.

xviii

36

39
40

41

44

45

46

51

60

61

62

66

67

68

71

74

78

4.2

4.3

4.4

4.5
4.6
4.7

4.8

4.9

4.10

4.11

5.1

Performance of the kinematic ﬁtter as a function of the X2 on double
b—tagged (with the tight Sethx algorithm) tf MC events passing the
lepton+jets selection ............................

Comparison of jet kinematic variables for events where the leptonic
b—jet is matched to a leptonic b parton (right events) with those events
where the leptonic b—jet is not matched to a leptonic b parton (wrong
events). The top two plots show the eta and phi of the jets in the
event. The bottom two plots show the PT and ET of the jets.

bb events selected by a single lepton trigger are used for B mixing
analyses. The b—jet that includes the trigger lepton is the “signal jet”
for which the ﬂavor at production and at decay is needed. ......

Fragmentation chain for B0. .......................
Fragmentation chain for B”. ................... ’. . . .
PT.rel is the track momentum transverse to the b quark momentum. .

The charge of the charged lepton from a semileptonic b decay is corre-
lated to the ﬂavor of the b quark. ....................

Jet charge purity obtained using different weight factors from 0.1 to 1.

Jet charge distributions for b and 6 jets that are tagged using the loose
Sethx algorithm on the top MC (Mtop = 175 GeV/c2) sample. Note
that entries at point +1 and -1 are two-track jets where both tracks
have the same charge sign .........................

f+ (the fraction of events that look like SM) distributions from pseudo—
experiments for SM and XM generated using different jet charge purity
(P JQ). If SM is true f+ should be 1, if the exotic case is true, f+ should
be 0. Refer to chapter 10 for the explanation of pseudo-experiments
and how we generate these plots. ....................

The back-to—back bb events were chosen from the dijet data sample
where one of the b-jets decays semileptonically to a muon (n). The
jet charge algorithm was applied to the away-jet which is expected to
have an opposite charge compared to the muon charge. ........

83

85

88

89

90

91

93

96

98

101

104

5.2 The PT,rel and vertex mass (Mvtx) of b, c and light jets from dijet MC.106

5.3 PT rel is the track momentum transverse to the jet axis. ....... 111

xix

5.4

5.5

5.6

5.7

5.8

5.9

5.10

5.11

5.12

PT,rel distributions for bottom (top plot), charm (middle plot) and
light quark/ gluon (bottom plot.) muon-jets for various away-jet ET
ranges. The distributions were obtained from heavy ﬂavor enriched
MC for bottom and charm jets and from dijet MC for light jets. . . .

Mvtx distributions for bottom (top plot), charm (middle plot) and
light quark/ gluon (bottom plot) away—jets obtained from the dijet MC
for various away-jet ETS ..........................

The top plot is the PT,rel ﬁt obtained by ﬁtting the data to the b and
c quark distributions from MC for the events with away-jets in the
ET range of 40—50 GeV. The bottom plot is the Mvtx ﬁt obtained by
ﬁtting the data to the b, c and light quark distributions from MC for
away-jets with ETs between 40-50 GeV. The complete ﬁt is done for
nine different away-jet ET bins. .....................

The fraction of different cases obtained using the PT,rel and Mvtx ﬁts
in the away-jet ET bin of 40-50 GeV. The lower limit for the bb fraction
is 72.5% if all of the non-b cases on the muon side are matched to the
b—jets on the away side. The upper limit for the bb fraction is 83% if
all of the muon-jets are b—jets and matched to b—jets on the away side.

The b fraction on the muon side as a function of the away-jet ET
obtained by ﬁtting the PT rel spectrum in a muon-enriched dijet data
sample using 1 fb ’1 of data. ......................

The b fraction on the away-jet side as a function of its ET in a muon-
enriched dijet data obtained by ﬁtting its Mvtx spectrum. ......

Fraction of bb events in a muon—enriched dijet data sample as a function
of the away—jet ET for data (circles) and MC (triangles). .......

The measured purity (PObS) calculated on jets in a muon-enriched dijet
data sample as a function of the away—jet ET ..............

The real purity of the jet charge algorithm (P JQ) as a function of the
away- jet ET for the data (blue triangles) and MC (red triangles). The
purity for jets matched to b quarks in the MC samples is the weighted
average between the purity in the generic dijet MC and the heavy ﬂavor
enriched dijet MC. ............................

XX

112

114

115

116

118
119
120

121

5.13

5.14

5.16

5.17

5.18

5.19

5.20

5.21

6.1

The real purity of the jet charge algorithm (PJQ) as a function of away-
jet ET obtained from generic dijet MC (red circles) and heavy ﬂavor
enriched dijet MC (inverted blue triangles). The parton level (hepg) bs
were matched to jets for the calculation of jet charge purity. The black
triangles correspond to P JQ obtained from heavy ﬂavor enriched dijet
MC but using the muon charge correlation to decide on the correct J Q
assignment instead of the parton level information. ..........

The scale factor as a function of ET for loose Sethx tagged jets calcu-
lated from the ratio between the J Q purity in the muon-enriched data
sample and in dijet MC. The red line corresponds to a ﬁt with zero
slope while the blue line is from a ﬁt to a line with non-zero slope. . .

The scale factor as a function of ET obtained from the ratio between
the jet charge purity in data and the heavy ﬂavor enriched dijet MC
only. ....................................

Mvtx distributions for tight Sethx tagged bjets obtained from the
heavy ﬂavor enriched dijet MC (labeled bottom HF) compared to ones

123

124

125

from the generic dijet (labeled bottom) MC for several away-jet ET bins. 126

The scale factor as a function of ET obtained from the ratio between
the J Q purity using tight Sethx tagged jets in a muon—enriched data
sample and in dijet MC. The red line is a ﬁt to a line with zero slope
while the blue line is a ﬁt to a line with non-zero slope. ........

The ET distribution for bjets in tf events. ...............

The PT,re1 distribution for bottom quarks (left plot) in three different
17 regions when the away-jet has an ET between 45 and 75 GeV. The
middle and right plots are the Mth distributions for the bottom and
light jets respectively in three different 17 regions when the away-jet has
an ET between 45 and 75 GeV. .....................

The scale factor as a function of 1) for away-jet ET ranges of 20-35 GeV
and 50-75 GeV. ..............................

The scale factor as a function of the number of primary vertices in an
event for away-jet ET ranges of 20-35 GeV and 50-75 GeV .......

Lepton+jets background fractions for the loose double tagged sample

before and after the selection requirements for the top charge analysis.

xxi

127

128

130

131

132

137

6.2

6.3

6.4

6.5

6.6

f]
j—i

8.1

8.2

8.3

10.1

10.2

10.3

10.4

The Feynman diagram of a W +bb event that may mimic a lepton+jets
tf event. The resulting gluon splits into a bb pair while the other
resulting product, the W boson, decays to a lepton neutrino pair. W +
(:5 events are produced in an identical manner ..............

The Feynman diagrams for the production of W + 0 events. .....

Feynman diagram of a multijet non—W event where the qq annihilation
resulted in a gluon and then produced two light jets with an additional
gluon jet from one of the light quarks. One of the light jets can be
misidentiﬁed as a lepton and if there is additional gluon radiation the
event can pass the lepton+jets event selection ..............

A drawing representing the 4 regions in isolation versus ET that are
used for the QCD background prediction .................

The left (right) picture is a Feynman diagram for s—channel (t-channel)
single top production ............................

The Jet Energy Scale (JES) uncertainties in the central calorimeter
(0.2 < n < 0.6) as a function of a jet’s transverse momentum. The
level of JES corrections we applied considers only the relative and
absolute J ES corrections ..........................

M [2b distribution for the correct blepton pairings (solid) and incorrect
b—lepton pairings (dashed). ........................

M l2b max distribution for which we made the right decision (dashed)

and for the wrong decision (solid) .....................
6* for different W polarization states ...................

The —2Ln)\ curve obtained from one pseuddexperiment assuming the
SM is true ..................................

f+ distributions for the Standard Model (SM) and exotic model (XM)
hypothesis obtained from 100,000 pseudo-experiments. ........

An example with the parameter of interest X for two hypotheses, H0
and H1. The ﬁlled area under H0 is the chosen rejection region. If the

observed X falls in this region H0 is rejected otherwise H0 is accepted.

f+ distributions obtained from pseudo—experiments assuming the Stan-
dard Model (SM) or exotic model (XM). The ﬁlled red area is the a
priori 1% for a that corresponds to a f+ of 0.2. ............

xxii

139

140

142

142

149

155

164

165

170

189

10.5

11.1

11.2

11.3

11.4

A.1

A2

A3

C.1

C3

The p—value distribution for the SM assuming the XM is true. The
dashed blue line represents the a priori a value of 1% (probability of
incorrectly rejecting the SM if SM is true) and its corresponding 1 — [3
value or Power of Test (probability of rejecting the SM if XM is true). 192

The W-chargexb—jet—charge points showing the number of SM-like and
XM-like data events (black squares) on top of the distributions ob—
tained from signal and background MC samples for the lepton+jets
channel in 695 pb"1. ........................... 198

The W—chargexb—jet-charge distribution showing the number of SM-
like and XM-like events in data (black squares) on top of the expected
distributions obtained from signal MC sample for the dilepton channel
in 955 pb—l. There are no background events for dilepton channel
therefore no distribution for backgrounds. ............... 198

—2Ln)\ curve for the pairs observed. The best f+ found is 0.88. . . . 199

1‘4. distributions for SM and XM. The red arrow indicates the observed
f+ value of 0.88. The area to the left of 0.88 under the SM curve is
0.35. .................................... 200

The jet charge distribution for b (black line) and 6 (red line) jets using
offline tracks (top plot) or using secondary vertex tracks (bottom plot). 203

Vertex of the positive (right) and negative (left) tracks on the :1: — y
plane. V3; (Vy) shows the .1: (y) position of the vertex .......... 204

PT distribution for the positive (red line) and negative (blue line) par—
ticles that come from the interaction point ................ 205

At the top is the M l2b distribution of the Wb pair that has the larger
liffb value'among the two correct Wb pairs. At the bottom is the M 12b

distribution of the Wb pair that has larger M 12b value among the two
wrong Wb pairs. The distributions include the events after the dilepton
event selection requirements ........................ 209

At the top is the M l2b distribution of the Wb pair that has the smaller
M l2b value among the two correct Wb pairs. At the bottom is the M [2b

distribution of the Wb pair that has the smaller M 12b value among the
two wrong W b pairs. The distributions include the events after the
dilepton event selection requirements ................... 210

The X2 distribution after lepton+ jets cuts and tagging the two b jets. 211

xxiii

C4

C5

C.6

C7

The jet charge of b—jets that are used for the ﬁnal top charge measure-
ment for the lepton+jets (left) and dilepton (right) channels ......

The distribution for the number of tracks used in the jet charge algo—
rithm for the lepton+jets (left) and dilepton (right) channels ......

Lepton PT distributions obtained after the lepton+ jets (left) and dilep-
ton (right) selection cuts and b—tagging ..................

The distribution for the PT of tracks used in the jet charge algorithm
for the lepton+jets (left) and dilepton (right) channels .........

Images in this thesis are presented in color.

 

212

213

214

215

CHAPTER 1

Theory

And the heaven, We built it with might, and We will
surely be extending it. And We have spread out the earth:
How excellently We do spread out! And all things we have
created by pairs, that you may reflect.

Adh—Dhariyat(The winds that scatter, 47-49) Quran

1 . 1 Introduction

In 1897 in Cambridge, England, J .J . Thomson experimented on cathode rays and
showed that they were indeed particles which were much smaller than an atom and
had a negative electric charge. Those particles came to be called electrons and the
view of the atom as a featureless, structureless, indivisible particle was shattered
forever. Then in the early 1900’s came Rutherford’s discovery of the atorn’s nucleus
and Chadwick’s discovery of the neutron. Accelerator experiments revealed that the
electron, proton and neutron were only the ﬁrst three of a long list of fundamental
particles. By the early 1960’s a hundred or so types of particles had been identiﬁed.
Physicists realized that their previous understanding was not sufficient to explain the
particles being discovered. In 1964, Cell—Mann’s and Zweig’s quark theory solved
these problems. They found that all these particles could be explained by a few types

of yet smaller objects which Cell-Mann called quarks. One revolutionary part of the

quark theory is that one has to assign the quarks fractional electric charges of +2 / 3
and —1/3 in units of the proton charge. The theory of quarks is now part of the
Standard Model (SM) that describes all particles and the interactions between them.
The SM has gradually expanded in scope and gained increasing acceptance with new
evidence from particle accelerators. One exciting confirmation of the SM was the
discovery of the predicted top quark at the Fermi National Accelerator Laboratory
(Fermilab) in 1995 by the CDF and D0 experiments. Since then measurements of the
top quark’s properties have been one of the primary aims of both experiments. The

goal of this research is to measure the top’s electric charge using data from CDF.

1.2 The Standard Model

A more detailed view of the Standard Model (SM) can be found in [1, 2]. A brief
overview of how the SM works is given in this section. Three of the four fundamental
forces (the electromagnetic, weak and strong) and the behavior of all known subatomic
particles through these forces is described within a single theoretical framework called
the Standard Model. According to the SM, all matter is built up from spin 1/2 point-
like particles, called fermions. Fermions come in two types, quarks and leptons, and
each type occurs in 3 families. Each family is the same in every respect except for the
masses of the particles. There are 6 quarks, 2 in each family as shown in Figure 1.1.
For every particle, there is also a corresponding anti—particle with a reversed charge
resulting in a total of 12 leptons and 12 quarks. All stable matter is made up of the
ﬁrst and lightest family of quarks, the up (u) and down ((1) quarks. Protons and
neutrons consist of triplets of the u and d quarks: a proton is made up of 2 up quarks
and 1 down (and) quark and a neutron of 2 downs and 1 up (udd). The heavier
quarks (charm, strange, bottom and top) also form particles similar to the proton
and neutron, however these are. unstable and decay very rapidly. The heavier quarks

can only be produced and observed in high energy collisions. Like the quarks the

lightest of the leptons, called the electron, is in every atom. But the muon (200 times
heavier than the electron), and the tau (3490 times heavier), can only be observed as

the product of high energy collisions or in cosmic rays.

FERMIONS
Leptons Spin=1/2 Quarks Spin: 1/2

Flavor MassGeWc’E

      

   

   

  

nunannno (v )

[iguz»»—(«:),- ,J» 1.7771 1 -1 lbottom(b)[~4.7s}a 1.7-173.74

 

 

Figure 1.1. The three families of fermions, their masses and electric charges. Each family
is designated with a different color.

Having placed the particles in the framework of the Standard Model, we can
now talk about how the model explains the interactions between all these particles.
The SM is a relativistic quantum ﬁeld theory and is consistent with both quantum
mechanics and special relativity. In this ﬁeld theory, the classical concept of a force
ﬁnds its new deﬁnition: Particles can change their identity and be created or destroyed
through the emission and absorption of spin 1 particles, called bosons. Figure 1.2
lists the bosons under the force they are associated with along with their masses
and charges. The Lagrangian of each set of mediating bosons is invariant under a
transformation called a gauge transformation, so these mediating bosons are referred
to as gauge bosons. The symmetry groups that are embedded in the mathematical
formulation of the Standard Model Lagrangian make the model a uniﬁed framework
to describe the quantum ﬁeld theories of electromagnetism, the weak and the strong
forces.

Quantum electrodynamics (QED) is a quantum ﬁeld theory that can generate

Maxwell’s equations from a relativistic quantum theory and was developed by a mun—

BOSONS

lUniﬁedElectroweak ‘ ' Mass 3 Electric
SP'"=1

‘ (GGV/Cz) Charge

 

 

 

 

 

 

Figure 1.2. Force carriers, their masses and electric charges.

ber of physicists in the early 1900’s. The symmetry group of the theory is the (1(1)
gauge group with the massless photon as its generator. During the 1960’s Sheldon
Glashow, Abdus Salam, and Steven Weinberg independently discovered that they
could construct a gauge—invariant theory of the Weak force, provided that the electro-
magnetic force is also included. The electroweak theory they proposed uniﬁed electro—
magnetism with the weak force at high energy scales in an overall SU (2) x (1(1) gauge
synnnetry. The SU(2) group, representing the weak force part, has three generators
and that means three massless gauge bosons to mediate the weak force. However,
the short range of the weak force indicates that it is carried by massive particles.
In order to make a gauge. invariant theory work for the weak nuclear force, theorists
had to produce heavy gauge bosons in such a way that wouldn’t destroy the consis-
tency of the quantum theory. The method they came. up with is called “spontaneous
symmetry breaking”, where massless gauge bosons acquire. mass by interzwting with
a scalar ﬁeld called the Higgs ﬁeld. The scalar ﬁeld interactions mix 11p the three
massless gauge bosons of S U (2) with the one massless gauge boson of U (1) and out
of the. mixture, comes three massive gauge bosons, now called the W+, W- and Z,
and one massless gauge boson, called the photon. The W and Z bosons mediate the

weak force by changing the flavor of leptmis and quarks, while the photon mediates

the electromagnetic force by changing the charge of particles. The electroweak theory
with its S U (2) x U (1) symmetry group later became. part of the EU (3) x S U (2) x U (1)
Standard Model that also includes the strong force. SU (3) is the gauge group of the
theory of the strong interactions that is also known as Quantum Chromodynamics
(QCD). There are 8 gluons that carry the strong force by changing the quark quantum
number named color. Each flavor of quark can take on three possible color values,
conventionally called red, green, and blue. One interesting property is that the car-
riers of the strong force, gluons, also carry color charge. This causes quite different
results than what we are familiar with in QED. As two quarks separate, the gluons
form narrow tubes of color charge and the force experienced by one quark remains
constant regardless of its distance from the other quark. Since energy is equal to
force times distance, as the quarks separate the total energy increases linearly with
distance unlike in QED. At some point the vacuum becomes so energetic that new
quark anti-quark (ch) pairs are created from it. This collection of new quarks (q) and
antiquarks ((7) then are rearranged into pairs (mesons)'or triplets (baryons) of quarks
that are color-neutral hadrons.1

To date, almost all experimental tests of the three forces described by the Standard
Model have agreed with its predictions. The Standard Model predicted the existence
of the W and Z bosons, the gluon, the top quark and the charm quark before these
particles had been experimentally observed. So far the predicted properties of these
SM particles have also been conﬁrmed experimentally. Despite the Standard Model’s
success it is not a complete theory of fundamental interactions, primarily because it
does not include the gravitational force but also because there are still many funda-
mental questions left unanswered. For example, why are there three types of quarks
and leptons? Why do the particles masses span at least 11 orders of magnitudes (See

Figure 1.3)? Is there some pattern to their masses? Are there more types of particles

 

1The general name for all color-neutral combination of quarks is “hadron”.

to be discovered at yet higher energies? Are the quarks and leptons really fundamen-
tal, or do they also have substructure? What particles form the dark matter in the
universe? As the ﬁeld of particle physics continues to push the boundary of the high
energy frontier, we are coming closer to the answers of these questions and extending
our understanding of the most fundamental aspects of nature. One way of doing that
is by measuring the fundamental properties of the top quark and checking if it indeed
behaves as the SM predicts.

 

 

 

 

 

 

200
150
The recent CDF and DO combined top mass
measurement is 170.9 +/- 1.8 GeV/c2
100
50
0.005 0.01 0.15 1.5 5.0
u d s c b
0
up down strange charm bottom top
QUARKS

Figure 1.3. A scale showing the masses of the fermions and bosons.

1.3 Top Quark

By the mid-1970’s the up, down, charm and strange quarks were all well established.
With the discovery of the Upsilon particle at Fermilab in 1977, the ﬁfth quark, bottom,
took its place in the Standard Model. However, the theory suggested that the bottom
quark should have an S U (2) partner named top. The CDF and D0 collaborations at

Fermilab began a top quark search that came to a successful conclusion in February

1995 [3, 4, 5]. Since then, the study of the top quark has been a primary focus of

both experiments. The top quark is the most massive fundamental particle in the

Standard Model, with a mass approximately twice that of the W and Z bosons and
35 times that of the next most massive fermion, the b quark (See Figure 1.3).

The top quark gains its heavy mass through its large coupling to the Higgs boson.
Actually the Higgs coupling is the source of the masses of all fermions and the quanta
of the ﬁeld, the Higgs boson, has a mass that is constrained by the masses of the top
quark and the W boson. Therefore, measuring the top mass precisely is important
for ﬁnding the undiscovered Higgs boson. Because of its large mass, top has a short
lifetime of 10’24 seconds which is shorter than the hadronization time scale of 10"23
s. This means the top quark decays before it hadronizes and therefore can give its

spin and charge information to its decay products.

1.4 Top Quark’s Production and Decay

At the current Fermilab Accelerator (Tevatron) energy of 1.96 TeV, top-antitop (t0
quark pairs are produced with a cross section of around 7 picobarns2 (pb) for a top
mass3 of 175 GeV/c2. This means that just 1 out of every 1010 collisions at Fermilab
contains a top quark. The main production mechanism of top quarks at the Tevatron
is pair production via quark-antiquark annihilation (a? —> t5) which happens 85%
of the time. The remaining 15% of the time if is produced by gluon-gluon fusion.
The leading order Feynman diagrams for the tt production mechanisms are shown in
Figure 1.4.

The top quark interacts primarily by the strong force but can only decay via the

 

21 barn (b): 10‘28 m2, 1 picobarn (pb) = 10“40 m2

3In high energy physics, the masses are given in units of energy per (‘2 (E = m ~ 02), mostly in
MeV/c2, GeV/c2, TeV/c2.
MeV=106 eV . GeV: 109 eV , TeV: 1012 0V.

G‘sli‘SﬁL‘r
q 1’
ff ~ ., r‘ -.
g 610-65507, (1'53: -.. p t g £33332 {C -"~' ”’3' ""M t g 2.6“ t
«33.. 5.1?) ‘5'}
“2,36 “a
‘3 + 33,353 ; -|— gamma
3 {59' 9‘2} .811
3 43¢) (23‘ .65“
_,,,.~.r.v~;,f\. 4-... - C}? F] = W4M“ - {“3 -
g rammmwl- f g‘ t g t

Figure 1.4. The leading order diagrams for tt— production at the Tevatron.

weak force. Almost 100% of the time the top quark decays to a W boson and a bottom
quark (t ——> Wb) due to the large coupling between the top and bottom quark, th,
via the Cabibbo-Kobayashi-Maskawa (CKM) matrix. The CKM matrix is a unitary
matrix that describes the probability of a transition from one quark ﬂavor to another
quark [1, 2].

The decay of ti— events can be classiﬁed based on the decay modes of the W boson.
A W decays to either a pair of quarks (qq) or a lepton-neutrino (21!) pair resulting
in three categories of decay channels. All possible tf. decay modes are represented in
Figure 1.5 where the fermions from W- (W +) are shown along the y(x) axis. The area
of each region in the ﬁgure is proportional to the branching fraction of the designated
decay mode. If both of the W’s produced in the tt— event decay to lepton-neutrino
(61/) pairs, the decay channel is called the dilepton channel. Decays of W’s to tan (T)
leptons are generally not included in top analyses due to the difﬁculty of identifying
the hadronic decay of the tau leptons. The signature for a dilepton event in the

detector is two leptons (an electron or muon), a. large amount of missing transverse

ff decay modes

I All hadronlc

lepton +jets
tau+ ets

-

 

Figure 1.5. Representation of ti decay modes. 3

energy, ET: coming from the undetected neutrinos and two or more jets4. This decay
mode only occurs 5% of the time but is the cleanest mode due to the small amount
of background processes that can mimic a dilepton tt_ event signature. Backgrounds

for the dilepton channel come from b5, WW, Z —+ TT and Drell-Yan (2,7 ——> ll)

production.
b
‘1 V1
t
W”
+
O O O 0 0 O _ I
_ i b
q q
W-
q.

Figure 1.6. The tree—level Feynman diagram for top quark production by qrj annihilation
and Standard Model top decay to the lepton+jets channel.

In the case when both W’s decay to qq pairs, it is called the all-hadronic channel.
Such a it— decay will have six or more jets in the event, two from b quarks and four
light quarks from the W decays. The all-hadronic channel is the hardest channel
to see the tf signal in due to the huge amount of background coming from QCD
multijet production processes. However this decay channel has the largest branching
fraction at 44% so more events than the dilepton channel. The last decay mode is

the lepton+jets channel which occurs 30% of the time. In this channel one W decays

 

4A jet is a spray of particles in detector coming from hadronization of a quark or gluon.

10

to a lepton-neutrino pair and the other W decays hadronically to two light quarks.
The topology of a lepton+jets event is a single electron or muon, some amount of
ET from the neutrino, and four or more jets, two from the b’s and two from the W.
The tree-level Feynman diagram of a lepton+jets event is shown in Figure 1.6. The
background in the lepton+jets channel is substantially smaller than the all-hadronic
channel, but there are still backgrounds from generic QCD events with a fake W
boson, W+multijet production, WW events and top events where only one top is
produced. The dominant background however is from W+multijet production which
can be suppressed by the identiﬁcation of the bottom (b) quarks in the event. There
are several methods for tagging b quarks at CDF which will be described in Chapter
4.

This thesis result uses the lepton+jets tf sample where both b quarks are tagged,
also called the “double-tagged lepton+jets sample”. In the end, this thesis result
is combined with a result from the dilepton channel for a ﬁnal CDF top charge
measurement. Chapter 8 is dedicated to brieﬂy explaining the measurement in the

dilepton channel.

1.5 Possible Techniques for Measuring the Top’s Charge

There are mainly two techniques that can be used to determine the electric charge of

the top quark:

o by measuring the strength of the electromagnetic coupling via photon radiation

in ft events.
0 by using the charges of the top decay products.

The ﬁrst technique is based on the direct measurement of the top quark electro-
magnetic coupling through photon radiation in It events. A top quark can radiate

photons (7) during its production and/ or its decay. All possible Feynman diagrams

11

 

graph 1

 

1 5
A
t
3
t
t
2
graph 4
1 4
t
t 5
A
t
2 3
graph 7

Figure 1.7. Feynman diagrams for tfy production by gluon-gluon fusion

12

   

graph 3

+ diagrams with d, s, c and b

 

Figure 1.8. Feynman diagrams for tb‘y production by qq annihilation

We

..cr
8
2

[I
+
t

Figure 1.9. Feynman diagrams for t —+ W'b’y

13

for it production by gluon-gluon fusion and by qr] annihilation are shown in Figures
1.7 and 1.8 respectively. In radiative top production, (pf) —> tfv), the cross-section is
expected to be proportional to the square of the top charge. The situation is more
complicated in the case of radiative top decay, i.e, [173 —-> it followed by t —> ery,
since a photon can also be radiated from the b quark or W boson. The Feynman
diagrams for tf decay associated with a photon can be seen in Figure 1.9. To mea-
sure the tOp charge with this method, we need to distinguish between the radiative
processes sensitive to the top charge and other radiative processes with the same ex-
perimental signature. At the Tevatron, ch annihilation dominates, so there is a huge
irreducible background coming from radiative processes. Studies done by U. Baur et
all. [6] show that CDF needs around 20 f b“1 of data to measure the top charge at 95%
conﬁdence level using (to events. However, this technique is the suggested method
for measuring the top charge at the Large Hadron Collider (LHC) where gluon-gluon
fusion dominates.

The second technique, using the top decay products, is more promising at the
Tevatron and is what is used for this thesis result. In the Standard Model the top
(t) quark decays into a W+(QW+ = +1) and a bottom (b) quark ((2,, = —1/3) while
the anti-top (f) quark decays to a W_(QW_ = —1) and an anti-bottom (b) quark
(Q; = +1 / 3). Adding the charges of the decay products together gives the t. (f) a
charge of +2 / 3 (-2 / 3). However, if the decay of the observed top is such that it decays
to a W— and a b quark, then the charge of t (i) would be -4/ 3 (+4 / 3) and would not
correspond to the Standard Model top quark. Such a possibility has been put forward
in reference [7]. In the Standard Model, top is the SU(2) partner of the left—handed
b quark and the right—handed b is a singlet [1, 2]. In reference [7] a fourth generation
of quarks is introduced and the right-handed b is allowed to mix with a heavy quark
(Q1) of charge -1/3 whose doublet partner(Q4) has charge -4/3. In this model, Q4

has a mass around 174 GeV/c2 (% the mass of the observed top quark) while the

14

left-handed top quark is heavier with a mass of 274 :l: 40 GeV/c2. According to this
scenario, our observed top is the exotic Q4 quark and the Standard Model top would
be the one at 274 :l: 40 GeV/c2. Below is shown the left-handed SU(2) doublets and
how the right-handed singlet, bR, is modiﬁed to mix with the fourth generation of

quarks (Q1. Q4) where 85 is the mixing angle. [7].

StandardModel —» < Z ) bR
l

Eroticlllodel —+ t QICUSGb + b31716};
b l Q4 R

We will determine the charge of the top quark observed at the Tevatron using its
decay products and check if it is the Standard Model top with charge 2/3 or the

exotic Q4 quark introduced above.

1.6 Overview of the Thesis

Chapter 2 is dedicated to the description of the Fermilab accelerator complex and
the CDF detector without which this measurement could not have been done. How
top events are selected out of millions of collisions at the CDF detector is explained
in Chapter 3. Chapter 4 describes in detail how we determine the performance of the
top charge analysis and each of the three essential ingredients for measuring the top’s
charge.

1. The charge of the W

2. The ﬂavor of the b—jet: To determine if the b-jet is coming from a b or b quark

3. The correct W b pairing: To assign the bjet with the correct W to ensure that
the b—jet and W come from the same top decay branch.

Chapter 5 is a detailed study to check how well the b ﬂavor tagging method works in
data. Chapter 6 describes how we take care. of the non-top events, called background,

that end up in our event sample despite the top event selection. Chapter 7 discusses

the sources of systematic uncertainties and the effect of each on our measurement.
Chapter 8 summarizes similar studies done in the dilepton channel. The total amount
of expected background and signal is given in Chapter 9. The next chapter explains
the statistical methods we chose for quoting our results. Chapter 11 is dedicated to

the ﬁnal result using both the lepton+jets and dilepton channels.

16

CHAPTER 2

Experimental Apparatus

A machine that was powerful enough to accelerate
particles to the grand unification energy would have to
be as big as the Solar System and would be unlikely to be
funded in the present economic climate.
Stephen Hawking (1942-..), a British theoretical physicist.

2. 1 Tevatron

The Tevatron is a large superconducting—magnet synchrotron1 located at Fermi N a-
tional Accelerator Laboratory (Fermilab) in Batavia, IL where bunches of protons (p)
and anti-protons (13) are accelerated and then made to collide. The counter rotating
beams of protons and anti-protons collide with a center of mass energy of ,/§ = 1.96
TeV at two locations where the CDF and D0 detectors have been placed. The Teva-
tron is housed in a tunnel with a radius of 1 km. In order to create energetic particle
beams, Fermilab uses a chain of accelerators. The Tevatron is actually the name of
the main circular ring, but is commonly used to refer to the entire chain of acceler—
ators that are shown in Figure 2.1. The accelerator complex and the CDF detector

used to collect the data for this thesis are explained below.

 

lA synchrotron is a type of circular accelerator where the strength of the magnetic ﬁeld that keeps
the beam in its orbit and the radio frequency found inside the accelerating region are synchronized
to the beam momentum and revolution frequency.

2.1.1 Proton source -

The Cockcroft—Walton pre—accelerator provides the first stage of acceleration. It takes
hydrogen ions off a Cesium target and produces 750 keV 11’ ions every 66 millisec—
onds. The linear accelerator, Linac, is approximately 500 feet long and receives the
H‘ ions from the Cockcroft-Walton pre-accelerator before accelerating them to an
energy of 400 MeV. This is accomplished by RF cavities2 carrying particles along
a wave of electromagnetic radiation. The beam is also focused at this point using
quadrapole magnets. The Booster receives the beam of H " ions from the Linac and
strips the electrOns off, leaving bare protons (H + ions).

The Booster is a synchrotron that uses magnets to bend the beam of protons
in a circular path. It is composed of a series of 75 magnets arranged around a 75
meter radius circle where the protons are accelerated to 8 GeV by the use of 18 RF
cavities along the circle. Then the protons are sent to a larger synchrotron, the Main
Injector, which is about half a kilometer in radius. The Main Injector is composed
of 18 accelerating RF cavities and can accelerate 8 GeV protons from the Booster
to 150 GeV every 22 seconds. The Main Injector also takes part in anti-proton (13)
production and acceleration that will be explained in the following subsection. The
proton and anti-proton beams are injected into the Tevatron from the Main Injector

which accelerates the beams to 980 GeV.

 

2An RF cavity is a gap placed into the beam pipe across which an electric ﬁeld is applied. They
are electrically resonant structures with a natural frequency in the radio frequency (RF) range [8].

18

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19

2.1.2 Anti-proton Source

To produce anti-protons, the Main Injector sends 120 GeV protons to the anti-proton
source, where they collide with a nickel target. The collisions produce a wide range
of secondary particles including many anti-protons. The secondary particles are sent
through a magnetic ﬁeld and the particles with different masses and charges curve
at different radii. The anti-protons are selected by negative expected curvatures that
have a wide range of momenta, averaging around 8 GeV. The Debuncher, a rounded
triangular synchrotron with a mean radius of 90 meters, comes into play next. , It
takes the anti—protons from the target by RF manipulation and performs stochastic
cooling [8] to cool the beams transverse energy and decrease the momentum spread.
Since anti-particles annihilate with particles, a storage system named the Anti-proton
Recycler was built inside the Main Injector tunnel to keep anti-protons away from
matter by keeping them in a circular orbit with the use of magnets. When a sufﬁcient
number of anti-protons has been produced, they are sent to the Main Injector for

acceleration and then injected into the Tevatron.

2.1.3 Collisions at the Tevatron

The Tevatron is a circular synchrotron, and contains superconducting magnets, made
of a niobium titanium alloy, cooled to 4.1 Kelvin and 8 RF cavities. Once all the
protons and anti-protons are loaded into the Tevatron, both beams are ramped to
980 GeV. The same set of magnets and RF ﬁelds are used for the acceleration of
the beams but the protons travel clockwise while the anti-protons travel in counter
clockwise direction since they have opposite charges. The beams are squeezed in both
beam directions using focusing magnets located on either side of both the CDF and
D0 detectors and made to collide at these locations. Ideally the collisions would take
place at the center of the detectors, but actually are distributed as a gaussian around

the centers.

20

The Tevatron can sustain both beams for hours, called a “store”. Both the proton
and anti-proton beams in the Tevatron are divided into 36 bunches, each containing
billions of particles at the beginning of a store. Each bunch is separated by electro-
static separators so that beam crossings occur every 396 nanoseconds. Each product
of a pp interaction is called an “event”. Most of the collision events are from “glanc-
ing” blows, with almost all the energetic particles moving along the beam pipe in both
directions. The glancing collisions are called “Minimum—Bias“ or “Minbias“ events.
Only a few hard collisions occur which produce energetic particles going off at large
angles. These hard collisions are the ones that will be detected by the CDF detector.

At collider experiments, the particle ﬂux produced by the accelarator is called
luminosity (L). Both cross-section and luminosity are measures of collision rate and
therefore measures of the amount of data collected. However, the cross-section covers
the physics of the particle interaction whereas luminosity depends on the properties
and performance of the accelerator. At the Tevatron, the “instantaneous luminos-
ity”, also called the peak luminosity. depends on the total number of protons and
antiprotons ( ’1), N13), the number of bunches of each type (B), the frequency of
bunch revolution (f0) and the cross-sectional area of the bunches (02) as given in the

following equation:
[VI] [\ij BfO

L:
4n02

(2.1)

The instantaneous luminosity is not constant through out a store but falls exponen-
tially with time due to the momentum spread in the transverse plane of the beam
direction and particle losses from collisions. The best peak luminosity obtained at
the Tevatron to date is 2.8 x 1032c-m‘23’1. The total luminosity or “integrated lumi-
nosity” is obtained by the total particle luminosity integrated over time. A summary
of the Tevatron parameters for Run II are shown in Table 2.1. More information on

the Tevatron can be found at [8, 9].

21

 

 

 

 

 

parameter Run II
l‘Fumber of bunches 36
bunch length [n1] 0.37
bunch spacing[ns] 396
protons/bunch (Np) 2.7 x 1011
antiprotons/bunch (Np) 3.0 x 1010
interactions / crossing 2.3
integrated luminosity [jib—1] 2000
peak luminositﬂcm— 3'1] 2.8 x 1032

 

Table 2.1. Tevatron parameters during the Run II data taking period.

2.2 The CDF Detector

The CDF detector is a multi-purpose solenoidal detector, about the size of a 3—story
house, designed to identify particles produced from pp collisions at the Tevatron. CDF
is speciﬁcally used to identify and measure the energy and momentum of electrons,
muons, photons and jets. An isometic view of the CDF detector can be seen in
Figure 2.2.

The CDF detector consists of several subsystems arranged coaxially around the
beamline. The innermost layers are tracking chambers, followed by electromagnetic
and hadronic calorimeters and then muon chambers. The tracking chambers are
located inside of a 1.4 T axial magnetic ﬁeld. The magnetic ﬁeld causes the trajectory
of a charged particle to bend within the tracking chambers and the curvature of the
trajectory is used to measure the momentum of the particle. The calorimeters that
are outside the tracking system and magnetic ﬁeld are used to measure the energy of
electrons, photons and jets. The muon chambers that are wire and gas detectors are
placed outside the calorimeter and used to identify muons. This chapter continues
with the basics of particle detection. Then we will introduce the CDF coordinate
system and give brief descriptions of each detector component. A more complete

description of CDF can be found elsewhere [10, 11, 12].

22

‘" “"°”"'°*"
\ A

    
 
  

V

Forward
Calorimeter

4

 

 

 

Silicon Detectors _
Solenord Magnet

Tracking Drift Chamber
(COT)

 

Figure 2.2. Isometric View of the CDF detector.

23

2.2.1 Basics of Particle Detection at CDF

Information from each detector subsystem is combined for particle identiﬁcation. The
particles are recognized by their electronic signals and their detection relies on the
way they interact with the detector material’s nuclei and electrons. Therefore, only
those particles that undergo strong or electromagnetic interactions can be detected.
The neutrino, which is free from both interactions. is inferred from missing transverse
energy. Both photons and electrons deposit energy in the electromagnetic calorimeter,
but photons, like other uncharged particles, do not leave a signal in the tracking
chambers. Hadrons (such as protons and pions 7Ti) start their energy deposit in the
electromagnetic calorimeter, but will be absorbed fully only in the outer hadronic
calorimeter, The only particles that traverse the entire detector are muons and they
leave signals in the outer muon detectors. A basic representation of particle detection

is shown in Figure 2.3.

Tracking Electromagnetic Hadron Muon
chamber calorimeter calorimeter chamber

             

photons
—b

electrons e:

muons
—>
+
r “" P
hadrons <]

\——>

n

Innermost Layer... ——} ...O.itermost Layer

Figure 2.3. Basic representation of particle detection

24

    
 
  

TIME-OF-FLIGHT DETECTOR

 

ENDPLLB HAW CALCRIMEI'ER

 

EM) PLLG EM CALORIDETER

 

  

 

 

l I
.5 \ . . . . m
SVX ll “INTERMEDIATE
5 LAYERS SILICON LAYERS

Figure 2.4. A quadrant of the longitudinal cross—section of the CDF detector.

25

2.0

3.0

2.2.2 CDF Coordinate System

The CDF detector is forward-backward symmetric about the transverse plane through
the interaction region. The z-axis is deﬁned to lie along the proton beam direction
(from west to east). The variable 45 is the azimuth around the z-axis and 9 is the polar
angle relative to the z-axis. Because 6 is not a Lorentz invariant variable, the rapidity
(Y) is used instead. Equation 2.2 is the expression for rapidity where E and 1);, are the
energy and z component of the momentum of the particle respectively. The rapidity
simpliﬁes to pseudorapidity (n) in high energy collisions where the momentum of the
particle is much greater than its mass. Equation 2.3 deﬁnes 7) as a function of 6. As
can be seen in Figure 2.4 6 = 900 corresponds to 7) = 0 and the lower the 0 the higher

the 7) value.

 

1 [by + p:
Y — nglE _ p2 (2.2)
0
7) = —-€n(tan(§)) (2.3)
A
y Transverse
[ plane

  
 
 

l PT = P - Sin 9 Scattering
angle 4)

______ . .__>

 

X

Figure 2.5. The projection of the particle’s momentum onto the transverse (a: — y) plane.
The beam is in the direction of the z-axis that is out of the page. The angle 6 is between
z-axis and the momentum of the particle.

At CDF the direction of an outgoing particle is represented by a point in r] — 9'9

space. We can not accurately measure the momentum along the z-axis (Pg) since

26

we can not know which parton from proton was collided with which parton from
the anti-proton and also particles are lost down the beampipe. So the variable used

instead is the momentum transverse (PT) to the beam.

PT 2 P - 3171(0) = (my? + P,2 (2.4)

where Pm and Py are the momentum components in the x and y axes respectively.
Figure 2.5 represents the PT of a particle’s momentum vector in the detector’s coor-
dinate system. Similarly, transverse energy is the energy perpendicular to the beam
direction.

ET 2 E ' sin(6) (2.5)

2.2.3 The Tracking Detectors

The CDF tracking systems sit inside a 1.4 T magnetic ﬁeld which is created by a 4.8
m long, 1.5 m radius solenoid. The precision reconstruction of a track’s momentum
is acquired using the curvature of the particle’s track in the magnetic ﬁeld which is

pointing in the z direction. The tracking system includes three silicon detectors and

the Central Outer Tracker (COT).

2.2.3.1 THE SILICON DETECTOR

The silicon detector is at the center of CDF and is the ﬁrst detector that particles
traverse after the initial collision. It consists of three subsystems: LayerQWl (L00), the
Intermediate Silicon Layer (ISL) and the Silicon Vertex Detector (SVXII). All three
subsystems use the same principle for a charged particle’s position measurement,
basically the ionization signal left behind in a semiconductor. When a charged particle
passes through the depletion region of a biased p-n semiconductor junction, ionization
produces electron-hole pairs and the electric ﬁeld causes them to drift in opposite

directions. By segmenting the p and n sides of the junction into strips and reading out

27

the charge deposition left on every strip, one can measure the path length traversed
in the detector by the charged particle and find its position. The SVXII and ISL
detectors are made of double-sided silicon—microstrips. In the double-sided detectors
the p side has strips parallel to the z-direction called axial strips, and the other
side has strips at an angle with respect to the z-direction called the stereo strips.
The stereo strips provide measurements in the r — <15 plane. Together with the axial
information a 3 dimensional reconstruction of each track is possible. This information
is readout from electronic chips that are mounted on the silicon sensors.

The SVXII detector is comprised of three cylindrical barrels, as shown in Fig-
ure 2.6, placed end to end, each is 29 em in length. Each barrel provides the support
frame for ﬁve layers of double—sided silicon microstrip detectors arranged in concen-
tric rings starting at a radius of 2.4 cm from the beamline and moving out to 10.6
cm. The three SVXII barrels cover the interaction point where the beams collide and
provides standalone track information in the pseudo-rapidity range of 1 < |n| < 2.

The design parameters of the SVXII detector are summarized in Table 2.2.

 

 

 

 

Number ofTayers 5
Number of ¢ wedges 12
Number of barrels 3
Barrel length 290m
Ladder length 20.90m
Radius: Layer 0 2.44cm
Radius: Layer 4 10.6c'm
Stereo angle 90, 90, 1.2, 90, 1.20
r - q‘) pitch 60. 62, 60, 60, 65am
7‘ — z pitch 141, 125, 5, 60, 141, 65pm

 

Table 2.2. Design parameters of the SVXII detector. The numbers in the last three rows ’
of the second column correspond to each layer from inward to outward.

The ISL detector is located concentrically outside the SVXII as shown in F ig-
ure 2.7. In the central region (Inl < 1) the ISL has one layer of silicon at a radius of
22 cm. In the region 1 < In] < 2 there are two layers of silicon at radii of 20 cm and

28 cm. The additional coverage provided by the ISL aids in linking SVXII hits to

28

COOLING TUB
\

  
 

PORT CARDS

SILICON DETECTORS

Figure 2.6. Portrait. of SVX barrels.

COT tracks in the region I17| < 1. Furthermore, in the |n| > 2 region where there is
little COT coverage the combination of the ISL and SVXII provides tracking in three
dimensions. The 77 coverage of each silicon system can be seen in Figure 2.8. The
design of the ISL is identical to the SVXII as far as the data acquisition and their
power supplies are concerned, but longer strips with a wider readout pitch are used
for the ISL since it sits outside of the SVXII. Being further away from the beam, the
ISL is also less affected by radiation damage. The double—sided ISL detector has one
side with axial strips at a pitch (the distance between the strips) of 55 um and stereo
strips at a 1.20 angle with respect to the z direction at a pitch of 73 pm on the other
side.

The Laych (L00) is a single—sided high—voltage silicon detector that sits directly
on the beam pipe, just 1.5 cm away from the beamline. It provides the position

measurement closest to the interaction point and covers 1 < |n| < 2. L00) was

29

 

~64cm

 

 

Figure 2.7. The silicon tracking detectors projected on the r — (:3 plane.

30

\

 

__ _ 310..
. "L"
”:2

\

 

R=29 cm f—-
'x ISL ' I I! "
—rﬁ .
Pan G-Ib ° 7

 

svxn —:i¢:// ﬁg,
— .I'
——n— _/
' LaerOO
90cm

Figure 2.8. The silicon tracking detectors projected on the r — 2 plane.

added to improve CDF’s impact parameter3 (d0) resolution. LayerlM compensates
for radiation damage to layers of the SVXII. It also helps to resolve any ambiguities
in matching COT tracks to SVXII tracks in the dense-track environment that is
expected at high instantaneous luminosities. More information on the CDF silicon

detectors can be found at reference [13].

2.2.3.2 THE CENTRAL OUTER TRACKER

The Central Outer Tracker (COT) is a 3 m long cylindrical open—cell drift chamber
located outside the CDF silicon detectors. It provides tracking data between 40 cm
and 132 cm radially from the beam pipe. The chamber is ﬁlled with a gaseous mixture
of argon, ethane and alcohol. It uses the signal information from electrons ionized in
a gas to calculate the spatial position of the ionizing particle.

The COT contains 96 sense wire layers, which are grouped into 8 superlayer. The
superlayers are divided into two types of cells arranged in alternating rows of axial

(parallel to beamline) and stereo (2—degree offset from parallel) wires. The ﬁve axial

 

3The distance between a. track and the beam axis in the r — (1) plane at the closest approach.

31

flold panel wlro—

    

ﬂold panel

Figure 2.9. The cross—section view of the COT cells.

layers are cells of 12 sense wires interleaved with potential wires as shown in Figure 2.9
and provide tracking information in the r — 4) plane, while the stereo layers are cells
of 6 sense wires that provide tracking information in the r — 2 plane. A 3—dimensional
track reconstruction is achieved by combining the information from all the cells.
When a charged particle passes through the COT chamber, it deposits a number of
ionized particles that drift toward and hit the sense wires in the electric ﬁeld created by
the potential wires These ionized particles are distributed along the track’s trajectory
and the signals on the sense wires are processed by COT electronics that provide hit
time and charge deposition information from each wire. To determine the moment
at which a charged particle passes through the COT, a time of ﬂight detector (TOF)
made out of scintillating counters is used. The TOF is located between the COT and
the solenoid as can be seen in Figure 2.4. With a resolution of 100 ps, the TOF system

also provides particle identiﬁcation for low momentum tracks. The momentum and

32

hit resolutions of the COT are 0.0017 GeV/c and 140 nm respectively.

2.2.4 Calorimetry

The measurement of particle energies is done using calorimetry. As particles pass
through the detector, they lose energy as they interact with the detector material
and form showers. The energy absorbed by the calorimeter is measured by the use
of scintillators that are connected to photomultiplier tubes (PMTs). The amount
of light collected by the PMTs is proportional to the amount of energy lost by the
particle. Different particles interact differently with the detector material. High
energy electrons lose their energy primarily through the radiation of photons, called
bremsstrahlung and form electromagnetic showers. However, for muons the electric
ﬁeld of the atoms in the calorimeter is generally not large enough to change its
direction and start a shower in the calorimeter. So muons generally pass straight
through the calorimeter depositing very little of their energy. Hadrons also are not
deﬂected by the electric ﬁelds produced by the atoms of the calorimeter material.
However, when a hadron passes sufﬁciently close to a nucleus, there are residual strong
interactions between the hadron and the protons in the nucleus. These interactions
result in a variety of processes that produce additional particles and slow down the
initial high energy incoming particle producing a shower of particles called a “jet” and
leaving energy in the calorimeter. The energy of a particle after traversing a distance
a: in the calorimeter material is given by E1; = Eoe"‘”/$0 where :30 is the radiation
length in the case of electromagnetic showering and nuclear interaction length in
the case of hadronic showering, E0 is the energy of the particle before entering the
calorimeter. The CDF calorimeter consists of electromagnetic and hadronic parts
that are made of alternating layers of absorbing and detecting material as depicted
in Figure 2.10. Lead and iron layers are used at CDF as the absorbing material

for the electromagnetic and hadronic calorimeters respectively. The reason behind

33

using a. much denser material for the electromagnetic calorimeter is to ensure that
the electrons are all absorbed in the electromagnetic portion of the calorimeter that
is placed before the hadronic portion.

Ugh t—sensitlve Detectors £59336,
(e.g., steel)

  

Particle
Path

Figure 2.10. A representation of a calorimeter structure where scintillators are sandwiched
between absorbing calorimeter material.

The CDF electromagnetic calorimeter system, placed just outside the tracking

chambers and magnetic ﬁeld, is made up of two subsystems: The Central Electro-
magnetic Calorimeter (CEM) and the Plug Electromagnetic Calorimeter (PEM). Sim-
ilarly the CDF hadronic calorimeter system has central (CHA) and plug (PHA) parts.
Figure 2.11 is a drawing of CDF with the calorimeter systems labeled. The central
calorimeters CEM and CHA are cylindrical shaped detectors ﬁlling the radius from
1.5 m to 3.0 m and z from —2.5 to 2.5 m. Each calorimeter piece has a support
structure called a wedge.
Figure 2.12 shows the structure of a single central wedge with alternating layers
of absorbing materials and scintillators. The light produced in the scintillators are
collected by acrylic lightguides and transmitted to the PMTs. The CEM is organized
into 24 wedges in phi each with 10 towers which are readout separately. The CHA
sits just outside of the CEM and is designed to match the geometry of the CEM.

To enable a more precise measurement of the transverse proﬁle of an electromag-

34

 

Figure 2.11. The CDF detector with the calorimeter systems labeled.

 

 

 

 

System Acronym
Central Electromagnetic Calorimeter CEM
Plug Electromagnetic Calorimeter PEM
Central Hadronie Calorimeter CHA
Plug Hadronie Calorimeter PHA
Wall Hadronie Calorimeter W HA
Central Preradiator CPR
Plg Preradiator PPR
Central Electromagnetic Shower Max detector CES

 

 

 

 

Table 2.3. The parts of the CDF calorimeter and their acronyms.

netic shower, a proportional strip and wire chamber, called the Central Electromag-
netic Shower Max detector (CES). is embedded in the CEM. This chamber consists
of cathode strips rurming in the azimuthal direction and anode wires running in the
z direction, enabling a 3 dimensional measurement of the showers. This is useful for
the precision matching of tracks to electromagnetic clusters. The Central PreRadia—
tor (CPR), placed before the central calorimeter helps to distinguish electrons from
hadrons. Electrons deposit some energy in the CPR due to their interaction with the

solenoid coil. Hadrons, on the other hand. are less likely to interact with the coil and

35

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Right Left P ‘mdes
Wave Shifter
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36

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should leave little or no energy.

The plug calorimeters have analogous components to the central system; electro-
magnetic and hadronic calorimeters and a preradiator detector. The plug calorimeters
cover the region from lnl > 1.1 to |n| < 3.6. Like the central calorimeters, the Plug
Electromagnetic Calorimeter (PEM) is followed by the Plug Hadronie Calorimeter
(PHA). Each PEM has 480 towers, organized into 12 tower groups in 77 and each PHA
has 432 towers organized into 11 towers. The Wall Hadronie Calorimeter (WHA) ﬁlls
the gap between the hadronic plug and central calorimeter and extends the hadronic
calorimeter coverage to the endwall region (0.8 < |1)| < 1.2). The properties, such as
the number of towers, 77 coverage and resolution, are summarized for each calorimeter
component in Table 2.4 with the names of each acronym listed in Table 2.3.

Each calorimeter is made up of multiple individual cells, over whose volume the
absorbed» energy is integrated. These cells are aligned to form towers typically along
the direction of the incident particle. Each calorimeter tower consists of an elec—
tromagnetic shower counter followed by a hadronic calorimeter. The top drawing in
Figure 2.13 is a lego plot of the energy deposits detected in each cell of the calorimeter
from an event with both an electron and a muon.

The calorimeters were originally calibrated using a test beam of known particle
types but they are still calibrated periodically using radioactive sources as well as with
Xenon and LED light ﬂashers. The energy measured in the calorimeter is corrected

for differences in response, non-linearities and time—dependent changes.

2.2.5 Muon systems

Because muons are more massice than electrons, they do not initiate electromagnetic
showers. They also do not interact strongly so do not shower in the hadronic calorime-
ter either (however muons with transverse momenta of 1 GeV/c or more will deposit

a small fraction of their energy in the calorimeters due to ionization). Therefore, the

38

3-SEP-l997 10:30 RE! 58796 Ev_6__nt4l7

 

An e-mu event

 

 

 

 

Collision in Calorimeter

Figure 2.13. Calorimeter towers for an electron and a muon shown in n — (1) space of the
calorimeter, obtained by rolling out the cylindrical calorimeter.

39

muon system is placed at the outer most part of the CDF detector. The CDF muon
system consists of four detectors: The Central Muon Detector (CMU), the Central
Muon Extension Detector (CMX), Central Muon Upgrade Detector (CMUP) and In-
termediate Muon Detector (IMU:BMU+BSU+TSU). A View of CDF with all the

muon systems labeled can be seen in Figure 2.14.

CMP CSP

 

MSK
west cux (miniskiri) east

    

Figure 2.14. The CDF detector with the muon systems labeled.

The CMU and CMX detectors are capable of detecting muons with PT > 1.4
GeV/c while the CMP and IMU can detect muons with PT > 2.2 GeV/c and 1.4 3
PT S 2.0 GeV/e respectively. If a hadron reaches the CMU chambers, it is generally
a pion 0r kaon. About 1% of all pions and 2 to 4% of all kaons can fake a muon
signal in the CDF detector. The CMP is less sensitive to these hadrons since it is
placed behind an additional 60 cm of steel. The CMU and CMP cover the central

region up to |71l < 0.6. The muons in the central region 0.6 S |1)| S 1 and the muons

40

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lll'w'"
lllilli...

— -
—
'—
n

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I

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Tl

Figure 2.15. CDF muon coverage.

41

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42

in the forward region 1 S |7}| S 2.0 can be identiﬁed by the CMX and IMU detectors
respectively. The 45 coverage of the muon system is not complete as can be seen in
Figure 2.15. The CMU and CMP cover 84% and 63% of the solid angle respectively
while the CMX chambers, located on the east and west ends of the CDF detector,
cover 71% of the solid angle.

The CMU detector is a wire and argon-ethane gas detector, while the CMP, CMX
and IMU are made up of both drift cells and scintillator plates. The inner and outer
surfaces of the CMP are lined with scintillator plates. Similarly, the CMX and IMU
drift tube chambers are backed by scintillator counters. Each counter is readout by a
single phototube. More detailed information, such as the number of scintillators and
drift tubes, can be found in Table 2.5.

Muons ionize the argon-ethane gas as they pass through the drift chambers and
the ionized particles are gathered by the sense wires. By using the hits on the sense
wires the path of the muon track segment, called a stub, can be found. A muon
is reconstructed if such a stub is found in one of the muon systems and can be
extrapolated back to a COT track. Muons reconstructed in both the CMU and CMP
chambers are called CMUP muons. There are also muons that are reconstructed
only in the CMU or the CMP muon chambers due to gaps in the muon chambers
coverage. These muons are called CMU-only and CMP—only respectively. Because
the CMU/CMP coverage is only up to lnl < 0.6 and there are gaps in (15 a muon
can miss the central muon detector but have a track in the COT. Therefore, a high
PT track without a corresponding muon stub can also be a muon candidate, called a

CMIO (Central Minimum Ionizing Object).

2.2.6 Luminosity Measurement and CLC detector

At hadron collider experiments the beam luminosity can be measured using the pro-

cess of inelastic proton anti—proton (p17) scattering that has a cross—section (am) of

43

roughly 60 mb. The rate of inelastic pf) interactions is expressed by:

l” ' fbc I ”in ‘ L (2-6)

where L is the instantaneous luminosity, fbc is the rate of bunch crossings and u is
the average number of p13 interactions per bunch crossing.

At CDF Cherenkov Luminosity Counters (CLC), long conical isobutane gas-ﬁlled
counters, are used for the luminosity measurement. The CLC is actually designed
to measure a accurately. There are two CLC detectors at CDF one located in the
direction of the proton beam and the other in the direction of the anti-proton beam.
There are 48 CLC cones per side, arranged in 3 layers of 16 cones each. Figure 2.16
shows the location of one of the CLCs in a quadrant view of the CDF detector. At the

ends of the detectors, there are light collectors that reﬂect light into photomultiplier

tubes (PMTs) that are protected from the magnetic field with an iron shield. Since

Calorimeter /

Plug
calorimeter

 

Tracker

 

 

 

 

 

 

 

t . . l “ ‘PMT
'~ Interaction Cherenkov
pount cone

Beampipe

Figure 2.16. The quadrant view of the CDF detector that shows the location of one of
the CLCs. The amplitude of the signal from the PMTs is proportional to the luminosity.

the CLC detectors point to the interaction point, they are sensitive to the primary

particles coming directly from inelastic collisions, while rejecting softer secondary

44

particles. Figure 2.17 shows the passage of a particle through a Cherenkov cone with
Cherenkov angle 0, which is 3.10 for a primary particle at CDF. Considering the
dependence of Cherenkov radiation to 6, to the length of the Cherenkov cone and the
efﬁciency of the PMTS, a single p13 collision is expected to generate a PMT signal of

around 100 photoelectrons.

 

 

 

 

particle 7,-M§"9 m.
-. -“—-—--RI—---‘—--—‘d
m lar cone as Ii ht collector
Y 9 9

Figure 2.17. The passage of a particle through a Cherenkov cone.

2.2.7 Triggers and Data Acqusition System

The pp‘ beams cross each other in the center of the CDF detector approximately 2.5
million times every second and almost every time a collision occurs several additional
particles are produced. However, for practical reasons CDF limits the number of
collisions that will be stored for further analysis on magnetic tape to z 75 events
per second. It is the trigger system that picks these saved events out of the data
ﬂow. The time allowed to decide if an event is interesting or not depends on the
separation between the accelerator bunches which was designed to be 132 ns. The
CDF trigger architecture was built in such a way that it would be “deadtimeless”,
meaning the trigger system should make a decision before the next collision occurs.
CDF has implemented a. 3-stage (3-level) trigger system to accomplish this. The data
flow through the trigger system is shown in Figure 2.18. Each level provides sufficient
rate reduction for the next level to have minimal deadtime. Each trigger level is

more sophisticated than the previous one and requires more processing time than the

previous level. Level-1 and Level-2 triggering is implemented with custom electronics
while Level—3 is implemented as a PC farm. A brief description of each level is given

below:

 

Dataﬂow of GDP “Desdﬁmeleu”
Trigger “and. DAQ

 

    
   
    

Detector 132 ns clock cycle

L1 storage
Pipeline . 7
42 Clock Ll Trigger
Cycles Deep
. L2 Buffers

L2 Tri mer
4 Events L“

 

DAQ Buffers

L3 Farm

Figure 2.18. Functional block diagram of the CDF data acqusition system.

0 Level—1

At the ﬁrst level of triggering only quick pattern recognition and ﬁltering al-

46

goritln'ns are used. Calorimeter, muon and COT tracking information are all
available at this stage. There are around 60 Level-1 triggers and they may
involve various combinations of leptons, tracks and energy depositions in the
calorimeter. The eXtremely Fast Track (XFT) processor identiﬁes tracks by
the patterns of hits that are left on the wires in the COT after a collision. A
limitation of the current XFT design is that at high luminosities, the trigger
rate is dominated by fake tracks that are incorrectly identified because of the
large number of overlapping low momentum tracks produced. in inelastic p15 col—
lisions. Also at Level-1, calorimeter towers are combined to form trigger towers
that have 677 x 545 of about 0.20 x 150. The tracks from the XF T are matched
to calorimeter trigger towers and / or muon tracks in the muon chMbers. Level—
1 also uses information about the total missing energy above a certain energy
threshold or the total energy deposited in the calorimeter. The number of events
selected by Level-1 and sent to Level—2 (the output rate) is around 50 kHz al—
lowing 5.5 [LS for Level-1 to decide if the event should be passed to the next

level.

0 Level-2

When an event passes the Level-1 trigger, it is then stored in one of four available
Level-2 buffers. The same trigger objects are reconstructed as in Level-1 but
with more information added. A clustering alogrithm is available at this stage
for the calorimeter enabling reconstruction of jets. Shower information from
the CES detectors is also added that helps to separate jets from electrons and
photons. The Silicon Vertex Tracker (SVT) provides information about tracks’
impact parameters. The tracking information from Level-1 is combined with
SVT information on impact parameters to trigger on decays of B hadrons4. All

of this takes approximately 20 as to make a decision and corresponds to an

 

4A hadron that contains a bottom (b) quark.

47

output rate of 1 kHz. If all four Level 2 buffers are occupied when a Level—1

accept is issued, the coming event is lost and some deadtime is introduced.

0 Level-3

Level-3 is a PC farm of around 350 computers. It uses full event reconstruction
software to assemble the data fragments that come from Level-2 into higher
level objects such as jets, tans, muons etc. The decision of whether the event
will be saved is done by a Level-3 ﬁltering mechanism which classiﬁes the events
according to analyses purposes. The accepted events are sent to the Consumer
Server Logger (CSL). The CSL writes the data to disk which is later transfered
to magnetic tape for permanent storage. The triggers applied at Level-3 reduce
the output rate to around 100 Hz. The output rate at each trigger level is

summarized in Table 2.6.

 

 

Trigger Level Output Rate (Hz)
Level-l 50000
Level-2 1000
Level-3 100

 

 

 

 

Table 2.6. Output rate at each trigger level.

2.2.8 Monte Carlo Event Generation and Detector Simulation

Monte Carlo (MC) event generators and detector simulations are tools that are widely
used in high energy physics. This analysis makes extensive use of MC event samples
to help measure the top charge and systematic uncertainties. It is with event gener-
ators that possible outcomes of high energy beam collisions can be generated. While
generating the physics of p13 collisions, the theoretical knowledge of QCD and elec-
troweak physics, in addition to information like a particle’s mass, lifetime and decay
channels are used. For this analysis tt MC events were generated with PYTHIA v6.2

[14]. The PYTHIA MC program is based 011 leading order QCD matrix elements

48

for the hard scattering process followed by coherent parton5 shower evaluation and
hadronization to simulate gluon radiation and fragmentation. In order to construct
a realistic simulation, one needs to convert these partons into hadrons. This needs
to be included when generating collision events. Since these processes take place at a
low momentum transfer scale, for which the strong coupling is large and perturbation
theory is not applicable, non-perturbative QCD needs to be applied. Perturbative
QCD processes like gluon or photon radiation from initial or ﬁnal state objects, called
initial and ﬁnal state radiation respectively, should also be included. PYTHIA ac-
complishes these with an interface to the CTEQSL parton distribution functions6
[15]. It also has an interface with the decay algorithm Ethen [16] to properly sim-
ulate heavy ﬂavor (bottom and charm) quark decays. We also used the HERWIG
MC [17] event generator for calibrating the jet charge and some systematics studies.
Like PYTHIA, HERWIG employs leading order matrix elements for the hard parton
scattering, followed by parton showering.

In MC, particles are generated according to simple distributions and then put
through repeated random processes to describe the theoretical complications. To
make the parton level MC and detector data comparable, a detailed detector simu-
lation program is needed, on top of the MC generators, that models the passage of
particles through the detector. The reconstruction algorithms, some of which will
be described in the next chapter, are applied to MC generated ﬁnal state particles.
The simulation of particle tracks is performed with the GEANT3 program [18]. For
the COT , a GARFIELD [19] simulation is used that inputs COT parameters. The
calorimeter uses a parametrization of the GFLASH [20] simulation package interfaced

with GEANT3. Further details of the CDF simulation can be found in reference [21].

 

5A constituent of a hadron (a gluon or a quark).
6The parton distribution functions give the probability density to find partons in a hadron with
a certain longitudinal momentum fraction of the protons momentum and momentum transfer.

40

CHAPTER 3

Event Selection

Scientific principles and laws do not lie on the surface
of nature. They are hidden, and must be wrested from nature
by an active and elaborate technique of inquiry.

John Dewey (1859-1952), an American philosopher.

The selection of top events is done by identifying the ﬁnal state objects from the
decay of the top quark. As explained in the ﬁrst chapter, top decays to a b quark
and a W boson. The W can then decay either to two quarks (e.g W —> ad) or to
a lepton and a neutrino (e.g W —> eye). This thesis focuses on the 30% of the ti
events where one W decays hadronically and the other decays leptonically called the
lepton+jets events. These events have a signature that is characterized by a lepton
(e or a), two b quarks, two light quarks and a neutrino. We do not use tau leptons
because it is hard to distinguish taus in our detector. A candidate lepton+jets top
event is shown in Figure 3.1 as observed in the CDF tracking and calorimeter system
. Since top events are energetic and central (away from the beamline), we restrict
ourselves to central leptons with [7}] < 1 and large transverse energy, ET. In this
chapter, the lepton triggers used to select the high momentum electron and muon
events will be presented. Then, the requirements imposed on the lepton+jets events

after reconstruction to acquire the top sample will be described. The remainder of the

50

chapter is dedicated to explaining how we do jet reconstruction, jet energy corrections,

the missing energy calculation and identiﬁcation of bottom quarks.

 

e+4 jet event

let #2 ""

 

s—_ 3 meters —>

'Tracking View

. \
anary
’ ‘ I Seize

"" .
\\ ellipses

q—Smm_.

Vertex View

\ . //’ _
W; r
1g,

 

 

 

Figure 3.1. The tracks and the calorimeter towers of objects from a. lepton+jets top event.

3. 1 Trigger Requirements

The primary selection of the top events is performed online (during data collection)
at the trigger level. Fortunately, an electron or a muon with large ET provides a
highly efﬁcient way to trigger on the top events. There are certain topological and

kinematic requirements applied at each trigger level.

51

3. 1 . 1 Triggering Electrons

The main detector characteristics of a central electron candidate event is a track in the
COT and energy deposition in the calorimeter, most of which is in the electromagnetic

portion. Below are the electron requirements at each trigger level:

0 Level-1

Level-1 requires a CEM cluster with ET > 8 GeV and an XF T track pointing
to this cluster with at least 10 (or 11) COT hits in 3 (or 4) superlayers. The
XFT track must have a momentum of PT > 8.34 GeV/c (a detailed description
of ET and PT for an electron can be found in Section 3.2.1). If the CEM tower
energy has ET 2 14 GeV, then the ratio of hadronic energy to electromagnetic

energy, EhM/Eem, is required to be less than 0.125.

O Level-2

At Level—2 online jet clustering is performed. The clustering starts with ﬁnd-
ing trigger towers1 with ET > 8 GeV, called seed towers. Then surrounding
towers, adjacent to the seed tower in 7), are added and the ratio of hadronic to
electromagnetic energy is required to be Ehad/ Eem < 0.125. The CEM cluster
is required to have ET > 16 GeV. The XFT track must point to the seed tower

of the cluster.

0 Level 3

At Level-3 we require a CEM cluster with ET > 18 GeV and Ehad/Eem < 0.125
matched to a COT track with PT > 9 GeV/c. The lateral energy, Lshr, which
is a comparison of the lateral shower proﬁle in the calorimeter cluster with that

of test beam electrons, is required to be less than 0.4 and the centroid of the

 

1The calorimeter towers are summed into trigger towers of 15° in d) by approximately 0.2 in n.
One trigger tower is generally made up of two calorimeter towers.

52

CES cluster must agree with the extrapolated track position to within 8 cm in

z (|.s.~.| < 8).

3.1.2 Triggering Muons

Muons are identiﬁed by matching muon stubs in the muon chambers with a recon-
structed COT track and requiring that little energy be deposited in the calorimeter
along the trajectory of the particle. The muon trigger requirements for each trigger

level are described below.

0 Level 1

The Level-l muon trigger requires a track segment in the CMU with PT > 6
GeV/c in coincidence with hits in the CMP, called a CMUP muon, or a track
segment in the CMX with PT > 10 GeV/c in coincidence with scintillators
placed on both sides of the chambers. The scintillator coincidence is required
to occur in a narrow time window centered about the interaction time in order

to reduce the rate from particles not associated with the primary interaction.

0 Level 2

At Level-2 the PT requirement for CMUP is increased from 6 to 9 GeV/c.
The muon segments are matched to COT tracks. No additional requirement is
imposed at Level—2 for CMX muons, so all CMX events passing Level-1 are sent

to Level-3.

0 Level 3

The PT requirement on the COT track for both CMUP and CMX muons is
increased to 18 GeV/c at Level—3. A match in a r — (b window of 10 cm between
COT tracks and muon stubs in the CMU is required. This requiren'ient is 20

cm for CMP stubs and 10 cm for CMX stubs.

3.2 Ofﬂine Reconstruction and Selection of Leptons

So far the events are distinguished only by a high ET electron or a high PT muon.
Ofﬂine, after a full event reconstruction is performed, we require the event to have a
lepton which is isolated from jet activity. Electron events are selected by requiring one
isolated electron with transverse energy ET > 20 GeV in the central electromagnetic
calorimeter. Similarly, muons are required to be isolated with transverse momentum
PT > 20 GeV/c in the central region (1) < 1). We restrict ourselves to events where
the leptons and other top decay products are well measured in calibrated regions of
the CDF detector. Next, in the ofﬂine, large amounts of missing transverse energy,
ET: that indicate the presence of a neutrino is required. In this way, we acquire
a sample that is enriched in W bosons decaying to a lepton and a neutrino. Then
the selection requirements (cuts) are optimized further to extract tt_ events from the
W sample by requiring three or more jets in the event. For this thesis, we use data
gathered at CDF between March 2002 and September 2005 that corresponds to 695
pb—1 of integrated luminosity. Below are the ofﬂine lepton selections ﬁrst for electrons

and then for muons along with a detailed description of each selection variable.

3.2.1 Electron Reconstruction and Selection

0 ET > 20 GeV where ET 2 E * 321nm)

ET is the transverse electromagnetic energy where E is the total electromagnetic
energy deposited by the electron in the CEM cluster and 0 is the polar angle
of the COT track pointing to the seed tower of the cluster. An electromagnetic
cluster is made up of a number of towers. The towers with E?" > 2 GeV are
called seed towers. The towers adjacent in pseudorapidity to the seed tower are
added to the seed tower in energy to form a cluster. The clusters are ordered in

a list. To prevent. multiple counting of the same tower in several clusters, towers

54

that have been allocated to a cluster are removed from the list. The addition of
towers continues until a maximum cluster size is reached. The maximum cluster
is deﬁned to have no more than three towers in pseudorapidity corresponding

to 0.33 and one tower in azimuth corresponding to 50.

PT > 10 GeV/c

PT is the projection of the electron’s momentum as measured by the COT
track associated to the electron onto the transverse :1: — 3; plane. The transverse

momentum of the COT track is measured by its curvature in the magnetic ﬁeld.

Ehad/Eem < 0.055 + 0.00045 X Etotal

The ratio of the hadronic energy (Ehad) in the CHA to electromagnetic energy
(Eem) in the CEM must be less than 0.055 plus a factor that is used to cor-
rect the total cluster energy (Etomj). The additional factor compensates for
the inefﬁciency of the Ehad/Eem selection at high energies since the high en—
ergy electrons are more likely to produce showers that leak into the hadronic

calorimeter.

E/P<2

A bremsstrahlung photon can be radiated when an electron passes through the
calorimeter. This photon deposits its energ in the calorimeter while stealing
from the electron’s track momentum. This effect is corrected for by requiring
the ratio of the electromagnetic calorimeter energy (E) to the COT track mo-
mentum (P) to be lessthan 2 for electrons with ET < 100 GeV or PT < 50

GeV/c. This requirement is removed for high PT tracks.

Fiduciality

Fiducial cuts are applied to ensure that the electron candidate is away from

calorimeter boundaries and the energy is well measured. The ﬁducial volume

for electrons covers 85% of the solid angle in the lnl < 1.0 region. A shower
position from the shower max detector (CBS) is used to make sure that the
electron is measured in the trusted regions of the detector. In order to match
a track to an electromagnetic cluster each track in the event is extrapolated,
assuming helical motion in the magnetic ﬁeld, to the plane of the CES. The
electron track is required to be within 21 cm in the z —— qb view of the shower
position of the CBS (:rC E S < 21 cm). The track is also required not to be in
a region (20 E S < 9 cm) where the two halves of the central calorimeter meet.
Also if the electron track falls in the region zC E S > 230 cm, it is removed since
the outer half of the last CEM tower has signiﬁcant leakage into the hadronic

calorimeter.

o —3.0< Q x61: < 15cm; 62 < 3cm

The CBS is also used to reject possible hadron contamination by requiring the
CBS cluster to match with a track. The position of the CBS clustes (6z) should
agree to within 3.0 cm in z and must satisfy -3.0 < Q x 6:1: < 15 cm where Q is
the charge of the track and 6:1: is the separation in the r — ¢ plane between the
CBS cluster centroid and the extrapolated track position. The cut is asyrmnetric
to account for photon radiation which does not bend in the magnetic ﬁeld and
causes a shift in the position of the CBS cluster compared to what we would

expect from the electron track alone.

2

Xstrip < 10
The distribution of electron energy deposited on each strip of the CBS detector
is compared to the shower proﬁle extracted from test beam electrons. The

comparison is done in the r — 2. view of the shower proﬁles using a X2 ﬁt. The

result from the ﬁt is required to be less than 10.

. Zvertex < 60 CHI

The distance between the intersection of the track with the beam axis in the
r — 2 plane should be within 60 cm. The interaction point at CDF is a Gaussian
distribution centered around 2 = 0 and has a width of 26 cm. With the 60 cm

constraint, we require the track to be within 20 of the interaction point.

Not a conversion

The aim is to reject electrons that come from 62—61" conversion of photons. Pho—
ton conversions are identiﬁed by the presence of another track of opposite sign
near the electron candidate. An electron candidate is ﬂagged as a conversion if
the r — 45 separation between the two tracks is g 2 mm and the difference in
their polar angle is |6c0t0| < 0.04. If a candidate electron is consistent with a
photon conversion it is rejected. However, if a third track can be combined with
the positron(e+) to form a photon conversion, the situation is most likely due
to a high energy bremsstrahlung photon emitted by the initial electron and the
candidate electron is accepted to be real. The efﬁciency for conversion removal

is 88 :l: 4% meaning we reject % 90% of conversion electrons.

Track quality cuts

We require a good three dimensional COT track that points to an electromag-
netic cluster. To ensure the electron track is well reconstructed, the track must
contain at least 3 axial track segments and 2 stereo segments with at least 5

hits on each track segment type.

Isolation < 0.1

Isolation is deﬁned as [30018 = ([3539no — Efial") / (E5119) where 159“" is the
calorimeter energy deposited in a cone with radius of 0.4 cm (see jet cone
in Figure 3.3) around the electron cluster centroid and E§le is the calorimeter
energy of the electron cluster. Isolation should be less than 0.1 or in other

words the ET in the cone should be less than 10% of the cluster energy. This

57

cut is imposed to isolate electrons from extra hadronic activity and to reduce
the possibility of electrons from semileptonic decays2. The isolation is corrected
for any energy that leaks into the neighboring calorimeter wedge outside of the

cone .

3.2.2 Muon Reconstruction and Selection

More stringent requirements regarding the amount of electromagnetic and hadronic
energy associated with muon candidates are applied after reconstruction than when
they were triggered on. Muons can be mimicked by hadrons that shower unusually late
or not at all and manage to escape the detector, so some of the selection requirements

below are applied to discriminate muons from charged hadrons.

0 PT > 20 GeV/c
Muons have the same basic requirements as in the electron case but the COT
track is required to have PT > 20 GeV/c instead of the 10 GeV/c for electrons.
o Fiduciality

As a ﬁducial requirement, the radius of a muon track at the point the track
leaves the COT must be greater than 140 cm to guarantee that the muon passes

through all 4 axial layers of the COT.

o Eem < maximum(2.0 or 2.0 + 0.0115 x (P — 100)) GeV

High PT muons do not deposit substantial amounts of energy in the electro-
magnetic calorimeter. The deposited energy must be less than the maximum of
2 GeV or 2 + 0.0115 x (P — 100) GeV where P is the momentum of the muon.

This requirement removes minimum ionizing particles from the muon sample.

0 Ehﬂd < maximum(6.0 or 6.0 + 0.0280 x (P — 100)) GeV

 

2A semileptonic decay is a b or c quark decay that includes a lepton (e.g. b —* ("i/X).

To minimize hadronic background, the energy deposited in the hadronic
calorimeter is required to be less than 6 GeV or 6 + 0.0280 x (P — 100) GeV

whichever is the maximum value.

Eem + Eli-ad > 0.1 GeV for stubless muon.

The CMIOs (stubless muons) are required to have non-zero energy deposition

in the calorimeter.

Idl’ICMU S 3 cm, |5417|CMP S 5 cm, MIICMX S 6 cm

The distance between the muon stub and the extrapolated COT track (I6;17|)
must be less than 3.0 cm in the CMU, 5.0 cm in the CMP and 6.0 cm in
the CMX. The cut on |6;c| is looser for CMP and CMX because muons that
reach these detectors transverse more material than CMU muons and therefore

experience greater deflection due to multiple scattering.

Zvertex < 60 cm

As for electrons, the 2 position of the muon track is required to be within 60

cm from the center of the detector.

Cosmic veto

Since cosmic rays do not originate from p13 collisions, they can be removed by
requiring a small impact parameter (do). The impact parameter is the distance
between the track and the beam axis in the r - 45 plane at the closest approach
as shown in Figure 3.2. If there are no silicon hits on the track, the (10 must
be 3 0.2 cm. If hits from the silicon vertex detector are attached to the track,
the requirement on do is more stringent with (10 < 0.02 cm since the track
resolution is greatly improved. Most cosmic rays leave back-to—back tracks in

the muon chambers of the CDF detector. So the signature of a cosmic ray is a

/ Particle track

d . / Interaction point
//’ X

 

Figure 3.2. Impact parameter do is the distance of closest approach of the particle track
to the interaction point.

large separation in gb between a reconstructed muon and any other muon stub

in the detector.

0 Track quality cuts

A muon track is required to have at least 3 axial and 3 stereo superlayers with

at least 5 hits on each superlayer (axial / stereo).

0 Isolation < 0.1

Like the electron candidates, muon candidates are also required to be isolated.
Speciﬁcally the ET (both electromagnetic and hadronic) in a cone with radius of
0.4 (see Figure 3.3) around the muon track must be less than 10% of the muon
PT. Isolation for muons is deﬁned as I so), = (E1539ne — E¥)/(P1‘f) where Eff.)ne
is the calorimeter energy deposited in the jet cone around the muon cluster
and E; is the energy of the tower associated with the muon track. A small
correction to the muon momentum (Péf) is applied (curvature corrections) due

to chamber misalignment.

60

 

Figure 3.3. A jet cone of radius AB = \/(A7})2 + (A95)?

61

calorimeter jet

 

 

particle jet

 

 

 

Figure 3.4. The initial parton experiences fragmentation leading to the creation of ener-
getic particles What we observe in the calorimeter is a shower of particles, called a “jet”,
that is collimated in the direction of the initial parton.

62

3.3 Jet Reconstruction and Corrections

A jet is formed from the scattering of a strongly interacting parton (a quark 0r
gluon). The initial parton experiences fragmention leading to the creation of energetic
colorless particles such as pions, kaons, and other hadrons that are emitted spatially
collimated along the initial parton direction. See Figure 3.4. In the detector, jets are
observed as clusters of energy located in adjacent calorimeter towers. The energy of
the initial parton can be approximated by summing the tower energies within a cone

of speciﬁed size. This procedure is called jet clustering.

3.3.1 Jet Clustering

'Jets for this analysis are reconstructed using a cone algorithm called JBTCLU [22].
Jets coming from top events usually have higher momenta and therefore are more
collimated than QCD jets so a smaller cone size (AR 2: 0.4) is used. Jet clustering
starts by creating a list of calorimeter towers above a ﬁxed ET threshold of 1 GeV,
called seed towers. Seed towers are then ordered in decreasing ET. A cluster is formed
by clumping together adjacent seed towers within a particular cone radius. If there
is any tower left outside of the reconstructed cones, a new cluster is started with it.

The n and (f) of the centroid (jet axis) of each cluster is then calculated as:

N tow

. . ET ' 49 '
2: ————..<.:3.::> «m
27:0 ET

Ntow .
cluster _ Z ET(i)”(i) (3 2)
77 — Ecluster '
i=0 T
where ET(i) is the transverse energy of tower i and the sum is taken over the
number of towers in the cluster. o,- and 7),: are the azimuth and rapidity of tower

i. ET weighted centroids are found for all clusters. Then, using the centroids as

seed towers, new cones are generated as explained above. The iterative procedure is

63

repeated until the jet axis is stable in 7) — cf) space, meaning the centroid of the energy
within the cone is aligned with the geometric axis of the cone. In some cases two
clusters can overlap. If the sum of the energies in shared towers exceeds 75% of the
energy of the smaller cluster, the two clusters are merged into one cluster. Otherwise,
towers in the overlapping region are assigned to the nearest jet in n — (25 space. The
approximate jet energy resolution is 0.1 x ET + 1.0 GeV. The ﬁnal product from jet
clustering is our reconstructed jet whose raw energy (Emw) is the scalar sum of tower

energies.
N tow

Eraw = 2 E, (3.3)
120

3.3.2 Jet Energy Scale (JES) Determination

Jets are reconstructed from energies measured in calorimeter towers as explained in
the previous section. However this energy does not exactly correspond to the energy
of the parton the jet came from. Jets may be mismeasured due to a variety of effects
like less of energy in cracks between detector components, loss of energy outside
the cluster cone, contributions from the underlying event, multiple interactions and
absolute energy scale. Jet energies are corrected back to the particle level and then
from there to the parton level by adjusting the measured energy for all of the above
affects, called the Jet Energy Scale (JES) corrections [23]. The corrected energy

(EEI'PH) can be expressed by the following equation with each variable described below:

w ‘. 1 hII UE 0C ‘
El?” : (£65m X frel X ftime X fscale _ ET ) X fabs - ET + ET (3-4)

, 0 Relative Jet Energy Scale (fl—(.1)

This J ES correction is applied to remove the 7) dependence of the calorimeter.
It accounts for non-uniformities and uninstrumented regions of the central, wall

and plug calorimeters. frel is extracted from dijet studies using PYTHIA MC

64

where one jet is central and well measured and the second jet is required to
balance the first jet, the so called “dijet-balancing“ approach. Jets are corrected
for any variation in the response as a function of detector 77. The relative J BS

is ﬂat up to [7)] = 0.2 but different corrections are. found for [7)] from 0.2 to 0.7.

Raw Jet Energy Scale (fscale)

The raw J BS accounts for the non-linear response of the calorimeter. The CDF
calorimeters respond differently to particles of various energies. The relevant
correction factor (fscalel is determined by using back-to-back photon+jet events
where the separation in (f) between the photon jet and the other jet is 1800. The
photon-jet sample is a good sample for studying the jet energy scale since photon
energy is measured precisely by the electromagnetic calorimeter. The average
PT imbalance in a photon-jet event is around 3% but the uncertainty for the
raw jet energy scale is inﬂated to 5% to cover the possibility of mismeasurement
of the photon energy and the possibility of low energy gluon radiation that can

occur in photon+jet events.

Time Dependent (ftime)

The response of the calorimeter towers changes with time due to calorimeter
deterioration and effects such as aging of the phototubes. The raw energy is

corrected by fame to take care of these effects.

Absolute Jet Energr Scale (fabsl

The absolute JES corrects calorimeter jets back to particle jets and accounts
for the fragmentation effects. The calorimeter simulation derives the absolute
correction over a wide range of jet PTs. The relevant correction factor (fabs) is
obtained using dijet PYTHIA events with Tune A [24, 25] parameters. Tune A

refers to the values of parameters describing multiple-parton interactions and

(GeV) Absolute Energy Scale

initial state radiation3 which have been adjusted to reproduce the energy ob-
served in the region transverse to the highest ET jet in jet data. For the deter-
mination of fabs, the two highest ET jets in MC are matched to the calorimeter
jets and the ratio between the particle and calorimeter jet PT is calculated.

The amount of the absolute J BS correction as a function of jet PT is shown in

 

    
   

 

 

Figure 3.5.
particle
_ T
f abs _< pigalorimeter > (3'5)

1.6 T—TI I IW—I If! I I I T T I I I I I I I T I I I r I I I I I I I I I I I I I I I I I I I -
1,5 """""""" Correction for cone 0.4 jets _‘
Uncertainty i6 :
1.4 .2
1
1.3 _
_ .4
I 1
1.2— __
1.1:— .-"'--'--m--..--m.....£
I: I LI 1 I I I I I I I I I I I I I l I 1 LI 1 I I l I I 11 I I I I I l I I I I I l l I I I I 1‘

 

 

 

50 100 150 200 250 300 350 400 450 500
PT jet (GeV)

Figure 3.5. Absolute JES correction as a function of jet PT.

0 Underlying Event (EgE)

 

3A massless virtual gauge boson (i.e. photon or gluon) that is radiated before a hard collision.

66

In order to go from the particle jet energy to the parton energy, the contribu—
tions from beam—beam remnants, referred to as the underlying event, must be
subtracted from the total jet energy. See Figure 3.6. The contribution from the
underlying event (EgE) is estimated from minbias events in a similar way to
the absolute JES calculation, but this time the particle jet is matched to the

parent parton. For a jet cone of 0.4 the correction is around 3 GeV.

Hard Collision
outgoing parton

   
    
 

Final State

Underlying event
K Radiation

Inltlal State
Radiation
Underlying event

Hard Collision
outgoing parton

Figure 3.6. An underlying event consists of beam—beam remnants plus initial and ﬁnal
state radiation.

0 Multiple Interactions (E¥ﬂ)

This correction takes into account multiple pp interactions that can occur in the
same bunch crossing. On average one p13 interaction is expected at a luminosity
L = 1 x 1030 cm_23_1 with 36 bunches. However, the number of interactions
goes up as the luminosity increases, i.e up to 3 interactions when L : 2 x 1032
cm‘2s_1. In case there are multiple interactions, there is a contribution (Eyl)

that should be subtracted from the total energy. The correction is parametrized

by the number of primary vertices observed in the event and amounts to 0.36

67

GeV per additional vertex.

0 Out-of—cone corrections (E190)

Another correction needed to correct from particle to parton energy is out—of—
cone energy. Part of the original parton’s energy can be deposited outside of
the jet cone due to fragmentation and ﬁnal state gluon radiation4. Out-of—cone
energy is evaluated by comparing the energy ﬂow outside the jet cone up to a
radius of 1.3. Using PYTHIA MC it was found that it is generally 15% of the
total jet energy. For example a 10 GeV jet needs a 1.3 GeV (13%) correction

as can be seen in Figure 3.7.

 

I I I I I I I I 7 I I I I I I I I I I I I I I I I I I I I I I I I I I I I

l

I

(GeV)

------------ Correction for cone 0.4 IGtS
uncertainty i6

   

Out-of-Cone

lllllllllllllllllllll

 

 

 

llllll

LLlllllllllllllIlIl

l l l I l l l l l
20 40 60 80 100 120 I40 I 60 I80 200
P7 particle-jet (GeV)

 

Figure 3.7. Out—of-cone JES correction as a function of jet PT.

 

4Photons or gluons radiated from ﬁnal state particles.

68

3.4 Missing Energy

Neutrinos escape the detector unnoticed since they only interact through the weak
force. We can infer the existence of a neutrino by using momentum and energy
conservation in the transverse plane. The raw missing transverse energy (ET) is
calculated from the negative of the vector sum of the transverse energy in all towers
of the calorimeter, as shown in Equation 3.6, where ft,- is the unit vector pointing

from the event vertex t0 the ith calorimeter tower.

Erdw: —Zb Tni (3.6)

The ET is corrected if there is a muon in the event since muons do deposit some
energy in the calorimeter. This is done by adding the transverse momentum of the
muon track (137m) into the above equation and subtracting the energy of the muon
(Bin) from the corresponding calorimeter towers. Similar corrections are done for
minimum ionizing tracks with PT > 10 GeV/c that pass loose matching requirements
with a muon stub or extrapolate to regions not covered by muon detectors. The
raw ET is also corrected for the jet energy mismeasurements that were covered in the
PCOI'I'

previous section. The corrected iT can be expressed as in Equation 3.7 whereP T090

and E???” are the corrected momentum and raw energy of the jets respectively.

E... _,,.. — < z — 5; Va)— Va- :Va. cm

muon muons (jets jets

3.5 Identifying b quarks

Identifying or tagging the b quarks in top events is crucial for the event selection.
The main background to top events is a W boson produced in association with a few

jets. Only a few percent of the W +jets background events contain a b or c quark jet

69

but there are two jets originating from b quarks in every tt— event. Thus tagging the
b—jet can signiﬁcantly reduce the amount of background.

There are three methods used at CDF to differentiate b quarks from other quarks.
The ﬁrst method looks for a low momentum lepton coming from the semileptonic
decay of a heavy ﬂavor hadron (b —> EUgX or b ——> e ——V EVgX ). The momenta of these
additional leptons from bottom quarks in t0p events are smaller than (or softer),
typically a few GeV/c, than leptons from W decays. Thus, this method is called
the Soft Lepton Tagger (SLT)[26]. The discussion of the SLT is left for Section 4.4
which describes b ﬂavor taggers. For the top charge analysis we will identify b—jets by
using the second method, called Secondary Vertex Tagging (Sethx), that makes use
of the long lifetime of B hadrons and will be described in the following subsection.
The last method is the jet probability method that considers the impact parameter
of each track within the jet and constructs a probability that a given jet is consistent
with coming from a zero—lifetime source. The details of this method can be found

elsewhere [27].

3.5.1 Secondary Vertex Tagger

The Sethx [28] algorithm takes advantage of the long lifetime of B hadrons. The b

0‘2‘4 seconds) to form a jet

quark hadronizes almost immediately (on the order of 1
of particles. Included in this jet are B mesons (such as BO, B+/—, B?) or B baryons
(e.g. A B, E, 2). A B hadron from a tf event travels a macroscopic distance away
from the primary interaction point before decaying into several charged and neutral
particles. The distance before decaying can be up to a few millimeters.

The secondary vertex algorithm selects tracks with a large impact parameter (do)
and reconstructs a vertex from these tracks. If the reconstructed vertex is displaced

in the transverse direction from the primary vertex, it is called a secondary vertex

(see Figure 3.8). The ability to distinguish tracks coming from the secondary vertex

70

        
 

Second vtx.

Figure 3.8. A drawing showing the primary vertex and secondary vertex with its associated
displaced tracks.

apart from the primary vertex depends on a good determination of the primary vertex

which will be described in the next section.

3.5.2 Finding the Primary Vertex

The primary vertex location in a given event can be found by ﬁtting well measured
tracks to a common point of origin. The ﬁrst step is to choose tracks which pass
a set of requirements. The tracks should have PT > 0.5 GeV/c. They should be
within 1 cm of the beamline (d0 < 1 cm) with an impact parameter signiﬁcance
Sdo E [do/ado] S 4 where ”do is the uncertainty on the impact parameter’s position.
For a COT track to be considered in the primary vertex algorithm, it should have at
least 2 stereo or 2 axial superlayers with at least 6 hits on each of the stereo and axial
superlayers. The algorithm begins with an input vertex chosen using the beamline
position information. The tracks are ordered by decreasing PT, keeping a maximum

of 50 tracks. A X2 for each track with respect to the vertex is then calculated and

71

tracks with a x2 > 20 are removed. The tracks that are left are then ﬁt again and
the removal of tracks with X2 > 20 is repeated until a vertex with no tracks over the
X2 cut is found. The uncertainty in the coordinates of the primary vertex is 10 — 20
pm and strongly depends on the 2 position of the vertex and the number of tracks.
At high luminosities, more than one collision can occur resulting in multiple event
vertices. For events with a high PT lepton the vertex closest to the highest PT lepton
is chosen as the primary vertex. For events with low momentum leptons, the vertex
with the highest total scalar sum of transverse momentum of the associated tracks is

used.

3.5.3 Finding the Secondary Vertex

The secondary vertex (Sethx) algorithm [28] ﬁrst looks for displaced vertices with
three or more tracks pointing to them. Every track in the secondary vertex must have
an impact parameter signiﬁcance Sdo > 2.5 and PT > 0.5 GeV/c with at least one
track having PT > 1 GeV/c. If this fails, the algorithm searches for two track vertices
with tighter requirements on the track quality with Sdo > 3 and PT > 1 GeV/c with
at least one track having PT > 1.5 GeV/c. The estimated uncertainty on the track’s
impact parameter 00 is largely determined by the SVXII detector resolution which
is currently around 50 pm. The tracks are then associated with a jet. As can be
seen in Figure 3.8 the distance in the transverse plane between the primary and the
secondary vertex is called ny. If the secondary vertex is signiﬁcantly displaced from
the primary vertex (SLxy E ley/anyl > 3) the jet is tagged. ny is a signed
distance that is positive if the vertex is on the same side as the jet and negative if it
is on the opposite side. A negative ny value is indicative of background.

The Sethx tagging method is independent of the type of B decay involved. B
hadron decay channels are numerous and most of them involve neutral particles whose

trajectories can not be reconstructed. Sometimes a B hadron decays to a charm

72

hadron which in turn decays to several particles producing a tertiary vertex making
the kinematics of the decay more complex. The disadvantage of the Sethx method
is that charm hadrons can not be distinguished from B hadrons. Even though charm
hadrons have a shorter lifetime than B hadrons they are tagged with a relatively
high efﬁciency of around 10%. Thus the Sethx tagger is actually a heavy ﬂavor
(bottom or charm quark) tagger. The efﬁciency of tagging b—jets using the Sethx
algorithm depends strongly on the jet kinematics. Studies were carried out at CDF
to determine the b—tagging efﬁciency as a function of jet ET. Figure 3.9 shows the
Sethx tag efﬁciency for b—jets from top decays as a function of jet ET and |17|. As
can be seen in the ﬁgure there is a loose and tight version of the Sethx algorithm,
each with slightly different track selection requirements resulting in different tagging
efﬁciencies and purities. The comparison of the. track selection cuts is shown in Table
3.1. As a result of optimization studies which will be presented in the next chapter,

we decided to use the loose Sethx tagger.

X (31'

threshold for ' vtx.
pass r seco

pass r seco

 

Table 3.1. Track selection criteria used in the Loose and Tight Sethx algorithms.

Studies at CDF revealed that the b—tagging efﬁciency from Monte Carlo samples
differs from CDF data as a result of higher tracking efﬁciency in the MC simulation
[28]. The ratio of the tagging efﬁciency in MC over the data, averaged over jet ET,
is known as the b—tagging scale factor and is used to correct the tagging efﬁciency in
MC. It is also possible to mistakenly tag a light quark (u, d, s) jet, which are then
called mistagged jets. Mistags are caused mostly by random overlap of tracks which

are displaced from the primary vertex due to tracking errors. The mistag rate is

 

   
 

0 Tight Sethx
5 o 6

.g Loose Sethx
E 0.5

a)

030.4

m

H

   

Top MC scaled to match data
Only b-jets with ITI|<1

 

  

20 40 60 80 100 120 140 180 1,80
JetET(GeV)

 

9
0)

Tight Sethx
Loose Sethx

   
 

.0
(II
I'll

b-tag efﬁciency
53 .0
LA 4:

.0
N
I II

E Top MC scaled to match data
Only b-jets with Er<15 GeV

0 Illllllj_|_l_l_lllllllJllllllIllllllllll I
0 0.2 0.4 0.8 0.8 l 1.2 1.4- 1.8 1.8 2
Jetn

$3

 

 

fiff '
I

 

Figure 3.9. The htagging efﬁciency using the Tight/Loose Sethx algorithm for b—jets
from top decays as a function of jet ET (left) and Inl (right).

74

 

rate
0
'o
0‘)

Tight Sethx
030.05 : Loose Sethx

mista
O
‘o
.p.
I‘IY

  
  

0.01 _- ' Onlyjets with |n|<1

 

 

0 ...I...I...i...1...|...i...|...
20 4O 60 80 100 120 140 180 180

Jet F.r (GeV)

 

 

rate
.0
0
LA
t

Tight Sethx
Loose Sethx

mistag
i:
[\J
01
l

0.02 '- ‘ ..... ,,

0.015

0.01 :-

0005 {Only Jets with ET> 50 GeV

 

 

0O 0.2 0.4 0.6 0.8 1 1.2 1.4 1.8 1.8 2
Jetn

Figure 3.10. Mistag rate in data as a function of jet ET (left) and |1)| (right).

parametrized as a function of jet variables like jet E , track multiplicity, 7), 96 and is
actually a matrix [29]. Due to imperfections in the tracking simulation, the mistag
rate in MC is generally smaller than that observed in data. This affects the number of
events where the assigned b jets are not actually from b quarks. Figure 3.10 shows the
mistag rate in data as a function of jet ET and Inl. The comparison of mistag rates
as well as btag efﬁciencies between the loose and tight Sethx tagger for a central

jet at a typical ET of 60 GeV is summarized in Table 3.2.

 

 

 

Sethx Tagger b—tag Efﬁciency Mistag Rate
Loose ' z 52% z 2.5%
Tight z 45% z 1%

 

 

 

 

Table 3.2. The b-tag efficiency and mistag rate for a central jet with ET = 60 GeV from
a top event.

76

CHAPTER 4

Determining Top’s Charge via its Decay

Products

We are all here to do what we are all here to do.
The Oracle to Neo, The Matrix Reloaded, 2003.

4.1 Introduction

As explained in the ﬁrst chapter, the charge of the top quark can be measured directly
through electromagnetic couplings using “77 events [6]. However, that measurement
needs more data than CDF will ever accumulate. Instead, since the top quark decays
before it can hadronize its charge information is passed to its decay products and
enables us to determine the top’s charge from the charges of the W boson and b
quark. However this is not enough because we have two top quarks (a t- and f) in
each event, so there are two W3 and two b—jets. The remaining question becomes
what is the correct association or pairing between the Ws and ()3. Getting the correct
association, along with the charge information of the decay products, will enable us
to answer if top decays into a W+ and a b or a W+ and a 5 (See Figure 4.1). The ﬁrst
case (and its charge conjugate) t —* W+b ( f —> W‘B) corresponds to a top charge
of +2/ 3 (—2/3) as expected in the Standard Model, while the second case t. —+ W+f)

(f —-> W’b) corresponds to a top charge of —4/ 3 (+4 / 3). In summary we need three

77

ingredients to establish the charge of the top quark:

1. The charge of the W
2. The ﬂavor of the b-jet: whether it is coming from a b or 5 quark

3. The correct W b pairing

 

Figure 4.1. To establish the charge of the top quark, we must determine which b—jet is
associated with the lepton from the W decay in the event.

The determination of the W charge is straight forward if we restrict ourselves to the
leptonically decaying Ws where the W decays to a lepton and its neutrino. In the
lepton+jets sample we assign the charge of the electron or muon in the event as the
charge of the leptonically decaying W. We then assume that the charge of the other W
(the hadronically decaying W) has the opposite charge. This chapter is dedicated to
the discussion of the other two needed ingredients, namely the Wb pairing and ﬂavor
tagging the b—jets. We will present the methods used to pick the correct Wb pairing
and to ﬁnd the correct ﬂavor of the b—jets and their relevant optimization studies.
Beforedescribing the methods we need to deﬁne how we quantiﬁed the performance

of our methods.

78

4.2 Deﬁnition of Performance

In order to optimize various algorithms that are part of this analysis, we need a
quantitative criteria for picking the best option. We have chosen to use a combination
of two quantities: efﬁciency (6) and purity (P). Efﬁciency is deﬁned as the number
of events remaining after a particular selection algorithm over the number of events
available before we applied the algorithm. The purity is the number of events that
are correct (based on MC information) over the number of events that the algorithm
selected.

More formally, let N+ be the number of events assigned by our analysis method
to be of the +2/ 3 hypothesis (that means 13+ + b or £— + b) and N- be the number
of events assigned to be of the —4/ 3 hypothesis (that means W + b or E" + b). Then

the measured asymmetry is given by:

N+ — N-
A = —— 4.1
while the true asymmetry is given by:
Nt — N3
= —— (42>
1V+ + N_

where N1 is the true number of events that are really +2 / 3 events by nature. Similarly

N: is the true number of —4/3 events. If we deﬁne the dilution (D) as:

Nright - Nwrong

 

D = (4.3)

Nright + Nwrong

where Nright and Nwrong are the number of correctly and incorrectly assigned events,

then a measurement of the true asymmetry is given by:

_ AIDCRS
A _ D (4.4)

which shows why D is called the dilution. If we had no incorrectly assigned events,

the dilution would be 1 and the measured asymmetry would be the same as the true

79

asymmetry. A dilution equal to 0 means that there is no power to distinguish between
right and wrong events and a negative dilution means that we are incorrect more often
than correct. It has been noted that the dilution can be considered a misnomer since
we really want as high a dilution as possible (more right than wrong). The dilution
is actually related to the purity (P) by D 2: 2P - 1. The dilution goes to zero when
the method in question gives the wrong answer 50% of the time (P = 50%).

The statistical uncertainty on the true asymmetry (A) is given by:

1 —1)2.4
”AZVinac ea

where N is the total number of events and e is the efﬁciency of the assigmnent method.
Since the uncertainty scales with 1/ m rather than 1/\/_1\7, 6D2 is the quantity
to optimize for a given algorithm of interest. In the rest of this chapter, we present
different methods tried for determining the correct Wb pairs and the correct b ﬂavors.
The decision of the optimal method is based on the comparison of (D2 values and

choosing the one with the largest €D2.

4.3 Wb Pairing

There is a twofold ambiguity in the pairing of the W boson with the b quark in a ti
event which must be resolved in order to determine the top charge. The resolution
of the ambiguity relies on ﬁnding the b—jet that is associated with the leptonically
decaying W, which will be called the ”leptonic b—jet”.

The problem of reconstructing lepton+jets events has been addressed in other top
analyses, for example in the W helicity measurement [30], where various methods
were explored. It was found that the best performance came from a kinematic ﬁtter
(described below in more detail) that correctly assigns the leptonic b—jet to the lep—
tonically decaying W between 60% and 70% of the time. The 10% difference comes

from different sets of requirements imposed on the ﬁtter as will be explained in our

80

optimization studies for the Wb pairing. Table 4.1 shows all the tests that were per-
formed on lepton+jets events from It? Monte Carlo to select the jet corresponding to
the true leptonic b parton the largest fraction of the time. Remember that we have
parton level information in the MC so “leptonic b parton” here implies the b quark

associated to the leptonically decaying W.

 

 

method Corr. b SJected
Kinematic Fitter 60 — 70%
Closest b—tagged jet to the lepton 54%
Furthest b-tagged jet from the lepton 49%
Closest of two highest ET jets to the lepton 35%
Closest jet to the lepton 30%
Randomly selected jet 25%

 

 

 

 

Table 4.1. The results of various methods tried in a previous top analysis [30] to match
jets to the correct b parton. The second column represents how often each method matches
a jet to the correct b parton (leptonic b—jet to the leptonic b parton).

In order to obtain the jet in the event which is most likely to be correctly matched
to the b parton coming from the top quark where the W decays leptonically, the
kinematic ﬁtter constructs a x2 using the MINUIT [31] program. Actually the kine—
matic ﬁtter calculates the top mass for each possible jet-to-parton combination in an
event and its corresponding X2 value. For each event with 0, 1, or ‘2 b—tags, there are
12, 6 or 2 different permutationsin the assignment of the four highest ET jets to the
partons from the top quark decay. For this analysis, we use 2 b—tags and choose the
jet assignments with the‘minimum X2 combination for the determination of the Wb
pairs. The X2 expression is shown in Equation 4.6. The ﬁrst two terms consider the
difference in momenta between the ﬁtted and measured values. Speciﬁcally the ﬁrst
term is the difference between the transverse momentum of the 4 jets and lepton.

The second is between the ﬁtted and measured momentum of the. unclustered energy.

81

Each difference is divided by the uncertainty in the measured value. The last four
terms are the mass differences l;)etween the. W and its decay products and between
the top and its decay products. Each of these terms is divided by the related decay

width of the W boson or the top quark.

 

 

 

 

 

 

., .- 2 AUE UE 2 2
2 (PT—‘13:?) (Pi —Pj ) (ij’MW)
: 23'11: .. ’es + 2":x. ,- + +
(N13,, — MW)2 + (Mm-,- - M.)2 (MW — Mt)2
Fix 1‘? I“?
(4.6)

In this fit, the transverse energy of the neutrino is deﬁned as the negative sum
of the lepton, jet and unclustered energies. The kinematic ﬁtter assigns 5.0 and 0.5
GeV for the masses of the b partons and the light partons respectively, with the charm
quark being treated as a light quark. The mass of the W (MW) is constrained to be
80.41 GeV and its width (I‘W) is taken as 2.12 GeV. Regarding the top mass, there
are two different modes that the kinematic ﬁtter may use. The constrained mode
where the two top quark masses are both constrained to a certain value with a chosen

width or the free mode where the top mass is free to ﬂoat.

4.3.1 Kinematic Fitter Optimization Studies for W b paring

As mentioned above, the kinematic ﬁtter gave the best performance for the determi-
nation of the correct Wb pairing in lepton+jets if events. We tried various ways to
improve the performance of this ﬁtter. As explained in Section 4.2 the performance
is driven by 602 where here 6 is the efﬁciency of the kinematic ﬁtter (or Cpairing) and
the purity (Ppairing = (D + 1) / 2) is how often the ﬁtter ﬁnds the correct Wb pairs.

We started with investigating if a X2 cut on the best ﬁt jet-to—parton assignment

82

improves the 602. Figure 4.2 shows the (D2 values obtained for different X2 cuts
where we kept the events with X2 less than the chosen cut. The ﬁgure shows that
6D2 is relatively ﬂat between 8 and 15. We chose to use X2 < 9 since it is also
used by several other CDF top analyses [32]. With this cut, we ﬁnd an efﬁciency of
56.2 :1: 0.3% and a purity of 83.0 :I: 0.3. The corresponding (02 is 0.25.

 

'33
£0

 

111T llllllllllllllllllTlTTI‘lIlllll]llllll

 

 

l l l l l l l l I I 1 1 l l_ 1 J A l

10 15 20 25

 

Figure 4.2. Performance of the kinematic ﬁtter as a function of the x2 on double b—tagged
(with the tight Sethx algorithm) tf MC events passing the lepton+jets selection.

The x2 study was done using a ti MC sample where the mass of the top quark was
set to 175 GeV/c2. Remember that the kinematic ﬁtter also places a constraint on
the top mass. For the above study, we used a constraint of 175 21:3 GeV/c2. However,
in search of improving the ﬁtter’s performance, we also tried other constraints such
as 178 i 6 GeV/c2 or 175 i 0 GeV/c2. No signiﬁcant change on the performance
was observed by imposing different top mass constraints. We also checked the free
(no constraint) mode which decreased the pairing purity by 14%. In the end, we
decided to use the constrained mode of the kinematic ﬁtter with the top mass set
to 175 :l: 3 GeV/c2. As mentioned in Section 3.5, there are different versions of the
Sethx tagger that we use to tag our b—jets. To see the effect of different b—tagging

requirements, we checked the pairing efﬁciency and purity using the loose and tight

83

 

 

tight tagger loose tagger
63,-th % 16 22
Ppairing % 83 83
Cpairing % 57 56

 

 

 

 

 

Table 4.2. Efﬁciency (Epairing) and purity (Ppairing) of getting the true leptonic b using
the kinematic ﬁtter on double tagged lepton+jets events. The ﬁrst column shows results
using the tight Sethx tagger and the second column shows results using the loose Sethx
tagger. ‘

Sethx algorithms. As shown in Table 4.2 there is a z 40% gain in the b—tagging
efﬁciency using the loose version but no loss in purity so we decided to use the loose
Sethx tagger.

This analysis is using double b—tagged events (events with 2 jets tagged as bs) but
we also checked the performance of the ﬁtter on single b—tagged events where only one
of the b—jets in the event is loose tagged. Although the overall efﬁciency (selection
acceptance + btag efﬁciency) is higher for single tagged events the pairing purity
decreased from 83% to 61%. An increase in the purity for single tagged events is
achievable if we only accept events for which the leptonic b assigned by ﬁtter is the
tagged jet and throw the event out if it is not. Results from this study are summarized
in Table 4.3 where eb—tag and Cpairing in the table correspond to efﬁciencies for b-
tagging and the x2 cut respectively. The ﬁrst two rows show the results when we
require exactly 4 jets in the event while the last two rows show results with 4 or more
jets in the event. A “YES” in the second colmnn indicates that the jet assigned as the
leptonic b is checked for tagging and event is picked only if the jet passes the check.
Therefore, the corresponding efﬁciencies (€b—tag) for “YES“ rows are much lower. In
the end we decided to use double tagged events because, even after increasing the
purity of single tagged events, the overall CD2 of the single tagged events was still
lower than double tagged events as summarized in Table 4.4.

Apart from all of the above checks where we focused on the fraction of events for

which the Wb pairing was correct, we also examined events for which the leptonic b

84

 

 

 

 

 

 

 

 

 

 

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' so;
; —Wrongevems -
no- .
: 5-
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- :
. 15*.
m- :
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)-
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- 5L
I C
D- lilLLLLlLlllJllllllllllllllLlll “:1IllllllllllllI|llllllllll|llllll1
445-1415 0 0.5115 2 a .2 -1o 1 23.
El Phi

 

8
lIlllllllllllllllll'Ill

 

 

 

 

 

Figure 4.3. Comparison of jet kinematic variables for events where the leptonic b—jet is
matched to a leptonic b parton (right events) with those events where the leptonic b—jet is
not matched to a leptonic b parton (wrong events). The top two plots Show the eta and phi
of the jets in the event. The bottom two plots show the PT and ET of the jets.

85

 

 

# of jets Sethx tag cheek Cb—tag% Epairing% Ppairing% eD2
= 4 ND 14.9 62.4 62.4 0.04
= 4 YES 4.2 17.6 77.8 0.05
>2 4 NO 17.5 73.3 60.7 0.03
>2 4 YES 4.9 20.3 76.4 0.06

 

 

 

 

 

 

 

 

Table 4.3. Performance of the kinematic ﬁtter for single b—tagged events. The 602 in
the last column is the product of pairing efﬁciency and the square of pairing dilution D

(D = 213mm,-lng — 1).

 

 

 

single tagge double tagged
Ppairing (‘70) 60. 7 83.0
602 0.03 0.23

 

 

 

 

 

Table 4.4. Comparison of the performance of the Wb pairing method using single tagged
events with double tagged events. The tight version of the Sethx algorithm was used for
b—tagging.

assigrmient was incorrect, called “wrong events“. For these events we checked which
parton the leptonic b—jet matched to at the parton level. We expected it to be matched
to the hadronic b parton which is the b parton that is associated with the hadronically
decaying W most of the time. As expected we found that the leptonic b—jet matched
to the hadronic b parton 75.1% of the time, one of the light quarks 14.3% of the
time and did not match to any parton the remaining 10.6% of the time. In order
to understand why the leptonic b actually turns out to be the hadronic b most of
the time in these wrong events, we compared some kinematic variables between the
two b—jets. No convenient cut was found that could separate the leptonic b-jet from
the hadronic b—jet in any signiﬁcant way. In the pursuit of kinematic cuts that can
increase the pairing purity we also compared kinematic variables for the events where
the reconstructed leptonic b matches to a leptonic b parton with those where there is
no such match. No clear separation in any of the variables was observed as can be
seen Figure 4.3.

As a result of our optimization studies, we decided to use events where both b—jets

86

are tagged with the loose Sethx tagger. The choice of the leptonic and hadronic
b—jets are based on the assignments of the kinematic ﬁtter where we constrain the top
mass to be 17 5 :l: 3 GeV/c2 and use a cut of X2 < 9. The efﬁciency and purity found
are epairing = 0.562 :1: 0.003 and Ppairing = 0.830 2f: 0.003.

4.4 Flavor Tagging the b Jet at Production

Determining whether a b—jet is from a b quark (b) or an anti-b (b) quark is called
“ﬂavor tagging”. The name “ﬂavor tagging” comes from B physics because in B
mixing analyses ﬂavor tagging the BS or B0 meson at its production as well as its

decay is essential- The top charge case is different in two ways:

1. The environment for top physics is different, for example the b—jets from top decay
have larger PTS than b—jets from B hadron decay, and therefore the B physics tools may
not be applicable in top’s high PT environment.

2. We are. only interested in the b ﬂavor at production.

In this section the methods used by the CDF B physics group to tag the ﬂavor of the
B meson at production will be presented. We will then discuss if they are applicable
to b—jets from top decay and ﬁnally mention the method chosen for the top charge
analysis. The chapter ends with a discussion of how to improve the b ﬂavor tagging
method used for top analyses.

To better understand the b—tagging methods used by the CDF B mixing group,
let’s quickly review their event selection and purpose. They study bb events selected
by a single lepton trigger (See Figure 4.4). Both b—jets are tagged by Sethx or some
other tagging method. The event selection is such that the b—jet that includes the
trigger lepton is the “signal jet” for which the ﬂavor at production and at decay is
needed. Production ﬂavor tagger methods are used to determine the ﬂavor of the

signal B hadron at the time of its production. There are two approaches used to

87

 

 

 

Opposite-side b jet signal b jet
(includes triggered lepton)

Figure 4.4. bb events selected by a single lepton trigger are used for B mixing analyses. The
b—jet that includes the trigger lepton is the “signal jet” for which the ﬂavor at production
and at decay is needed.

construct a production ﬂavor tagger; one is a same-side ﬂavor tagger (SST) and the

other is an opposite-side ﬂavor ta.gger(OST).

4.4.1 Same-Side Tagging (SST)

A same—side tagger is applied on the “signal jet” and uses the correlations which exist
between the B meson in the jet and the charge of the ﬁrst charged particle in the
fragmentation chain. This correlation comes from the physics of the fragmentation
process, with the creation of light quark pairs out of the vacuum and formation of
new hadrons. As an example take the formation of B0 which happens when a dd pair
is created and the (7 couples with a b quark. See Figure 4.5. If the second created
quark pair is mi, a negatively charged pion (7F) is the next hadron. But if the second
created quark pair is dd, a no is the next hadron but is neutral so does not have any
tagging power. However if we keep going down the fragmentation chain, the ﬁrst
encountered charged hadron is again a 7r‘. In the case of a B0 (Figure 4.6), the
ﬁrst charged particle in the fragmentation chain is a 7r+. To summarize, the nearest
charged 7r indicates the ﬂavor of the BO meson (a 7r” indicates a B0; a 7r+ indicates
a BO). A BS meson is the same as BO except a kaon (K) is produced instead of

a pion(7r). CDF uses two different SST methods which are brieﬂy described in the

88

 

 

b._ b b-

_B° _B°
<” <"
d d

75' n"
U , _
(7’ d

\ <

d

115'
<”
U

Figure 4.5. Hagmentation chain for B”.

89

 

b b I:

(7"! d
‘\6 <3
(G

\a

 

<

Figure 4.6. Hagmentation chain for B”.

90

BO

11:0

1V

following subsections.

4.4.1.1 MINIMUM PTJQI METHOD

In SST methods one tries to ﬁnd the ﬁrst charged hadron in the fragmentation chain.
Because the charged hadrons from the fragmentation process at the time of production
have small impact parameters with respect to the primary vertex, they appear to come
from the primary vertex. One wants to distinguish between the primary vertex tracks
coming from the B production and the secondary vertex tracks that are coming from
the B hadron decay. The minimum PT,rel method relies on the fact that the particles
produced in the fragmentation chain have small momenta transverse (PT,re1) with
respect to the direction of the b quark momentum (as shown in Figure 4.7). In this
method, the track with the smallest PT,rel in a cone of radius 0.7 is chosen as the
ﬁrst charged particle in the fragmentation chain. Once we determine the ID of this
particle, meaning identifying if it is a K or 7r, we can deduce the ﬂavor of the‘B
meson. The B physics group at CDF uses the mean energy loss rate of a charged

particle in a material (dE/dat) for K -7r separation.

 

Figure 4.7. PT rel is the track momentum transverse to the b quark momentum.

91

4.4.1.2 VOTING SST METHOD

In some cases, the minimum PT,rel method chooses one of the daughters (decay prod—
ucts) of the B meson instead of the hadron from the fragmentation chain. If a track
from the B meson has a small impact parameter with respect to both the primary
and the secondary vertex, the track may look like it is coming from the primary ver-
tex. Voting SST method tries to distinguish primary tracks and secondary tracks by
summing the charges of all tracks in the b-jet cone instead of using a single track.
Each track’s charge is multiplied by a factor that depends on the probability of it

being a B daughter track.

4.4.2 Opposite Side Tagging (OST)

In order to study B hadron mixing, bb events are chosen where one of the the b-jets
includes the trigger lepton and is called the “signal b”. The methods described up
to this point were directly applied to the signal b—jet to ﬁnd its ﬂavor at production.
The second approach is to determine the ﬂavor of the other b and infer the ﬂavor of
the signal b at production by using the fact that the two b quarks are produced with
opposite ﬂavors. The next two subsections will describe the OST methods used at

CDF.

4.4.2.1 SOFT LEPTON TAGGING (SLT)

This method looks for a lepton from the semileptonic decay of the opposite side B
meson (b ——> EVgX). This method is called soft lepton tagging (SLT) because the
lepton from the semileptonic decay is softer (has lower PT) than the trigger lepton on
the signal b side. A b quark always decays to a negative lepton while a b quark always
decays to a positive lepton (b -—) X 6+, b ——> X 6') as shown in Figure 4.8. Therefore
the charge of the lepton tags the ﬂavor of the parent b. The SLT algorithm, which

was also devised for identifying b—jets from top decays, is used for ﬁnding the lepton

92

 

W+-

(Q=-1/3)

Figure 4.8. The charge of the charged lepton from a semileptonic b decay is correlated to

the ﬂavor of the b quark.

93

from the semileptonic b decay. The PT threshold for these leptons is PT > 2 GeV.
Similar requirements to the ones explained in Section 3.2.2 are imposed on these
low PT leptons. One main difference is that these leptons should be embedded in
a jet or non-isolated. The main problem with using the soft lepton tagged b—jets is
the presence of BdBd and BSBS mixing. Another problem is cascade decays where
the b decays to a charm which in turn decays to a lepton. (b —-> E -r X 8+ or
b —-+ c -—) X 6’). Both the mixing and cascade decays change the sign correlation

between the soft lepton and the parent I).

4.4.2.2 MOMENTUM WEIGHTED JET CHARGE

The Jet Charge (JQ) method uses the charge information of the tracks associated
with the bjet. This idea relies on the fact that the charges of the tracks in a heavy
ﬂavor jet are correlated to the charge of the initial heavy quark the jet is coming from.
The jet charge algoritlun does not take a direct sum of the charges of the tracks in
the jet, but instead weights each track by its momentum projected onto the jet axis

as it sums over the charges of the tracks as shown in Equation 4.7.

2L1 0103(1)“
E? (17151)“

where qi and pi in the JQ calculation are the charge and momentum of track 2'. re-

JQ=

 

(4.7)

spectively, and EL is the unit vector along the jet axis. The weight factor :1: is used to
emphasize different parts of the PT spectrum. In the case where :17 = 0, equal weight
is given to all tracks. A low z gives more weight to low momentum tracks while a
high 2: gives more weight to high momentum tracks. The jet charge is normalized to
1 after dividing by the weighted momentum sum.

From all the ﬂavor tagging tools presented above, we concentrated on the OST
algorithms and in the end chose the weighted jet charge (JQ) algorithm as the b
ﬂavor tagger for the top charge measurement. Note that for B mixing analyses OST

algorithms are applied on the opposite side jet to determine the ﬂavor of the signal

04

jet. In our case. we have no such distinction on our bjets. We directly apply the
algorithm on the b—jet to get its ﬂavor. The OST (SLT and momentum weighted JQ)
algorithms are applicable to b—jets from top decay while the SST (PT,rel and Voting
SST) algorithms are much harder to apply. To be able to apply the SST algorithms we
need to explicitly know the type of B hadron. Even if we knew this, the particle ID of
the ﬁrst charged particle in the fragmentation chain is also needed. The dE/dx used
for this purpose will not work for top physics due to the decrease in the resolution
of dE/dx at large momenta. What can we gain from the SST studies then? We
can deﬁnitely make use of the main idea of separating primary tracks that are more
likely coming from the fragmentation chain than from secondary vertex tracks that
are coming from the B hadron decay. Turning to the OST algorithms, let’s ﬁrst look
at the soft lepton tagging algorithm (SLT). A drawback of using the SLT is the low
branching fraction for semileptonic B decays. The SLT method is also not ideal in a
high occupancy jet environment due to the difﬁculty of reconstructing low momentum
leptons. The SLT has much lower efﬁciency compared to the jet charge algorithm.
One other complication is that the SLT purity has to be corrected for cascade decays
(b -—> 5 —-> X 3+ or b —-> c —+ X F") and'the B ﬂavor mixing rate. A quick study was
done using SLT on top MC samples applying different PT and vertex cuts and the
purity of getting the correct b ﬂavor is optimized up to 70%. Using the momentum
weighted jet charge algorithm, we get a similar purity as in SLT but much higher

efﬁciency, therefore a higher €D2 value as will be presented in the next section.

4.5 Optimization of the Momentum Weighted Jet Charge

Algorithm for the Top Charge Measurement

As mentioned above, we chose the momentum weighted jet charge (J Q) algorithm to

tag the ﬂavor of b—jets from top decays. This section presents the studies performed

95

on lepton+jets events from top MC samples to acquire the highest purity (P JQ) and
more importantly, the highest 6.02 where e is the efﬁciency of the jet charge algorithm
(CJQ) and the purity (P JQ = (0+ 1) / 2) is how often the algorithm assigns the correct
sign for a b—jet (+ for b and - for b). We declare a jet as a b—jet if the calculated jet

charge using Equation 4.7 is negative and as a b—jet if it is positive.

0.7

 

Purity

0.68

0.66

0.64

0.62

0.6

5

le—ITIIIIIII—[ITTIITIIITIIIII

§

 

 

 

OT
3
O
L
O
03
53

Figure 4.9. Jet charge purity obtained using different weight factors from 0.1 to 1.

The ﬁrst attempt to optimize J Q was by varying the weight factor (1;) in Equa-
tion 4.7. Figure 4.9 shows how the purity changes as x increases from 0.1 to 1. It is
ﬂat between 0.4 and 0.8. So we chose :1: = 0.5 and used it throughout the following
studies. This choice gives equal weight to low and high momentum tracks. Other
than implementing the jet charge algorithm using different weight factors, we also
tried using the transverse momenta (PT) of the tracks in the jet, instead of their total
momenta (P). No signiﬁcant improvement in 6D2 was observed. We further tried to

increase eD2 by imposing cuts on the quality and the number of tracks used in the.

96

jet charge algorithm. Certain requirements on the number of tracks and the tracks’
momenta increased eD2 but were not used due to a bias found in the jet charge algo-
rithm between b and b—jets (The J Q purity obtained using only b—jets was found to be
different from the purity obtained using only b- jets. Various studies are documented
- in Appendix A). We tried to eliminate the charge bias by trying different PT and
impact parameter cuts on the tracks in the jet. The ﬁnal selection requirements on

the tracks, which reduces the charge bias, that were used for JQ are given below:

Tracks must be in the silicon detector (Sethx tracks)

Jet cone size < 0.4

Only good tracks with |dO| < 0.15 cm

Tracks with PT > 1.5 GeV/c

Number of tracks > 1

Note that we require the jet to have more than one track since the probability of a
single track to carry the jet charge information is small. This requirement decreased
the efﬁciency only by 2%. The jet charge distributions obtained from loose Sethx b-
tagged jets in top MC using the above selection requirements are shown in Figure 4.10.
A jet is said to be a b—jet if the calculated J Q is negative and a b—jet if it is positive.

Once we know the ﬂavor of the b and which W boson it is associated with, we
know the charge of the top quark they came from. Even though in the lepton+jets
channel, there is only one lepton and thus only one side of the event where we can
infer the W charge from the lepton, we can also apply the jet charge algorithm to the
b—jet associated with the hadronically decaying W. Three possibilities were studied to
see if the value of 602 could be improved. As the ﬁrst possibility, we tried accepting
events where the two b-jets (the two tagged jets) were required to have the opposite

sign (OS) from each other, meaning a b and b. The resulting purity was 70%, but the

97

 

50° — b Jet charge

400 — bbar Jet charge

300

200

100

r

Illllllllllllllllllllllll
u . y .

 

 

 

 

 

 

.c:

A

Figure 4.10. Jet charge distributions for b and b jets that are tagged using the loose
Sethx algorithm on the top MC (Altop = 175 GeV/c2) sample. Note that entries at point
+1 and —1 are two—track jets where both tracks have. the same charge sign.

98

efﬁciency was reduced by z 50%. The second option was to also accept events where
both jets had the same sign. The sign assignment was decided upon by comparing
the two jet charge values and assuming the jet charge algorithm gave the correct
result if the leptonic b—jet charge was greater (smaller) than that of the other jet
and was matched to a generator level b (b). We dropped this option because of its
low purity of 52%. The last option was to use all the events, but each event would
provide two separate top charge measurements. One corresponds to the leptonic side
and the other is obtained from the hadronic side, where the assumption is that the
hadronic W charge is the opposite of the one assigned to the leptonically decaying
W. In this way, we can also get a measurement from the hadronic side of the event,
depending on the charge of the b—jet assigned to the hadronically decaying W. The
same purity is obtained for the leptonic and hadronic side (0.610 :1: 0.003 for leptonic
vs 0.606 :1: 0.003 for hadronic) and the efﬁciency increases by a factor of 2.

 

 

 

 

 

 

 

method €JQ% P JQ% (evts. passed X?) eD2
opposite sign (OS) 50.0 :t 0.4 70.9 :l: 0.5 0.09
using pairs 98.00 :l: 0.07 60.8 :l: 0.3 0.06

 

Table 4.5. Performance of the jet charge algorithm on b—jets tagged by the loose Sethx
algorithm in the top MC sample (Mtop = 175 GeV/c2). €JQ and PJQ are the efﬁciency and
purity for J Q respectively. The ﬁrst row is for lepton+jets events where we require both
b—jets to have opposite sign. The second row is when we check the J Q performance for the
leptonic and hadronic sides separately. The purity results are the average of both sides.

Among the three options presented above, we concentrated on the ﬁrst and last
options. Table 4.5 helps to understand why we picked the last option where we use
both sides of the tt- event and make two separate top charge measurements per event.
By using pairs we get an 6D2 2 0.06. A high €D2 means better performance, so
one may tend to think the ﬁrst option (both b—jets in the event are required to have
opposite sign) that gives €D2 = 0.09 is better. However to correctly compare the 6D2
values one must realize the 0.06 value is per Wb pair but when using both sides of

the event this must be multiplied by two so we should compare 602 = 0.09 for OS to

99

602 : 0.12 for using pairs.

As a result of the optimization studies done. with the weighted jet charge algorithm,
we decided to make two separate top charge measurements per tt— event applying the
J Q algorithm on both the leptonic and hadronic b—jets. The weight factor in the J Q
calculation was chosen to be 0.5 and the sum is done over the tracks associated with
the jet that are deﬁned as good tracks by the tight Sethx algorithm and have a PT
> 1.5 GeV/c. With these selections, we acquired a jet charge efﬁciency of 98% and
purity of 61% with a corresponding CD2 of 0.06.

Determining the ﬂavor of the b-jets in a top event is the hardest and most chal-
lenging part of the top charge analysis. The purity of the method chosen for ﬂavor
tagging the b—jets is what drives the sensitivity of the analysis. To better visualize
this, let’s look at Figure 4.11. The ﬁgure shows the distributions for the fraction
of events (f+) that look like Standard Model assuming different purities. If the jet
charge purity decreases from 0.69 to 0.60 and its uncertainty doubles, the separation
between f+ distributions for Standard Model (SM) and Exotic model (XM) dimin—
ishes considerably. There are a couple of ideas we thought of, summarized in the next

section, to improve the b ﬂavor tagging.

4.6 b Flavor Tagging Improvements

As shown in Figure 4.11 the top charge measurement is very sensitive to the value of
the jet charge purity (P JQ) and its uncertainty so knowing the P JQ with precision
is crucial for the top charge analysis. One promising way to improve the top charge
measurement would be to improve the jet charge purity. One way to do this is to
improve the momentum weighted jet charge algorithm. Remember that we use all the
tracks in the jet cone that pass certain PT and impact parameter cuts. However, only
tracks from the fragmentation chain carry b ﬂavor information. So a study, similar

to the “Voting SST method” explained in 4.4.1, can be done on bjets from the top

I 00

 

 

 

 

 

-0.5 0 0.5 1 1.5

 

PJQ=0.691-0.1

Figure 4.11. f+ (the fraction of events that look like SM) distributions from pseudo-
experiments for SM and XM generated using different jet charge purity (PJQ). If SM is
true f+ should be 1, if the exotic case is true, f+ should be 0. Refer to chapter 10 for the
explanation of pseudo—experiments and how we generate these plots.

decay to separate primary vertex tracks from secondary vertex tracks. The optimal
way to ﬂavor tag b—jets however, would be to combine all possible b ﬂavor tagging
methods like soft lepton tagging, weighted jet charge algorithm methods and Voting
SST in a neural net 1.

For this thesis the strategy chosen to measure the top charge is to count events
that look like the Standard Model and compare it with the number of events that
look like the exotic quark model. We could use the information contained in the
shape of the jet charge distributions. In other words, we can compare the data
and MC JQ distributions and perform a ﬁt. However, this approach involves some
assumptions, such as believing the JQ distributions from MC represent the shape

for the backgrounds accurately. A less shape dependent way to use the JQ shape

 

1A neural network is a way of combining many variables into one single variable using a. model
of a biological neuron [33].

101

information is to change our criteria for declaring a jet a b or a 6. Remember that we
claim a jet corresponds to a b if the calculated jet charge is negative and to a b if it
is positive. However, a jet with a jet charge 0.7 is more likely to be a b jet than a jet
with a charge of 0.006. In other words, the jet charge purity is different in different
bins. So instead of using one JQ value to decide if the jet is b or b, we could divide

the J Q distribution into several bins and calculate the jet charge purity for each bin.

102

CHAPTER 5

Calibration of Flavor Tagging in Data

Most institutions demand unqualified faith; but the
institution of science makes skepticism a virtue.
Robert K. Merton (1910-2003), an American sociologist.

5. 1 Introduction

The biggest challenge in measuring the top charge is to tag the ﬂavor of the b—jets
in top events. In the previous chapter we introduced the jet charge (JQ) algorithm
to identify the b—jets as b or b (ﬂavor tag) in a high PT environment. Using tt— MC
we matched the b—jets to the b—partons and the number of b—jets for which the JQ
algorithm gave the correct charge sign over the total number of b—jets was deﬁned as
our jet charge purity. Calculating a jet’s charge (ﬂavor) is sensitive to the details of
the fragmentation process, thus results obtained from the MC are not guaranteed to
perfectly match the results in data. Therefore, we have also studied the performance
of the jet charge algorithm directly in the data.

For the purpose of this study, we need a data sample that is enriched in b—jets. A
subset of the dijet data sample can be enriched in bb pairs by b—tagging the jets and
doing a careful event selection. In these events, one of the jets is identiﬁed by requiring
a muon, coming from the semileptonic decay of a b, to be within the jet. This jet is

referred to as the “muon-jet”. Another jet that is back-to-back (180O away in 05) from

103

 

Figure 5.1. The back-to—back bb events were chosen from the dijet data sample where one
of the b—jets decays semileptonically to a muon (n). The jet charge algorithm was applied
to the away-jet which is expected to have an opposite charge compared to the muon charge.

the muon—jet is required and referred to as the “away-jet” as shown in Figure 5.1.
If the muon-jet and away—jet are indeed from bb, they should have opposite charges.
The charge of the muon-jet is taken to have the same charge as the muon. The
jet charge algorithm is then applied to the away-jet which is expected to have the
opposite sign compared to the charge of the muon. The observed purity (Pobs) can
then be determined as the number of pairs with opposite sign (OS) correlation over
the total number of jet pairs.

The difﬁculty in this method is the determination of the fraction of events that
are really from bb (fbb) among those events that survive the selection requirements.
After selection we may still have contamination from muons that are produced by
charm decays or are fakes. In addition, a light quark can be incorrectly assigned as
the away-jet. In order to determine the heavy ﬂavor content of the selected events
in the dijet data we have identiﬁed two variables that are powerful in discriminating

between bottom quark jets and charm or light quark jets. These variables are the

104

transverse momentum (1911,01) of the muon relative to the muon-jet axis and the
invariant mass of the secondary vertex (ll/WK) on the b-tagged away-jets. Figure 5.1
shows the PT,rel and Mvtx distributions for b, c and light quark jets from dijet MC.

This section is followed by a description of the data and MC samples used for
this study. Section 5.3 presents the event selection, while the method is described in
detail in Section 5.4. Results are in Section 5.5. Note that the measurement is done
with bb events with an average ET of 30 GeV. However, the b-jets coming from top
decays have ETs in the range from 60 GeV up to 150 GeV. The extrapolation of the
R ;Q result obtained from dijet data to higher ET jets is the largest systematic and
is covered in Section 5.6. The rest of the systematic uncertainties on P JQ and the

conclusions can be found in Sections 5.7 and 5.8 respectively.

5.2 Data and MC Samples

For this study we have used muon-enriched data samples. In addition several dijet MC
samples, which differed by the generated jet PT threshold, and a muon-enriched MC

sample were also used. All of the samples used for this study are listed in Table 5.1.

 

Description of samples used
Data sample
CMUP muon PT > 8
Pythia dijet MC samples
with muon PT > 7 GeV/c, |n| < 0.8
jet PT > 15 GeV/c
jet PT > 18 GeV/c
jet PT > 40 GeV/c
jet PT > 60 GeV/c
jet PT > 90 GeV/c

 

 

 

 

 

Table 5.1. Data and MC samples used for the. calibration of the jet charge algorithm.

105

 

III

40<away ET<50
0'3 — bottom
0-25 ----- charm

— light

 

 

  

mfg‘TlT'ﬁrl’T—I—WITWTII

 

 

 

 

 

0.25
0.2 4O<ET<5O
0.15 ' ' ----- charm

 
 

.......... light

  

0.1

 

0.05

 

TIIIIIIUIIIIIITFII'ITTT
-e

if

 

 

J l

D

Figure 5.2. The PT,rel and vertex mass (Alvtx) of b, c and light jets from dijet MC.

106

0.4

 

 

 

 

 

 

 

 

 

0.35 i
E r— 40<away ET<50
0'3;— — bottom
0-253 ----- charm
0.22- — light
0.15 E:—
0.1——
0.05 t—i .
°6‘ 'W‘E
Ptrel
0.25
0.2 4O<ET<50
0.15

T ----- charm

 

0.1

 

0.05

llllllIIITIIIllI—TIIIIIIT

 

 

 

 

 

o0

 

Figure 5.2. The PTrel and vertex mass (illvtx) of b, c and light jets from dijet MC.

106

5.3 Event Selection

In this study the events were required to have only two high ET jets plus a muon.
The muon must be a CMUP muon matched to a jet of cone size 0.4 (the muon-jet)
and the second jet (away-jet) is required to be separated in q) from the muon-jet by
more than 2 radians. The muon-jet direction is corrected due to the shift caused
by the presence of a muon. Equation 5.1 expresses the corrected momentum vector

(Peon) where 133“ and 13'“ are the three momentum vector of the muon—jet and muon

respectively.

.. _. 2 ..
Pcorr = Rjet + (1 —' '17“) Pp (5-1)
lpul

All of the requirements applied to the muon and away-jet are given below:
0 Muon track PT > 9 GeV/c
e Muon track |z0| < 60.0 cm
0 Muon CMU stub (drl < 3.0 cm
0 Muon CMP stub [de < 3.0 cm
0 Distance to primary vertex |20 — Zvertexl < 5 cm
0 Muon track isolation> 0.1
o Muon track must pass through every layer of the SVXII detector
0 Muon jet ET > 9 GeV
0 Away jet ET > 15 GeV
0 Away jet |7)| <15

0 Away jet must have at least two good secondary vertex tracks.

107

In order to enhance the b content of the sample, we require that the away—jet is tagged
by the loose Sethx tagger and the muon-jet is tagged by the tight Sethx tagger.
All of these criteria construct a dijet sample that has a high fraction of events coming
from bb. However, as can be seen in Table 5.2, when we study the MC we still have
contamination from other types of events. In the table events are classiﬁed depending
on the result of matching the jets to partons, where n and AJ implies “muon—jet”
and “away-jet” respectively. For example a = b, AJ 2 c in the ﬁrst column means

the muon jet is coming from a b quark and the away-jet is coming from a c quark.

 

 

 

Cases pretagged(%) tagged(%)

bb )u = b, AJ 2 b 7 86.8
bc a = b, AJ = c 2.4 2.8
bl p = b, AJ 2 nonb, none 5.4 6.6
cc uzc, AJ=c 8.4 1.7
cb n = 0, AJ 2 b 2.2 0.4
cl )1 = c, AJ = nonb, nonc 3.2 0.8
fq nzfakesl Asz/c/l 1 1

 

 

 

 

 

Table 5.2. Classiﬁcation of events in the heavy ﬂavor enriched MC. The muon (,u) and
away-jets (AJ) were matched to partons within a cone of 0.4 and classiﬁed accordingly for
different cases. The fakes category includes those events where the reconstructed muon did
not match a generator level muon or those where, although there is a matched muon, the
jet is not from a b or c quark. The “Pretagged” column corresponds to the fraction of each
case when only the away-jet is b-tagged (loose) and the “tagged” column to the case where
the muon-jet is also b—tagged (tight).

Of special interest are the CE events which also have an expected opposite sign
correlation between the muon charge and away- jet charge like bb events. Even though
charm hadrons have shorter decay lengths, smaller impact parameters and decay
products with lower PT compared to the ones from B hadrons, they can still pass
our stringent selection cuts due to their similar event topology to bb events. The
performance of the jet charge algorithm is different for c—jets than b—jets. It. would
be beneﬁcial to know the purity of the jet charge algorithm for c—jets (PC). However
we can not measure PC directly from data since we do not have a method to identify

c—jets in the detector. Luckily, the cf? acceptance is greatly reduced by b—tagging the

108

muon—jet as can be seen in Table 5.2 for the cc case. There is no charge correlation
between the two jets for the other cases such as cb, cq but their presence dilutes the

purity. The dilution to the observed purity will be discussed in the next section.

5.4 Method

By selecting events with a pair of jets, one containing a CMUP muon and the other
being located opposite to it in (b, we can now calculate the JQ purity. Due to the
charge correlation between the muon and the away- jet in bb events we expect the
event to have an opposite sign (OS) correlation, but because our JQ algorithm is
not perfect some events will have the wrong assignment and give a same sign (SS)

correlation. The observed purity is deﬁned as:

 

N
05 (5.2)
Nos + Nss

Pobs =
where. N03 and N S 3 correspond to the number of opposite or same Sign events respec—
tively. However, this equation needs a few corrections. First, the muon contained in
the muon-jet, may not come directly from a b semileptonic decay, but from a cascade
decay (b —+ c ——> a). This would change the charge of the muon and a SS event would
be the correct ﬂavor assignment. In addition a SS event is expected if B mixing oc-
curs. Besides these effects the data sample is not necessarily allrbb events, as already
shown in Table 5.2. These “background” events weaken the purity, since no charge
correlation is expected (the special case of CE was discussed in the previous section).

Taking all these into consideration Equation 5.2 is modiﬁed and the observed purity,

Pobs, is deﬁned as:

Pobs = fb5(1- fcasmix)PJQ + f1;(3fcasmix(1 _ PJQ) + fccpc + (1 — be ‘l' fcc)0‘5 (5-3)

where P JQ is the purity we actually want to measure, that is, the performance of

the J Q algorithm on b—jets. We will refer to it as the “real purity” from now on and

109

this is the purity we want to compare with P JQ obtained from MC in the previous
chapter. Keep in mind that the observed purity is the fraction of 03 events over
total events (Equation 5.2). Then one might think that since cc and bb are the only
OS events, Pobs should be equal to be - Pb + fw- - PC where fbb and for: are the
fraction of bb and c5 events respectively and PC is the jet charge purity for charm jets.
However as we mentioned before be has to be corrected by the fraction of events that
undergo cascade decays or B mixing (fcasmix) that change the OS correlation to a SS
correlation. So the ﬁrst term in Equation 5.2 is the fraction of bb events that do not
undergo cascade decays or B mixing times the purity of getting the b charge correct.
In other words the purity of getting OS correlation for b—jets. The second term is the
fraction of bb events that do mix or cascade decay times the purity of getting the b
charge incorrect. Note that for these events if the calculated b charge is correct the
two b—jets will have a SS correlation, but we want the contribution to the OS events
so we must multiply the second term by the purity of getting the b charge incorrect
or 1 — P JQ. The third term is the fraction of CF: events times the purity of getting
the c quark’s charge correct, but remember that we do not have a way to determine
PC. Since the fraction of 0 events is small after our event selection we assume there
is no correlation between the charges of the two jets and assign a purity of 0.5 for
PC. Finally the last term is the fraction of the events that do not have any charge
correlation between the muon and away jet (all cases in Table 5.2 except bb and CE)

times the purity of getting an opposite sign correlation for these events.

5.4.1 Measuring the bb fraction

The problem now turns to measuring the bb fraction (fbb) in the data sample. In
order to extract the b content on the muon side, a previous CDF study [34] used the
PT,rel (diagram in Figure 5.3) distribution of the muon with respect to the jet axis

to ﬁt the data. We have chosen the same method and obtained PT,rel distributions

110

for b and c quarks from the heavy ﬂavor enriched MC sample and for light quark and
gluon jets using the dijet MC sample. The plots are shown in Figure 5.4.1 for various
away-jet ET ranges. Although some dependence on the away—jet ET is seen for the

heavy ﬂavor, there is none for the light. case.

i
‘.

 

Figure 5.3. PT rel is the track momentum transverse to the jet axis.

For the away-jet side, we use a variable that has been shown to be a powerful
discriminator of b—jets from charm and light jets in a previous CDF analysis [35]. This
variable is the invariant mass of the secondary vertex (Mvtx) found in the jet. To
calculate Mm, we start with the tracks which were assigned to the secondary vertex
by Sethx algorithm. The momentum three—vector measured by COT is turned into
four-momenta by assuming that each track is a charged pion (m7r = 0.1396 GeV/c2)
to compute an energy (E,) for track 0'. The four-momenta are then added up to get
the vertex four-momentum, pl).

A/IE... = p" -p,.. = (2 En? — (Zn)? (5.4)
' 2'

7.

Distributions for b, c and light quarks were obtained from the dijet MC, where
the jets have to pass the same cuts as listed in Section 5.3. In the case of light jets,
only events where no heavy ﬂavor was present were used. Figure 5.4.1 shows the
Mvtx distributions for various away-jet ET ranges. To produce the Mvtx plots we
used a mixture-of MC samples with different jet PT thresholds. Instead of trying
to reweight the MC to obtain the correct jet ET spectrum or trust the heavy ﬂavor

enriched MC to reproduce it (especially at high ET where there is a lack of statistics

111

 

 

 

 

 

 

   
   
    

 

 

 

 

 

 

 

 

 

 

0.25_
E bottom
02: .t':
: "'j [___ —20<away ET<35
o.15~ ““ L ---50<away ET<75
0.1]
035 a ti" :j:'_'§......-..-
------ 1..........,
0 4 L ] gj+, 1 . """ km
a 1 2 3 4 5
Ptrel
0.4
0.35 charm
0.3
—20<away ET<35
0-25 ~~50<away ET<75
0.2 .. 90<away ET
0.15
0.1_
0353 "Ms-"Mm?
. 1 M 1
co 1 2 3 4 5
Ptrel
0.4
0.35 light .
0.3
—20<away ET<35
0-25 w50<away ET<75
0.2 w90<away ET
0.15 -
0'1.“
0.05}
co L ' 1 t 2 3 4 5

Figure 5.4. PT rel distributions for bottom (top plot), charm (middle plot) and light
quark/gluon (bottom plot) muon-jets for various away-jet ET ranges. The distributions

were obtained from heavy ﬂavor enriched MC for bottom and charm jets and from dijet
MC for light jets.

112

and the mistag rate is larger), we decided to perform the analysis as a function of ET
with the assumption that the distributions are ET independent in each ET range.
This is also practical, since we need to study the ET dependence of the purity to be

able to extrapolate to the high ET b—jets coming from top decays.

5.4.1.1 FITTING PROCEDURE

The fraction of b quarks in the muon-jet (away-jet) was determined by ﬁtting the
PT,rel (Mm) distribution from the dijet data sample to MC distributions from the
different quark ﬂavors. This fraction was measured as a function of the away-jet
ET for the various ET bins given in Table 5.3. The distributions for b and c jets
were taken from heavy ﬂavor enriched dijet MC while generic dijet MC samples were
used for the light jets. To illustrate this procedure, Figure 5.4.1.1 shows the ﬁts, for
one away-jet ET bin, to PT,rel for the muon-jet side and Mvtx for the away-jet side.
In the PT,rel case we use only b and c distributions because the PT,rel spectrum for
charm and light quarks are similar and the ﬁtter can not distinguish between them
(see Figure 5.1). For the Mvtx ﬁt we use separate distributions for the b, c and light
quarks. The b—fraction from the PT,rel ﬁt shown in Figure 5.4.1.1 is 89.5 :1: 2.7%
indicating that for R: 10% of the events the muon-jet is not from a b—jet. The Mm

result is 83.0 :t 2.6% indicating that for 17% of the events the away-jet is not a b—jet.

 

En EI range (GeV)
1st 10 3 ET 3 20
2nd 20 5 ET 3 25
3rd 25 5 ET 5 30
4rd 30 5 ET 3 40
5th 40 3 ET 3 50
6th 50 g ET 3 60
7th 60 3 ET 3 70
8th 70 3 ET 3 90
9th 90 3 ET 5 120

 

 

 

 

 

Table 5.3. The nine different away—jet ET bins used for the PT rel and Mvtx ﬁts.

113

 

- bottom
0'25? — 20< ET<35

0.2E """ .-... ..... 50<ET<75

o.15_ “““““ 90<ET

F
t .

0.1[_t t..--
g

0.05 r

.......

 

lllllllllllllLlJllLlllllllllllllllllll-:?-""o':”:':':=1
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Mm

 

 

 

 

 

0.4
0-35 charm
— 20< ET<35
0.3
0.25 .---- ..... 50<ET<75
0.2 "'1 m... 90< ET
0.1 5
0.1 _ ':::'::;
095} 22:23...- .,
Um”: t-n-h- - i

 

 

 

E Thrillinduuliu. LL“
00 0.5 11.5 2 2.5 3 3.5 4 4.5 5

"w:

 

0.4
0-35 light
0.3
0.25
0.2
0.1 5
0.1
0.05

— 20<ET<35
----- 50< ET<75
....._. 90<ET

   

Inter-w-
.....

«nu-n.

 

 

00 0.5 1 1.5 2 2.5 3.35%; 4.5 s

"m

Figure 5.5. Mth distributions for bottom (top plot), charm (middle plot) and light
quark/ gluon (bottom plot) away~jets obtained from the dijet. MC for various away-jet ETs.

114

 

    
    
  
 

1000 40<away ET<50
- b
- c
+ prediction
—-— data

if = 1.32

  
    
   
  
 

 

 

40<ET<50

- b

- c

- light
+prediction
+data

x2 = 1.42

  

 

Figure 5.6. The top plot is the PT.rel ﬁt obtained by ﬁtting the data to the b and c
quark distributions from MC for the events with away-jets in the ET range of 40—50 GeV.
The bottom plot is the Mvtx ﬁt obtained by ﬁtting the data to the b, c and light quark
distributions from MC for away—jets with ETs between 40—50 GeV. The complete ﬁt is done
for nine different away-jet ET bins.

115

fraction of dlfferent cases

 

 

 

muon jet away jet
From PTJelf From Mvtx ﬁt
cc, cb.c|. fq t} 10.5% 17%
%
”79
bb \caSe
b)(: 89. 5% 83V
0
' bé
_.L_-,-._th_.__._ ,. v__r

 

 

 

Upper limit for b5 fraction = 83%
Lower limit for bb fraction = 83% -10.5%=72.5%
used bb fraction(average of two limits): 77.8:5.9%

Figure 5.7. The fraction of different cases obtained using the PT,rel and Mvtx ﬁts in the
away-jet ET bin of 40—50 GeV. The lower limit for the ()5 fraction is 72.5% if all of the non—b
cases on the muon side are matched to the b—jets on the away side. The upper limit for the
bb fraction is 83% if all of the muon-jets are b—jets and matched to b—jets on the away side.

116

In order to get the bb fraction, we need to combine the results from the ﬁts for the
b fraction in the muon-jet (89.5 i 2.7%) with the result in the away-jet (83.0 :1: 2.6%).
If we assume that a muon—jet is always from a b then the maximum bb fraction is 83%
becase the away-jet is a b 83% of the time. This is an upper limit since the muon-jet
is not a b 10.5% of the time. The other extreme occurs when the away-jet which is a
b (83%) is always matched to a non-b muon-jet (10.5%). SO the lower limit on the bb
fraction is 83% — 10.5% = 72.5% (see Figure 5.7). The bb fraction is then calculated
as the average of the upper and lower limits giving 77.8 :l: 5.9%. The uncertainty of
5.9 is calculated as the quadrature sum of 5.3, which is the difference between the
average and upper / lower values for beI and the uncertainties from the ﬁts. Note that
77.8 :1: 5.9% is the be result for the away-jet ET bin of 40 < ET < 50 GeV. We

repeated the same procedure for the remaining eight ET bins listed in Table 5.3.

5.4.1.2 MIXING AND CASCADE CORRECTIONS

As mentioned before, the muons in our data sample are not only produced from
b -—+ a but also from mechanisms like b —-> c —> a. The latter case will change the
expected muon charge and the correlation with the away—jet charge is of the same
sign, instead Of the opposite sign. The same effect is obtained if B mixing occurs. We
have measured the amount of cascade decays and B mixing from MC samples that
include both of these effects. To include all possible cases we have deﬁned feasmix

used in Equation 5.3 as:

fcasmix : feasOS(1 — fmix) + (1 — fcasOS)fmix (5'5)

where [C3503 (1 — fcasOS) includes only the b —> c —> n (b —+ 5 —> a) case and is
measured over a MC sample of non-mixing events. fmix is the fraction of B mixing.
The ﬁrst term is for the case when the cascade decay has OS and there is no mixing.
The second term is the case where the cascade decay does not result in OS but mixing

occurs. Both fcasOS and fmix were measured from MC by matching reconstructed

117

B hadrons to their generator level informI-Ition. The. measured values for feasOS and
fmix in heavy ﬂavor enriched dijet MC when the away-jet ET < 50 GeV are fcaSQs =
0.109 :t 0.005 and fmix = 0.154 :1: 0.005. In the high ET region when the away-jet has
ET > 50 GeV, the values for fcaSOS and fm-1X are fcasOS = 0.165 :1: 0.017 and fmix =
0.147 :l: 0.015. Remember these values are for the cascade and B mixing fractions in
a heavy ﬂavor enriched dijet MC sample. These fractions may change depending on
how the MC models the B production rates and the semileptonic branching ratios.
Therefore we also measured fcasOS and fmix from generic dijet MC and conﬁrmed
that they are consistent with the values obtained from the heavy ﬂavor enriched dijet
MC. In the end the fcasmix we obtained using Equation 5.5 was 0.229 :1: 0.029 for the
low ET region and 0.263 :l: 0.031 for the high ET region.

1.2

 

 

1_1 , ,1. Dijet data 1

  

b fraction on [.1 side

0.7

IIII[IIIIIIIIIIIIIITIIIIIIIIIIIIII

 

 

i I l I l I L L I I I I I I I I I
20 40 60 80 100 120
away let ET

1

 

Figure 5.8. The b fraction on the muon side as a function of the away-jet. E T obtained by
ﬁtting the PT rel spectrum in a muon-enriched dijet data sample using 1 fb ‘1 of data.

118

 

do

1.2

IOI'I OI'I away 8|

 

il‘ bljet liata j

- I
o... ~ Ic-uo - ----. ..... ..o....u-uqu-.uo-n-u-o-y-n-oos-unu'u - --..- cucu- o...-
a u I

 

b fract

0.4

 

0.2

ﬁf!TII!III!IFI!III!IIIT

 

 

M

 

OLIIIIIIIIIIIIIIII

l I I I I L
20 40 60 80 100 120

Figure 5.9. The b fraction on the away—jet side as a function of its E T in a muon-enriched
dijet data Obtained by ﬁtting its Mvtx spectrum.

119

5.5 Results

By following the previously described procedure we ﬁt the PT,rel spectrum of the
muon-jet for a muon-enriched dijet data sample and found the b fraction to be close
to 92% when the away-jet has ET % 20 GeV. As presented in Figure 5.8, the b fraction
decreases to R: 85% at high away-jet ET values, where the probability Of ﬁnding fake
muons increases. The result of ﬁtting the secondary vertex mass of the away-jet to
ﬁnd the b fraction on the away-jet side is shown in Figure 5.9 for the same data
sample. In this case the b fraction decreases from 90% to 40% as the away—jet ET
increases from 20 to 100 GeV due to the fact that the probability of tagging a light

jet as a b—jet increases with jet energy. We combined the b fraction on the muon side

 

1.4

1.2

b5 fraction

 

0:4

 

0.2

 

 

 

WIIIII!III[I—TITWI!IIT!III!I

I I I I I I I I I J

j. I I I
20 40 so so 1 oo

J_I I I I I I I I
120

E,

Figure 5.10. Fraction of bb events in a muon-enriched dijet data sample as a function of
the away-jet ET for data (circles) and MC (triangles).

with the b fraction on the away-jet side as described in Section 5.4.1.1 and obtained

the bb fraction (fbb) for each away— jet ET bin as shown in Figure 5.10. The bb fraction

120

from heavy ﬂavor enriched dijet MC is also shown in this ﬁgure and although the drop
is not as large as for the data it is still present. In addition to the fbb fraction we
also need the observed purity (Pobs) before we can calculate the real purity of the jet
charge algorithm. Using Equation 5.2 we calculated Pobs for each away—jet ET bin.
The results are shown in Figure 5.11. A decreasing trend in Pobs is seen, similar to

be, because lower values of fbb dilute the purity of the jet charge algorithm.

 

: : -

§|A ' Bi‘j'éiliéié’jw

 

We

  

Observed Purity
O
is

 

S

 

33

u - l
o..~...-o.-----..--..........uo-..--o----------n...-...----..- - -.--. ..... p...- o
- e u

E

.u-n-En-u-I- III-I Inn-II -o-o-"- non-onc-nuonnnuuo- III?-....I v-nnuu-uca-u----"-----.--on-cuucu...-aunt--young-cu...noon-gnuusco-ou-Ina-

 

 

0|
IlllIIIIIIIIITIITII]ITIIIIIIIIIIIIIITTI

I ILMMILJILII

i I
20 40 60 80 10 120

1=_r

 

O

b.
-
-
—
y—
p-
h
_
_
_
b

Figure 5.11. The measured purity (Pobs) calculated on jets in a muon—enriched dijet data

sample as a function of the away-jet ET .

The real purity of the JQ algorithm (P JQ) from data was obtained by inserting
the Pobs and bb fraction values shown in Figures 5.10 and 5.11 into Equation 5.3. The
resulting P JQ distribution for data and MC are shown in Figure 5.12. For the P JQ
from MC we calculated the purity using two different MC samples (generic dijet and
heavy ﬂavor enriched dijet) because our data are actually somewhere between these

two extremes. The P JQ values (red triangles) for MC in Figure 5.12 are the weighted

121

average between these two MCs. Figure 5.13 shows the calculated P JQ for the two
MC samples separately. In addition, in the MC samples the charges of the b—jets were
inferred from the charges of the b partons they matched to. This is not possible in
data (we don’t have parton information) so as a cross-check we took the charge of the
b—jets from the charge of the muon in the heavy ﬂavor enriched dijet MC (the black
triangles in Figure 5.13). This was done to look for any bias in our method of using

the parton level information in MC.

 

-l

 

 

 

 

 

 

 

 

a v MC (dijet and HF)
0 § E i s
m 0-7 . ' I "if" I
0.6
0.5
0.4
0'3 : : : . 3 i
0.1 ..
o L I I L I I L I 4 I I L I LL l I I I M I I I l I

 

 

Figure 5.12. The real purity of the jet charge algorithm (P JQ) as a function of the away—jet
ET for the data (blue triangles) and MC (red triangles). The purity for jets matched to b
quarks in the MC samples is the weighted average between the purity in the generic dijet
MC and the heavy ﬂavor enriched dijet MC.

5.5. 1 Scale Factor

To be able to use the real jet charge purity (PJQ) for any sample, in particular for

the high ET b—jets in top events, we decided to present P JQ as a scale factor between

122

-I

 

 

3.. eneric ME
°°° HF MC (hepg)

°'° ‘ FMC(muonQ)

0.6
0.5

 

 

 

Real Purity

 

    

 

1 L L L S L
l O O V I I
0 0 I s I b
o 4 .............;......................,;.-.....................;,......................r.......................;,......................;........ ..
C . .
i I . . I I
l l . . . .
. . . . . .
o 3 .............t...-...................'.......................f.......................l.......................'.......................|........ ..
I .
i i . 2 i :
I I l I I I
. . . . . .
. . . .

0.2

 

Figure 5.13. The real purity of the jet charge algorithm (P JQ) as a function of away-jet ET
Obtained from generic dijet MC (red circles) and heavy ﬂavor enriched dijet MC (inverted
blue triangles). The parton level (hepg) bs were matched to jets for the calculation of jet
charge purity. The black triangles correspond to PJQ obtained from heavy ﬂavor enriched
dijet MC but using the muon charge correlation to decide on the correct JQ assignment
instead of the parton level information.

123

data and MC. Figure 5.14 presents the result for the jet charge scale factor (S JQ)
calculated from the ratio between the J Q purity in the muon-enriched data sample
and the dijet MC samples. The red line is a ﬁt to a straight line with zero slope while
the blue line was a ﬁt to a line with non-zero slope. The nominal S F JQ is taken from
the horizontal red line and is 1.03 i 0.02. The blue line ﬁt will be used to get an

uncertainty on the S F JQ due to the ET dependence and will be explained in Section

 

 

 

 

 

 

 

 

 

 

 

 

 

5.6.
h
9- 1-4:- x’lndf 6.302/8
E E , 1 .027 i 0.01 671
2 1.2_—
a: 3 _ +
8 1:— W'*llll =:::-:::::.:::::::: ::::::::::::::r. ------------
0.8E— l
T- u
0.6_—
0'47 x’lndt 5.33517
02; 90 1.064:0.04139
' ; p1 0.001153: 0.001207
07+1l‘‘l"#ll11IIII]LL,|l
20 40 60 . 80 100 120
ET

Figure 5.14. The scale factor as a function of ET for loose Sethx tagged jets calculated
from the ratio between the JQ purity in the muon—enriched data sample and in dijet MC.
The red line corresponds to a ﬁt with zero slope while the blue line is from a ﬁt to a line
with non-zero slope.

5.5.2 Method checks

As mentioned previously, the jet charge purity (P JQ) from MC was Obtained by

taking a weighted average between the jet charge purity in a generic dijet MC sample

124

and a heavy ﬂavor enriched one. As a cross check we used the P JQ from the heavy
ﬂavor em'iched dijet MC only to calculate the S F JQ. The resulting plot is shown
in Figure 5.15 and gives a SF JQ of 1.01 :l: 0.02. It is consistent with the nominal
S F JQ from Figure 5.14. We also compared 111-’1th distributions from the heavy ﬂavor
enriched MC with the ones from the dijet MC (Figure 5.16) and made sure that the
distributions were the same. In addition the entire S F JQ study was repeated using
tight Sethx tagged jets instead of loose tagged jets. The resulting plot is shown
in Figure 5.17 and gives a SFJQ Of 1.02 :i: 0.02 which is consistent with the result
from using the loose Sethx tagger. All the cross checks of the S F JQ agree with our
nominal value of 1.03 :l: 0.02.

 

 

 

 

 

 

 

 

 

 

 

 

 

.3 1-4:— xalndf 11/8
g : p0 1.01i0.01917
0 1.2:- -
Tu ~ .
o L .W .: ... + .............................................
(D 1: A?“ .........
0.3:— + .................
t 11 .............
0.65— - a
0'4";— {Inch 3.325/7 * ,k
02; p0 1.126i0.04705
: p1 0.0035121: 0.001302
07 L I l l JMI I I I J L I I l I I l l I I l l l
20 40 60 30 100 120

ET

Figure 5.15. The scale factor as a function of ET Obtained from the ratio between the jet
charge purity in data and the heavy ﬂavor enriched dijet MC only.

125

 

 

 

 
 
  
   

 
   
  

20<E,<25
—botlom
- -botl0m HF

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5.16. Mvtx distributions for tight Sethx tagged b-jets obtained from the heavy
ﬂavor enriched dijet MC (labeled bottom HF) compared to ones from the generic dijet
(labeled bottom) MC for several away-jet ET bins.

126

 

 

 

 

 

 

 

 

 

 

 

&
.3 1.4-_- x’lndf ‘ 7.45/8
E 12: p0 101832001643
2 “~— +
a g .
8 1:- 'We;==.=====:::i::.:::::.ZZZILIIIIIIIIII """""
0.3;-
0.6:— -
0'4: find 6.182/7 *
0.2; w 1.059i0-03943
; [)1 0001233 1- 0.001007
o’..1..LI...1.III...I..LI.
20 40 60 80 100 120

Figure 5.17. The scale factor as a function of ET obtained from the ratio between the J Q
purity using tight SeCVtx tagged jets in a muon-enriched data sample and in dijet MC. The
red line is a ﬁt to a line with zero slope while the blue line is a ﬁt to a line with non-zero
slope.

127

5.6 Dependence on ET, 77 and Number of Vertices

5.6. 1 ET Extrapolation

The calibration of the jet charge algorithm was performed on a bb enriched data
sample where the ET of the b-jets ranged from 20 GeV to 60 GeV, but the result
is to be used in tf events where the b—jets have higher ETs as shown in Figure 5.18.
Although the scale factor was assumed to be constant with ET, an uncertainty was
assigned to account for any possible dependence on ET. To get this uncertainty, the
ratio between the data and MC jet charge purities was ﬁt as a function of jet ET with
a line of non—zero slope (the blue line in Figure 5.14) and the result was weighted by
the b—jet ET distribution in tf events from Figure 5.18. The percentage difference
between this weighted scale factor and the nominal one (the red line in Figure 5.14)

was added as a systematic uncertainty of 2.9%.

 

0.08
0.07
013
0.05
0.04
0.03
0.02
0.01

+
+

 

lIlllIllIllIIIllIlllllIllllIII'IIIIIIIIIIIII
+
+

 

0
0|
0
_I
O
O
.I
8
B
O

ET(GeV)

Figure 5.18. The ET distribution for b—jets in tf events.

128

5.6.2 I] and Number of Vertices

Not only was a dependence with respect to ET studied but also any dependence
with respect to the n Of the jets and the number of primary vertices in the event.
Both of these studies were done in two different away-jet ET bins, to ensure that
any dependence seen was not due to ET. Figure 5.6.2 shows the PT,rel and Mvtx
distributions for b and light quark jets in 3 different 7) ranges when the away-jet ET
is between 45-75 GeV. The distributions show no dependence on the n of the jets.
We also calculated the jet charge scale factor S F JQ for different jet 1) ranges for two
different away-jet ET bins. No signiﬁcant dependence on 77 is observed as can be
seen in Figure 5.20. We did a similar study for the number of primary vertices in the
event. Figure 5.21 shows the scale factor for two away-jet ET bins as a function of

the number of vertices in an event. and shows no signiﬁcant dependency.

5.7 Systematic Uncertainties

This section explains the sources of systematic uncertainties in measuring the scale
factor. We distinguish between ones related to the procedure used to ﬁnd the b
fraction in muon-jets and those corresponding to the b fraction in away—jets. An
ET dependence uncertainty of 2.9% as dwcribed in Section 5.6.1 was also added. A

summary table is presented at the end of this section.

5.7.1 PT,rel Tag Bias

For the nominal S F JQ result, the PT,rel distributions were Obtained from MC samples
where the tagged b—jets were matched to b quarks. An uncertainty may have been
introduced due to the fact that in data we don’t know if the b-tagged jet is correctly
matched to a b quark. To address this we recalculated the scale factor using 131,91

distributions that were obtained from tagged bjets where we did not explicitly check

129

b-jet templates

 

04
0.35 45< away jet ET <75 GeV

03 0 15<n<0 3
”5 ----o.5<n<o.7

 

 

 

 

   
 
 
 

b-jet templates
0.4
0.35 45<Er<75 GeV
03 —0-15<n<0-3
035 ----- 0.5<n<0.7

--- 1.1<n<1.3

 

°oo.511522.533.544.55

 

Vtx mass
light jet templates
0.6 ,
: 45<ET<75 GeV
“'5? — 0-15<n<0-3
0.4} O.5<n<0.7
0 3s 1.1<n<1.3
0.2:» '7'
0.1:— """

 

 

 

: ILIIAIIIIIIIIIJI IIIIIIII LIIAJI
(50.115225133544515
Vtxmass

Figure 5.19. The PTrel distribution for bottom quarks (left plot) in three different 1)
regions when the away-jet has an ET between 45 and 75 GeV. The middle and right plots
are the Mvtx distributions for the bottom and light jets respectively in three different 7)
regions when the away-jet has an ET between 45 and 75 GeV.

130

 

 

 

 

 

2 1.4—
8 : '—-1>-—u
E .—
2 1.2:
m : .

0.83- +

0.6:—

02; . 50<ET<75

0:1! IlllllllllllJlllllllLlllljl||lgl
-1.5 -1 -o.5 o 0.5 1 1.5

Figure 5.20. The scale factor as a function of 1} for away-jet ET ranges of 20-35 GeV and
50—75 GeV.

that the tagged jet came from a b quark. The percent difference for the S F JQ with

respect to the nominal value was 1% and is taken as a systematic uncertainty.

5.7.2 I’ijl non-b Bias

The PT,rel ﬁts were done using only two templates, one obtained from bottom jets
and the other from charm jets. An additional template for light quarks was not used
because the charm and light quark distributions were similar. This was discussed in
Section 5.4.1 and is shown in Figure 5.2. Despite their similarity the charm and light
distributions may affect the S F JQ differently. We recalculated the scale factor using
the light quark distribution instead of the charm one. The percent difference with

respect to the nominal scale factor was 0.1% and is added as an uncertainty.

131

 

1.4

1.2

 

F

 

 

 

 

Scale Factor

 

H»—
r—‘o—c
*—0—+
J

0.8

 

0.6

. 50<ET<75

0.4

0.2

llilllllll{ITTTTTTWTITTTITITII

 

 

o llllllllllllJlllllllllllllllLllllllllllllllllll

0.5 1 1.5 2 2.5 3 3.5 4 4.5
NZVertex

 

Figure 5.21. The scale factor as a function of the number of primary vertices in an event
for away-jet ET ranges of 20—35 GeV and 50—75 GeV.

132

5.7.3 A'Ivt’x Bias

Any error in the tracking system and/or simulation will effect the Mth (invariant
mass of secondary vertex) distributions since the mass is calculated by using tracks.
Actually a study done at CDF using MC shows that we miss 3% of the COT tracks at
the track reconstruction level. Missing tracks may cause smaller Mm values resulting
in a 3.5% shift in the Mvtx distributions [36]. To account for this track reconstruction
inefficiency, Mm distributions for bottom, charm and light jets were shifted by 5%
and the scale factor was recalculated. With the conservative shift of 5%, the percent
difference with respect to the nominal SFJQ result was found to be 1.8% and is

assigned as an uncertainty.

5.7.4 Alvtx Fits

Although the b fraction on the away—jet side was obtained by ﬁtting the AIM dis-
tribution from data to three Mvtx distributions (one for bottom, one for charm and
the other for light jets), we repeated the study using only two distributions. First we
recalculated the S F JQ using only the bottom and charm (bc) distributions for the
Alvin: ﬁt and then we recalculated using only the bottom and light (bl) distributions.
The percent differences with respect to the nominal three distribution case are taken
as systematic uncertainties. The results are 1.6% and 0.4% for the be and bl cases

respectively.

5.7.5 Summary

Table 5.4 lists all the systematic uncertainties on the SR [Q from the sources men—
tioned above. The uncertainty from the ET extrapolation discussed in Section 5.6.1
is also included. The systematics are shown as the relative uncertainty in % on the

SF JQ. The total systematic uncertainty on the. SE IQ is 3.9%.

133

 

 

 

Systematic source Relative Syst. Uncertainty (%)
PT,rel Tag Bias 1.0
PT,rel non-b Bias 0.1
1”th Bias 1.8
Mvtx ﬁt with bl 0.4
ET Dependence 2.9
Total 3.

 

 

 

 

Table 5.4. The relative systematic uncertainties on the scale factor from the PT,rel ﬁt,
Mvtx ﬁt and ET extrapolation. The “("1th ﬁt with be” implies the ﬁt is performed using
bottom (b) and charm (c) jet Mvtx distributions. Similarly the “ vtx ﬁt with bl” implies
the ﬁt is performed using bottom (b) and light (I) jet Mvtx distributions.

5.8 Conclusion

A method to calibrate the Jet Charge (JQ) algorithm, used to determine the ﬂavor
of b—jets from data, was presented in this chapter. The procedure compared a muon-
enriched dijet data sample to similar MC samples. The fraction of bb events was
determined by ﬁtting the data to PT,rel and Mm distributions and using the expected
correlation between the charge of the away-jet and the charge of the muon from the
muon-jet. The purity of the JQ algorithm was found after correcting for cascade
decays and B mixing. The result of the study is a data to MC scale factor which
is shown in Figure 5.14. The measured scale factor for loose Sethx tagged jets is
1.03 :t 0.02(stat)i0.04(syst). This scale factor will be used to correct the jet charge
purity obtained from MC. The details of how we do this correction will be presented

in Chapter 9.

134

CHAPTER 6

Backgrounds

Last night, in private, I asked the wise old man
To reveal to me the secret of the world.

Softly he whispered, Hushl, in my ear:

It‘s something you learn, not words you can hear.

I asked, ”What should I do?”, He said, ”That’s it.
Keep asking what to do.”, I asked, ”That’s it?

Is that the best that you can do?”, He turned to me:
”Truth seeker, stick to this: What should I do?”
Rumi (1207-1273), a Turkish suﬁ.

6. 1 Introduction

Even though the event selection presented in Chapter 3 is optimized to pick tf lep—
ton+jets events, different non-lt— processes that mimic the lepton+jets event signature
may enter our analysis sample. These processes are called backgrounds and come from
W+multijet and non-W events. One example of W+multijet production is W+Heavy
Flavor (W+HF) events that include a W boson produced in association with jets that
come from b or c quarks. W bosons can also be produced along with jets from light (u,
d, s) quarks. These W+Light Flavor background events are also called mistags since
they can mimic the top sample only if the light quark jets are mistakenly tagged as

b—jets. Other possible W+multijet backgrmmds come from diboson (WW, Z Z, WZ )

events and events that include only one top quark called single top events. The
non-W background, also called QCD background, is basically multijet events that do
not include the production of a W boson. Since only a small fraction of background
events contain jets coming from b or c quarks, tagging both b—jets using the Sethx
algorithm signiﬁcantly reduces the background contribution.

The expected contribution from each background has already been calculated for
the CDF top cross-section (a) measurement [29], so we rely directly on their back-
ground estimation which is given in the second column of Table 6.1. The expected
numbers of background events (Nb) after the top charge analysis selection require-
ments are presented in the last column of Table 6.1. They are obtained by multiplying
the background predictions from the cross-section analysis (second column) by the
total efficiency of the selection requirements for the top charge analysis which is the

product of the pairing and jet charge efﬁciencies as shown below.

€total : 6pairing ' éJQ (6.1)

The uncertainties on each background are statistical only. For the lepton+ jets channel
the fraction of each background that has two jets tagged by the loose Sethx tagger
is shown as a pie chart in Figure 6.1. The left diagram shows the fractions for the
cross-section analysis and the chart on the right shows how these fractions change
after the selection requirements for the top charge analysis are applied.

For the top charge analysis, in addition to the number of background events, we
need to know if some of the backgrounds are more likely to mimic Standard Model

like (N+) events or exotic quark like (N_) events.

N+

P = —— 6.2
b N+ + N_ ( )

We deﬁne the purity (Pb) on each background type as the number of events assigned

as N+ over the total number of events passing the selection cuts (see Equation 6.2).

136

 

Table 6.1. Table of expected background events (N b) for the top charge analysis in the
lepton+jets (L+J) channel for 695 pb‘1 of data. L+J a prediction is the number of back-
ground events from the cross section analysis. Third column is the total efficiency of the
top charge selection requirements.

Background Fractions
for the loose double tagged sample

After lepton+jets selection After top charge selection

 

 

Figure 6.1. Lepton+jets background fractions for the loose double tagged sample before
and after the selection requirements for the top charge analysis.

137

A Pb value of 0.5 is equivalent to saying that the background events are as likely
to be assigned as Standard Model top events as exotic quark events. Therefore,
we sometimes refer to Pb as the charge asymmetry and a purity of 0.5 means the
background is charge symmetric. This chapter describes each background source to

the top events in the lepton+jets channel along with the charge asymmetry it exhibits.

6.2 W+Heavy Flavor

6.2.1 Production and Estimation

Heavy ﬂavor production in association with a W boson contributes signiﬁcantly to
the background in the btagged lepton+jets sample even though W+Light Flavor
dominates the sample before b-tagging has been applied. Remember that for the top
charge analysis we tag both b—jets using the loose Sethx algorithm. In this case,
55% of the background events are from W+Heavy Flavor (W+HF). A W+HF event
is the result of gluon splitting as shown in Figure 6.2 where pp —-> W9 is followed by
the gluon splitting to bb, g —> bb. Gluon splitting can also produce ch events that
may mimic the tf lepton+jets event signature if one or both of the 0 jets is tagged as
a b.

Several Monte Carlo generators are capable of performing matrix element calcu-
lations for W+jets. The MC generator used to model “W + 4 jet” events in this
analysis is ALPGEN [37]. The ALPGEN MC calculates exact matrix elements at
leading order along with providing proper treatment of heavy quark masses, spins
and color ﬂows. On these ALPGEN events a simulation of parton fragmentation
with a shower algorithm based on the HERWIG [17] program and a decay algorithm
based on Ethen [16] are used. The estimation of the amount of W+HF background
requires special care since imprecise values of heavy ﬂavor fractions (the number of

events expected to contain a heavy ﬂavor quark) and / or mistakes in the detector

138

simulation can cause significant errors on the W +HF prediction. The number of
W+jets events in the data before b—tagging is measured. The number of events we
expect from other backgrounds is then subtracted off and the remaining amount is
multiplied by the W+HF fraction and b—tagging efﬁciency to calculate the amount of
W+HF in the b—tagged lepton+jets sample. For the top charge analysis we expect
0.8 i 0.2 W+HF background events.

I)
q‘ 9 , /
, 4...,“ 5
g
lily,
I 1,“: .. l
-q- .1» w V

Figure 6.2. The Feynman diagram of a W + bb event that may mimic a lepton+jets tf
event. The resulting gluon splits into a bb pair while the other resulting product, the W
boson, decays to a lepton neutrino pair. W + CE events are produced in an identical manner.

6.2.2 Charge Asymmetry

As mentioned before, we need to make sure that there is no bias towards either the
Standard Model or exotic model case for each of the backgrounds. In other words,
we must ensure that the jet charge purity for each background (Pb) is 0.5. The main
problem in the pursuit of measuring Pb is that once the top charge analysis cuts have
been applied, such as the double b-tag requirement and X2 cut, there are only a few
events left in the background samples. In such cases, we calculated Pb by loosening
these requirements, such as using events with a single or no b—tag. The number of N +
and N _ type events in the single b—tagged W + bb and W + cc Monte Carlo samples

and their corresponding purities are shown in Table 6.2. The Pb for W + bb and

139

E
s

 

 

 

 

9 W0” .__1 ” _ C

Figure 6.3. The Feynman diagrams for the production of W + 0 events.

W + cf: events agree with 0.5 within their uncertainties.

The one W+HF sample where we do see a charge asymmetry is in the W + 6
events. The c quark is generated with a W" and E is generated with a W+, as shown
in Figure 6.3, so a W + 6 event will look like a N... type event. Remember we require
the lepton+jets events to have 4 or more jets but W + c events typically have only
one jet. W + c events can only pass our selection requirements if there are at least
three additional gluon jets produced and the c jet is tagged as a b—jet. Therefore it
is really hard for a W + c event to enter our sample. Since the amount of W + c
background we expect in our sample is very small, we assumed a Pb of 0.5 :l: 0.0 for
W + 0 events. Nevertheless we checked for the expected charge asymmetry in W + 0
events requiring only one jet. Table 6.3 shows the number of N+ and N_ type events
and the corresponding Pb for the W + 0 sample requiring only one jet in the event.
The ﬁrst row in the table shows the charge asymmetry where we have not done any
parton level check. Once we require the c jet in the event to be matched to a c quark
(second row), the charge asymmetry is slightly higher z 62% conﬁrming the expected
charge asymmetry. The result in the third row is obtained using only events where

the c jet does not match to the c quark.

140

 

 

W+HF # of tags NW1 NT N. Pb

_ 2tags 223 111 112 0.50:1:003
W+bb ltag 1329 658 671. 0.50:t0.01
Pretag 2127 1085 1042 0.511001

 

 

 

 

 

 

 

 

 

2 tags 28 10 18 0.36 :l: 0.09

ll" + CE 1 tag 515 268 247 0.52 :t 0.02
Pretag 2194 1134 1060 0.52 :l: 0.01

7 tags 22 10 12 0.45 :t: 0.1

W' + C 1 tag 438 224 214 0.51 :l: 0.03
Pretag 2369 1256 1113 0.53 d: 0.02

 

Table 6.2. The charge asymmetry (Pb) from MC for W+HF background events. The
Ntotal column shows the total number of events left after applying the lepton+jets and
top charge selection cuts on the MC sample. The N + and N. columns show how Ntotal is
shared between SM-like events (N+) and exotic-like (N_) events respectively.

 

1V+ 1V— Pb
No parton level check 1072 672 0.61 :l: 0.01
jet matched to c quark 1026 634 0.62 :t 0.01
jet not-matched to c quark 46 38 0.55 :i: 0.05

 

 

 

 

 

 

 

Table 6.3. The charge asymmetry (Pb) for W + c loose Sethx tagged events requiring 1
jet in the event. Pb of 0.5 indicates no charge asymmetry. The ﬁrst row in the table shows
the result where we have not done any parton level check. Once we require the c jet in the
event to be matched to a c quark (second row), the charge asymmetry is slightly higher.
The result in the third row is obtained using only events where the c jet is not matched to
a c quark.

6.3 QCD (non-W)

6.3.1 Production and Estimation

Because quarks have color charge, they can radiate gluons and this radiation can be
detected as jets in the CDF detector. If one of these jets is misidentiﬁed as an isolated
lepton, the QCD event can pass our lepton+jets sample selection. Due to the fact
that these events do not include production of a W boson, they are also called non-
W events (see Figure 6.4 as an example). There are several reasons that an object
identified in the detector as a lepton is not actually a lepton coming from the decay of
a W boson. The ﬁrst possibility is that a jet can fake a lepton if part of the jet passes

the isolation requirement. The second possibility of a non-W background is direct bb

141 -

2x
/

CI
1.! “PA“

6\
jet
9 ‘1
jet

Figure 6.4. Feynman diagram of a multijet non-W event where the qt] annihilation resulted
in a gluon and then produced two light jets with an additional gluon jet from one of the
light quarks. One of the light jets can be misidentiﬁed as a lepton and if there is additional
gluon radiation the event can pass the lepton+jets event selection.

or CE production. In bb events, it is possible that a real lepton from the semileptonic
decay of a B hadron can pass our isolated lepton requirements. A third possibility
is a photon conversion that is misidentiﬁed as an electron or a high momentum pion

that satisﬁes the muon criteria.

 

 

Figure 6.5. A drawing representing the 4 regions in isolation versus ET that are used for
the QCD background prediction.

One of the methods at CDF for estimating the QCD background in the b—tagged

lepton+jets sample is called the Iso vs. ET method where the isolation of the lepton

142

(Iso) is plotted against the missing transverse energy, ET. The plot is divided into
4 regions, named A, B, C and D as shown in Figure 6.5. The isolation and ET cuts

used for each region are given below:

A: 130 > 0.2, ﬁT < 15 GeV
B: [80 < 0.1, 12} < 15 GeV
C: [so > 0.2, ET > 20 GeV
D: 1.90 < 0.1, ET > 20 GeV

Note that higher values of isolation do not indicate more isolated leptons. For exam—
ple, I so = 0.1 for electrons means the energy in a cone drawn around the electron
cluster is 10% of the cluster energy (see Section 3.2.1 for details). Therefore lep-
tons with I so < 0.1 are much more isolated from the jet activity than leptons with
I so > 0.2. The large ET and small isolation region, region D, is where top events are
concentrated. The events in region A have large isolation values so they are events
with non—isolated leptons and small ET. This region is enriched in QCD background
and has only a small amount of W events. To get the number of non-W events in the
signal region (region D), Equation 6.3 is applied to the b—tagged lepton+jets sample,

where N A: N B: NC, N D are the number of events in regions A, B, C and D.

N -
ND = NC x 43 (6.3)
NA

The total number of non-W background events in the signal region is estimated as the
number of non-isolated lepton candidates in the high ET region scaled by the ratio of
isolated to non-isolated lepton candidates in the low ET region, which is dominated
by background. We expect 0.4 :i: 0.3 QCD background events in the lepton+jets

channel after the top charge selection requirements.

143

6.3.2 Charge Asymmetry

In order to estimate the charge asymmetry for non- W events, we used the Isolation
versus ET method as described above. Running over the lepton+jets top data sam—
ple we tried to calculate the charge asymmetry for each region. To prevent double
counting of the same physical object, for example non-isolated electrons and muons,
jets that were matched to a lepton within a cone of AR < 0.4 were removed. We also
applied an additional correction to the ET for the presence of non-isolated muons as
explained in Section 3.4. After all of the top charge selection requirements were ap-
plied, there were almost no events left in any of the regions so we could not calculate
the purity.

Since we could not get a direct QCD purity result from the top data sample, we
tried to calculate the purity using other data and MC samples. To better understand
the details of the studies tried, let’s review again the different sources of QCD

backgrounds. QCD arise from

1. events where a non-isolated lepton passes isolation requirements
2. multijet events where a jet fakes a lepton
3. events where a photon conversion is misidentiﬁed as an electron or

events where a high momentum pion is misidentiﬁed as a muon.

Out of these three cases the type of events for which we expect to see a charge
asymmetry towards Standard Model top are bb and c5 events which are only a subset
of the ﬁrst case. Here we will describe the studies we did to measure the charge
asymmetry due to the ﬁrst and second cases.

For the ﬁrst case, we choose bb events from the dijet data and calculate the purity

for these QCD events. The dijet data include leptons that are coming from the decay

144

 

 

180 vs. MT region N+ N- Pb

A 117446 113567 0.5082t 0.001
B 61612 55178 0.528 :t 0.001
C 4137 3662 0.530 :1: 0.006

 

 

 

 

 

 

Table 6.4. Purity (Pb) of events from dijet data before b—tagging is applied on the jet that
is back-to—back from the jet including the lepton.

 

 

150 vs. E1 region N+ N- Pb
A 6448 5376 0. 55 :l: 0. 01
B 1489 1282 0.54 :l: 0. 01
C 339 263 0.56 :l: 0. 02

 

 

 

 

 

 

Table 6.5. Purity (Pb) of events from dijet data after b—tagging is applied on the jet that

is back—to—back from the jet including the lepton. We use the purity in region A for the
QCD background.

of heavy ﬂavor hadrons. For a bb event to pass our lepton+jets selection cuts, the
lepton from the semileptonic decay of the B hadron must be chosen as the isolated
lepton. Since the charge of a lepton from a semileptonic hadron decay is correlated
to the ﬂavor of the b and our Wb pairing method will most likely match this lepton
with the b jet it is coming from, the event will look SM-like. Therefore we expect
to see a tendency towards SM—like top events from bb background events. For the
selection of bb events from the dijet data we required a b—tagged jet that is back-to-
back in azimuth to the jet the lepton came from. Tables 6.4 and 6.5 show the purities
found for each iso vs. ET region for the events chosen before and after b—tagging the
jet opposite the lepton jet. For the tagged case in the QCD-enriched region A, we
measured a purity of 0.55 :l: 0.01.

To check the purity for the second type of QCD events we used a dijet MC
sample where a jet was assigned to be a fake electron if the jet passed the following

requirementsgz

Jet ET > 20 GeV
Jet r) < 1.1

 

9These. selection cuts come from a fake lepton study done at. CDF [38].

145

Number of tracks in jetZ 4

0.8 < EC‘IIl/Etotal < 0.95

where Emu / Emt a1 is the fraction of electron energy as measured in the electromagnetic
calorimeter to the total energy of the jet. The charge of the fake lepton was taken
from the curvature of the highest PT track in the jet. We found a purity of 0.50:t0.01 .
which veriﬁed that there is no charge asymmetry for QCD events with a fake lepton.

As a result of the above studies, we decided to use the result of 0.55:1:001 from the
study done using data for the overall QCD background. This is however a conservative
result since 0.55 was obtained from bb events which is the only charge asymmetric
component of QCD events and will actually be diluted by other charge symmetric
QCD events. We used the 0.55 for the purity but made the errors asymmetric using

+0.01 and —0.05 to cover the charge symmetric result of 0.5.

6.4 Mistags (W+Light Flavor)

6.4.1 Production and Estimation

One other type of background to the lepton+jets sample are the W boson events
produced in association with light quarks (W +Light Flavor) where a light quark jet
is tagged as a b—jet. These jets that are tagged as b—jets even though they do not
contain a true b quark are called mistagged jets. To calculate the background from
mistags, we make use of the transverse decay length (ny) of the tracks coming from
the secondary vertex.

As mentioned in Section 3.5.3, ny is a signed distance and if a secondary vertex
is reconstructed on the opposite side of the primary vertex from the jet direction it
has a negative value. In the negative 1ny case, the jet is much more likely to have

come from a light quark than a b quark. By parameterizing the negative va values

146

as a function of the jet ET, 77 and number of Sethx tracks in the jet, the probability
to mistag a jet can be given by a matrix known as the mistag matrix [29]. A jet that
has at least two Sethx tracks as described in Section 3.5.3 is called a “taggable jet”
and the size of the mistag background is estimated by weighting each taggable jet
with its mistag rate in the lepton+jets data sample before b—tagging. In the case of
double tagged events using the loose Sethx tagger, we expect 0.1 :l: 0.1 events to be

from mistags.

6.4.2 Charge Asymmetry

In order to check the charge asymmetry in the mistags, MC samples of W+1 or
more light quarks (W+LF) were generated using MADGRAPH+PYTHIA with the
W required to decay leptonically. Due to low statistics in the samples after the top
charge analysis selection, the requirements on the number 'of b—tags was loosened. By
checking the single and pretagged samples instead of the double tagged sample, we
conﬁrmed that there was no charge asymmetry introduced by mistags that would
bias the top charge measurement towards the Standard Model or exotic model (See

Table 6.6). So we use a Pb of 0.5 :l: 0.0 for the mistag background.

 

 

 

 

 

 

 

 

# of tags mm] N+ N_ Pb

2 tags 7 2 5 0. 3 i 0. 2
1 tag 350 192 158 0. 55 :l: 0.04
Pretag 3766 2025 1731 0.54 :l: 0. 02

 

Table 6.6. Jet charge purity (Pb) for the mistags background obtained from W+LF MC.

6.5 Diboson

6.5.1 Production and Estimation

The diboson background consists of WW, WZ and Z Z events. In a WW event, if

one W decays to a lepton-neutrino pair and the other to two light quarks plus if

147

there is at least one gluon jet from initial or ﬁnal state radiation, the event can mimic
a lepton+jets ti event. Similarly, a Z Z event can pass our selection cuts if one of
the Z bosons decays hadronically to cc? or bi) pair while the other Z decays to two
leptons. The large ET requirement can be satisﬁed if one of the leptons from the
Z goes undetected giving the appearance of missing transverse energy. For the WZ
background to mimic a lepton+jets tf event, the W boson must decay leptonically and
the Z to a cf: or b5 pair. The ALPGEN event generator is used to predict the amount
of diboson backgrounds in the sample. The ALPGEN events are then put through
the HERWIG program for hadronization and parton showering. The estimation of

the diboson background events is obtained by using Equation 6.4.

Nbckg I 0 ‘ BR ' SF ' ( Z det ‘ 6accept ‘ etag) (6-4)
lepton

where (accept, is the acceptance efﬁciency of the process (WW, WZ or Z Z ) The frag
is the b-tagging efﬁciency and f Ldt is the integrated luminosity. The sum is taken
over all possible lepton types. Here a and BR represent the theoretical cross-section
and branching ratio for a given process (W W, WZ or Z Z) and SF is the btagging
scale factor. Since the diboson cross-section is small, we expect only 0.04 i 0.02

diboson events after the top charge selection.

6.5.2 Charge Asymmetry

There is no physical mechanism in diboson events that can cause a bias toward +2 / 3
or —4 / 3 events. The expected symmetric behavior was conﬁrmed by measuring the
charge asymmetry in diboson MC samples as shown in Table 6.7 and 0.5 was used

for the diboson background purity.

148

 

 

 

 

 

 

 

# 0f tags Ntotal N+ N- 1};

ﬂags 4 2 2 0.5 :l: 0.1T
1 tag 94 40 54 0.43 i 0.06
Pretag 570 303 267 0.53 :l: 0.02

 

 

Table 6.7. Jet charge purity (Pb) for diboson background obtained from diboson (WW +
WZ + Z Z ) MC samples.

6.6 Single Top

6.6.1 Production and Estimation

‘1 t q or
W“ w
b t
9
CT s-channel '5 t-channel E

Figure 6.6. The left (right) picture is a Feynman diagram for s-channel (t-channel) single
top production.

At the Tevatron, in addition to ti pair production via the strong interaction, a
top quark can also be produced singly through the electroweak interaction. A single
top event can be produced in association with a b quark through qtj annihilation (3-
channel). It can also be produced through the W—gluon fusion process (t-channel) in
which an initial gluon splits into a b5 pair and a b quark interacts with a virtual W as
shown in Figure 6.6. The single top background is just 1% of the total background to
the loose b—tagged lepton+jets events and obtained by running on MadEvent MC [39]
events generated for s-channel and t-channel seperately. The single top prediction

was calculated in a similar manner to what was done for the diboson prediction. The

149

expected number of single top events is 0.13 :l: 0.01 after the top charge selection.

6.6.2 Charge Asymmetry

Even though single top events are considered background for if events, they are
not actually a background for the top charge measurement since we could measure
the charge of the single top quark in the event. However, our event selection was
optimized for if events and by treating single top as a background we checked our
expectation of seeing a charge asymmetry towards N+. If the matching between
the lepton and b-jet is correct, the event should contribute to N+ because it was
generated as SM top. We ran on MadEvent MC data and performed our event
selection. When we count the number of events for which the b jet is conﬁrmed to be
coming from a top decay using the MC generator information, the relative number of
N+ events increases as expected. Even though this asymmetry is suppressed due to
incorrect pairing assignments and the imperfectness of the jet charge calculation, we
still observe a charge asymmetry of 0.58 :l: 0.02 for the case where we count all events
whether or not the pairing was correct. Once we make sure that our Wb pairing
method picked the correct pair, the charge asymmetry goes up to 0.69 :l: 0.03. The
results are summarized in Table 6.8. We used a Pb = 0.58 :l: 0.02 for the single top

background.

 

Pb
no parton Evel check 0.58 :l: 0.02
b jet coming from top 0.69 :l: 0.03

 

 

 

 

 

Table 6.8. Purity for the b—tagged single top MC events.

6.7 Background Summary

We started with the backgrounds from the CDF top cross-section analysis [29] and

then applied the top charge sele(’-tion requirements to ﬁnd the expectation for each

background in this analysis as shown in Table 6.1. In addition we need the background
purity to determine whether the background looks more like the Standard Model or
the exotic model. The measured Pb was 0.5 for most of the backgrounds indicating
no charge asymmetry. Two places we observed a slight excess of SM-like events were
from the QCD and single top backgrounds. Table 6.9 shows the purities obtained for

all of the backgrounds.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Background ] # of b—tags f 73b
W+HF
Ttags 0.50 i (I03
W + bb 1 tag 0.50 d: 0.01
Pretag 0.51 :l: 0.01
2 tags 0.36 :t 0.09
W + cc ltag 0.52 :l: 0.02
Pretag 0.52 :t 0.01
2 tags 0.45 i 0.11
W + c ltag 0.51 :l: 0.03
Pretag 0.53 :l: 0.02
Mistag
2 tags 0.29 :t 0.17
ltag 0.55 :l: 0.04
Pretag 0.54 :l: 0.02
Diboson
2 tags 0.50 i025
ltag 0.43 :l: 0.06
Pretag 0.53 :l: 0.02
0.01
can I 10.55:...

 

 

Table 6.9. Background Purity Pb (Charge Asymmetry) for each background calculated
from the equation Pb :2 N+ / (N + + N_). A purity of 0.5 implies charge symmetry.

151

CHAPTER 7

Systematic Uncertainties

What men really want is not knowledge but certainty.
Bertrand Russell (1872-1970), a British philosopher.

Apart from the statistical uncertainty introduced due to the ﬁnite statistics in our
data sample, there are errors that can arise from uncertainties in the CDF detector’s
performance, errors in the calibration of calorimetry and tracking systems, as well as
imperfections and assumptions in the analysis method or MC modeling. Systematic
uncertainties are introduced to cover these errors. The uncertainty on the acceptance
of signal and background events is included in the predictions obtained from the cross-
section analysis [29]. For the top charge measurement, we have studied how systematic
uncertainties affect the efﬁciencies (e) and purities (P) of the Wb pairing and jet
charge. The systematic uncertainties associated with the top charge measurement

are listed below and will be explained in detail in the following subsections.

0 Jet Energyr Scale

Initial / Final State Radiation

Top Mass Uncertainty

b—Tagging

Parton Distribution Functions (PDF)

0 Monte Carlo Modeling

7.1 Jet Energy Scale

O

The energy of jets measured using calorimeter towers does not correspond exactly
to the energy of the initial parton that the jet came from so the jet energies must
be scaled back to particle or parton level as described in Section 3.3.2. All of the
various sources of uncertainty in the CDF jet energy scale listed below can cause a
discrepancy between the modeling of jets in Monte Carlo and the actual jets observed

in data.

0 Relative Jet Energy Scale

Raw Jet Energy Scale

Absolute Jet Energy Scale

Multiple Interactions

Underlying Event

Out-of-cone Corrections

In CDF there are different levels of jet energy scale (JES) corrections where for
each level one or more of the sources of J ES corrections are applied. For this thesis,
we have used the level of JES corrections that corrects jets back to the particle level.
Therefore multiple interactions, underlying event and out-of-cone corrections that
correct jet energies from the particle level to parton level were not considered in this
analysis, so no systematic uncertainty was taken for these.

As explained in Section 3.3.2, the relative JES corrections remove the r] depen-
dence of the calorimeter. The amount of uncertainty on the energy of a jet differs with

different 17 ranges and the largest uncertainty (8 7%) is assigned in the region with

153

[77] > 2. The amount of systematic uncertainty for jets in the region 0.2 < [77] < 0.6 is
shown (dashed green line) in Figure 7.1 as a function of jet PT. The raw J ES correc-
tion, which accounts for the non-linear response of the calorimeter, is around 5%. For
the absolute J ES, the jet energy measurement relies on the detector simulation and
fragmentation model, so the uncertainty on the correction comes from calorimeter
simulation errors and the uncertainty in the fragmentation modeling which increases
with increasing PT of the jets. The dashed blue line in Figure 7.1 shows how the
amount of the systematic uncertainty changes with jet PT for the absolute J ES cor-
rection. The jet energy corrections simply scale a jet’s four—vector by a factor, so its
angle is unaffected but its energy and momentum will change.

In order to determine the jet energy scale uncertainty on the pairing and jet
charge efﬁciencies and purities, we shift the jet energies up and down by the total
uncertainty (or 10) which is calculated by summing the uncertainties from the various
J ES corrections. Then we recalculate the pairing and jet charge efﬁciencies and
purities for these shifted samples. The results are shown in Table 7.1. We calculate
the deviation (in percent) of each shifted sample from the unshifted sample and take
the average of the two results as the systematic uncertainty. There is no signiﬁcant
error introduced by the J ES on the jet charge efﬁciency and purity. The uncertainties

on the pairing efﬁciency (if-pairing) and purity (Ppairing) are 3.1% and 1% respectively.

 

 

Jet energy (pairing % Ppairing % EJQ % P JQ%
Nominal 56.3 :l: 0.3 84.3 :l: 0.3 98.0 :l: 0.07 60.7 :l: 0.3
+10 57.1 :l: 0.3 85.0 :l: 0.3 97.95 :l: 0.07 60.7 d: 0.3
—10 53.6 :l: 0.3 83.3 :1: 0.3 98.03 :1: 0.07 60.8 2]: 0.3

 

 

 

 

 

 

 

Table 7.1. Pairing and jet charge efﬁciencies and purities obtained by shifting the jet
energies up and down by 10.

 

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20 4o 60 80 100 120 140 I60 I80 200
Corrected jet PT (GeV)

 

Figure 7.1. The Jet Energy Scale (JES) uncertainties in the central calorimeter (0.2 <
n < 0.6) as a function of a jet’s transverse momentum. The level of JES corrections we
applied considers only the relative and absolute JES corrections.

7.2 Initial/ Final State Radiation

For the top charge measurement, we assumed that the four highest ET jets in the
event were the jets associated with the partons from the top decay. However MC
studies indicate that sometimes at least one of the four highest ET jets does not come
from the tf decay. In such cases the jet is usually from initial or ﬁnal state radiation.
The initial state radiation (ISR) uncertainty is assigned due to the possibility of
picking a gluon or photon jet that was radiated before the pp interaction as one of
the objects from the top decay. Similarly, gluons or photons radiated from ﬁnal state
particles, called ﬁnal state radiation (FSR), can enter our selection. Because a gluon
jet is totally uncorrelated with the if decay products, ISR/FSR has the potential
to degrade the pairing and jet charge purities. We checked how the efﬁciencies and
purities changed if we used a top MC where the amount of ISR (FSR) was changed by
varying the QCD scale parameter AQC’D- We used two different MC samples for ISR
(F SR) where one of the MC samples included less ISR (FSR) and the other included
more ISR (FSR) compared to the default MC sample (see Table 7.2). The AQCD
was doubled for the more ISR/FSR and halved for the less ISR/FSR samples. We
calculated the percent difference between each shifted sample and the default sample
and cite one error (for the ISR/FSR combined) calculated as the sum in quadrature
of the largest shifts for 18R and FSR. The ISR/FSR gives an uncertainty of around
1.4% on the jet charge purity but has no signiﬁcant effect on the jet charge efﬁciency.

The uncertainties on the pairing efﬁciency and purity are 2.3% and 1.2% respectively.

 

 

 

 

 

 

 

ISR/FSR Cpaim Ppairing % €JQ o P JQ %

Nominal 56.3 :1: 0.3 84.3 :1: 0.3 98.0 :1: 0.1 60.7 :1: 0.3
ISR less 55.2 :1: 0.5 83.9 :1: 0.6 97.9 :1: 0.1 59.9 :1: 0.6
ISR more 54.7 :1: 0.5 85.1 :1: 0.5 97.8 i 0.2 60.8 :1: 0.6
FSR less 55.6 i 0.5 83.7 d: 0.6 98.1 :1: 0.2 60.5 :1: 0.6
FSR more 56.6 :1: 0.6 84.3 :1: 0.6 97.8 :1: 0.2 60.6 :1: 0.6

 

 

Table 7.2. Pairing and jet charge efﬁciencies and purities obtained from top MC samples
that contain more or less ISR (FSR) with respect to the default sample.

156

7 .3 Top Mass Uncertainty

The mass of the top quark is used as a constraint in the reconstruction of tf events
in the kinematic ﬁtter. Our nominal purity and efﬁciency values were obtained with
a top mass constraint of 175 GeV/c2 on a MC input sample of equal top mass. We
looked at the efﬁciency and purity variations when a different top mass was used as
an input to the ﬁtter. We have run on MC samples where the generated top mass was
170 or 180 GeV/(:2, but used a constraint of 175 GeV/c2 in the ﬁtter. The results are
given in Table 7.3. We calculated the difference in purity between the value obtained
from the 170 GeV/c2 sample and the default sample. We did the same with the 180
GeV/c2 sample and took the average of the two results as the top mass systematic
which is 2.4% for the pairing purity (Ppairing) and 0% for the jet charge purity (P JQ).
The systematic uncertainties on the efﬁciencies were calculated in the same way and
resulted in 1% for the pairing efﬁciency (Cpairing) and 0% for the jet charge efﬁciency
(CJQ). Considering the latest top mass result [40] and its uncertainty of 170.9 :t 1.8
GeV/c2, we conclude that 2.4% and 1% for the pairing purity and efficiency are
actually conservative results since a 5 GeV difference was used between the top mass
value of the default MC sample and the other MC samples chosen to investigate the

top mass uncertainty.

 

00

TOP mass Cpairing / P pairing % 6JQ % PJQ %
175 GeV/02 56.3 :l: 0.3 84.3 :l: 0.3 98.0 a: 0.1 60.7 :t 0.3
170 GeV/c2 54.7 :1: 0.4 81.0 i 0.5 97.9 :t 0.1 60.8 :t 0.5
180 GeV/C2 55.5 i 0.4 85.0 i 0.4 98.0 :l: 0.1 60.7 :t 0.5

 

 

 

 

 

 

 

 

Table 7.3. Pairing and jet charge efﬁciencies and purities obtained from top MC samples
where the generated top mass was changed to 170 and 180 GeV/c2 but the kinematic ﬁtter
was still constrained to 175 GeV/c2.

7 .4 b-tagging

In our tf MC sample, 25% of the events are double b—tagged. However, this per-
centage is sensitive to the amount of initial and ﬁnal state radiation. Hard gluon
bremsstrahlung either in the initial or ﬁnal state can produce a jet which can be
mistaken for the b quark jet. These are called mistagged jets. As explained in Section
3.5.3 the mistag rate is actually a matrix and generally is smaller in MC than that
observed in data. This affects the number of events where the assigned b—jets are not
actually from b quarks.

For ﬁnding the uncertainty introduced due to errors in b—tagging, we applied the
mistag matrix on non-heavy ﬂavor jets and assigned those jets as tagged if their mistag
probability was greater than a given random probability. This way we increased the
light ﬂavor content in the MC. However to get the same composition as in data, we
need to decrease the heavy ﬂavor content at the same time. For heavy ﬂavor jets, we
made use of the ratio of the b—tagging efﬁciency in MC over the data which is known
as the b—tagging scale factor. If the jet was tagged we threw a random number that
we compared with the b-tagging scale factor of 95%. If the random number is smaller
than 0.95, we kept the jet as tagged but if it is larger, we declared it as untagged.
By applying the mistag matrix to non-heavy ﬂavor jets and the b—tag scale factor to
heavy ﬂavor jets in our default tf MC, we obtained a new sample. We calculated
the non-b fraction (fnonb) which is the number of double-tagged events where one or
more of the tagged jets was not matched to a b quark, in both the newly obtained MC
sample and the default MC sample. By dividing the fnonb from the new MC by the
fnonb from the default MC, we obtained a non-b scale factor (S Fnonb) of 1.05 :l: 0.05.
We assigned 100% error on the S Fnonb which accounts for a 20% increase on the
mistag probability. How the SFnonb is used for the top charge measurement will be

covered in Chapter 9 and is not used as a systematic uncertainty here.

7 .5 Parton Distribution Firnctions (PDFs)

As mentioned earlier, quark conﬁnement requires outgoing partons to combine with
other quarks in order to form color-neutral hadrons thus making it impossible to ob-
serve bare quarks and gluons. However it is possible to construct parton distribution
functions that represent the probability density to ﬁnd partons in a hadron with a
certain longitudinal momentum fraction (2:) of the proton’s momentum and momen-
tum scale (Q2) which is the square of the momenta involved in the event. These
functions are extremely difﬁcult to calculate theoretically but are instead constrained
by particle physics experiments. Several sets of parton distribution functions (PDFs)
are available such as CTEQ5L [15] and MRST [41]. Our default MC uses the PDF
set CTEQSL. Since different PDFs can affect event kinematics, a set of CTEQ and
MRST PDFs are compared to the nominal PDF set and the effect on our efﬁciencies
and purities is taken as a systematic uncertainty. Instead of generating a different
set of MC for each PDF set, we reweight one MC sample. To do this, each event.
in the default MC sample is reweighted by the relative probability of this event in a
different PDF set given the event’s Q2, that is the momentum fractions of the inter-
acting partons from the proton and anti-proton. We calculated the efﬁciencies and
purities for each of the PDF sets, compared each to the default CTEQSL result and
added the differences in quadrature. As a result we assign a 1.1% and 0.3% system-
atic uncertainty for the pairing eﬂiciency and purity respectively. The calculated jet
charge efﬁciency and purity using different PDFs were the same within errors as in

the nominal (CTEQSL) case so no error was assigned.

7 .6 Monte Carlo Modeling

We assign an uncertainty to account for different models in different MC generators.

For example different parton showering models are used in the PYTHIA and HERWIG

159

MCs that may affect the efﬁciency and performance of the analysis method. We
compared the pairing and jet charge efficiencies and pairing purity obtained from

HERWIG tf MC with the results from our default PYTHIA MC sample (see Table

 

 

7.4).
MC samﬁe flaking:K Epairing % 5.11%
PYTHIA 56.3} 0.3 84.3 :i: 0.3 98.0 :E 0.1
HERWIG 56.1 :t 0.5 84.6 :i: 0.5 97.9 :t 0.1

 

 

 

 

 

 

Table 7 .4. Pairing and jet charge efﬁciencies and pairing purity obtained from PYTHIA
(default sample) and HERWIG MC.

We take the percent difference in the pairing efficiency between HERWIG and
PYTHIA as the systematic uncertainty on the (pairing which is 0.8%. Similarly the
percent difference in the pairing purity Ppairing is 0.3%. Because we calibrate the jet
charge purity in data, no systematic due to the MC generator is assigned for P JQ.
The systematics that arise from the calibration of the jet charge purity using data

were addressed in Chapter 5.

7.7 Systematics Summary

Table 7.5 summarizes the sources and size of the systematic uncertainties for the top
charge measurement in the lepton+jets channel. Out of all the sources of systematic
uncertainties we considered, the largest systematic on the pairing eﬂiciency was found
to be from the jet energy scale and the next largest from ISR/ F SR. We did not assign
any systematic uncertainty for the jet charge efﬁciency since the result was always
the same as the nominal within errors. Regarding the pairing purity the largest
uncertainty is due to shifting the top mass while the largest uncertainty for the jet
charge purity is from ISR/FSR. The combined uncertainties on the efﬁciencies and
purities are calculated by adding the individual uncertainties in quadrature assuming

they are uncorrelated. The total uncertainty on the pairing efﬁciency and purity are

160

 

 

 

 

‘ Systematics (1n % (pairing Ppairing EJQ P JQ
2.3 1.2 0 1.4

MC modeling 0.8 0.3 0 -

J ES 3.1 1.0 0 0

PDF 1.1 0.3 0 0

Top Mass 1.0 2.4 0 0
total 4.2 2.9 0 1.4

 

 

 

 

 

 

Table 7.5. Summary of the systematic uncertainties in % where pairing and jet charge
efﬁciencies (e) and purities (P) are presented. Because the JQ is calibrated on data we do
not assign a systematic uncertainty on jet charge purity (PJQ) due to different MC modeling
effects.

found to be 4.2% and 2.9% respectively, while the total uncertainty on the jet charge
purity is 1.4%. How these uncertainties are used to get the uncertainty on the top

charge result will be explained in Chapter 9.

161

CHAPTER 8

Studies in the Dilepton Channel

What we observe is not nature itself, but nature exposed
to our method of questioning.

Werner Heisenberg (1901-1976), a German physicist.

8. 1 Introduction

As we mentioned earlier, the ﬁnal CDF top charge measurement is based on the
combined result from the lepton+jets and dilepton channels. This chapter brieﬂy
describes the studies done in the dilepton channel. As in the lepton+jets channel,
the dilepton selection starts with the standard high PT lepton samples. Because the
dilepton events have two leptons and more missing transverse energy from the two
neutrinos in the event, the selection requirements are different than the lepton+jets
event selection. In summary the dilepton selection consists of two leptons with ET >
20 GeV, two or more jets with ET > 15 GeV, ET > 25 GeV, HT > 200 GeV (where
HT 2 PT,lepton + ET.jet.+ ET) and a treatment to remove Z boson events. The two
highest ET jets in the event are assumed to be the two b—jets where one of them is
tagged using the tight Sethx algorithm. Details of the dilepton if selection can be

found in reference [42].

162

8.2 Wb Pairing

In the dilepton channel, there are 2 b—jets (1)1,b2) and 2 leptons (11,12), hence two
possibilities for matching the b—jet with the correct lepton (llbl and 1202 or I102 and
1201 ). We calculate the invariant mass of the lepton and b—jet (Mjb) for all four lb
pairs and make use of the fact that the incorrect pairing is likely to have a large M 12b

value where M 1% is deﬁned as in Equation 8.1.

Mi. = (51+ 13702 — (a + a)? (8.1)

As can be seen in Figure 8.1, the M [2,) distribution for incorrect pairings has a long
tail at large M 12b while the be distribution for correct pairings is populated in the
low be region. For example, if the M 12b value of the llbl combination is the largest
among the four M 12b values, then we know that l 1 b1 is most likely an incorrect pairing.
So we choose the other combination 1le which also implies 12 should be matched to

b1 as the correct combination.

 

 

 

 

 

 

 

A‘Ilzbimax Ont Cpairing Ppairing D 502
no out 1 0.686 i 0.004 0.4 0.1
5,000 0.990 :1: 0.001 0.688 :l:0.004 0.4 0.1
10,000 0.859 :l:0.003 0.722 :1: 0.004 0.4 0.2
15,000 0.627 :1: 0.004 0.812 :1: 0.004 0.6 0.2
22,000 0.369 :1: 0.004 0.959 :1: 0.003 1.0 0.3
30,000 0.226 :1: 0.003 0.994 :1: 0.001 1.0 0.2

 

 

Table 8.1. List of various M 12b max cuts and their performance for dilepton events with

one jet tagged with the tight Sethx algorithm. Higher performance is indicated by a high

cD2 where f. is the pairing efﬁciency (Cpairing) and D (D = 2 x Ppairing — 1) is the dilution.

What about the case where all 4 M 1% values are close to each other? Picking
the correct lb pair is harder in this case compared to a case where the correct and
incorrect pairings have very different M 12b values. The distribution for the maximum
11112,) (M fbmax) value of the four invariant mass values as shown in Figure 8.2 can then

help us distinguish between the correct and incorrect pairs. As expected M 12b max have

163

 

 

hump
HMO. 1117

 

 

 

 

 
   
 

 

 

 

: Mun 12300.04
m :— HB I008
so E—

70 E- nght decrsron
so I . .

5 ..__......-...__.__- Wrong deCISIon

50:

405

30 .L

20 L5?

1o 55"” :;~. 3 .-,
0 hrJl—IHA nl 111'?"I‘|:.‘"r'.:-:-::‘f'-l-I‘l_'-"l .F' ‘1 I--l -l'|L‘p--iu 11102
o 200 400 son 1000

MleZ

Figure 8.1. 0112b distribution for the correct b—lepton pairings (solid) and incorrect b—lepton
pairings (desired).

164

 

 

 

 

50

30

20

10

 

lb
I ‘l I
.III LI] [ I:'l'l
- r—I I-I- ..
I I "l‘llkl‘d ‘_ ‘ l|_-| - X102

lffllllllllll'llll'lllllllT
r I

,.

(D

(D

'0

   

 

Figure 8.2. 11,112,) max distribution for which we made the right decision (dashed) and for
the wrong decision (solid).

165

small values when we made the wrong decision and greater values when we made the
correct decision. An improvement can be achieved by rejecting events that have
M 12b,max below a certain value. By removing events with M l2b,max < 22, 000 GeV2/c4,
we keep most of the correctly paired events and get rid of most of the incorrectly
paired events. Table 8.1 shows the performance of using different M l2b,lnax cuts. For
the events with M l2b,max < 22, 000 GeV2/04, we obtained a pairing efﬁciency of 37%
and purity of 96%. The pairing efﬁciency (ﬁpairing) is the number of events remaining
after the M 12b,max cut over the total number of dilepton candidates containing at least
one tight Sethx b—tag. The pairing purity (Ppairing) is the ratio of the number of
correctly paired events containing at least 1 tight b—tag where the 2 jets are indeed

matched to b quarks over the total number of events with M 121) max > 22, 000 GeV2/c4.

 

Sample 6pairing P pairing £02
1 tighﬁtag 0.369 :t 0.004 0.959 {0.003 0.311
Pretag 0.374 :1: 0.003 0.960 :1: 0.002 0.317

 

 

 

 

 

 

 

Table 8.2. Comparison of pretagged dilepton events with events where one of the b—jets is
tagged by the tight Sethx tagger. Higher performance is indicated by a high CD2 where e
is the pairing eﬂiciency, Epairing’ and D (D = 2 x Ppairing — 1) is the dilution. The loss of
efﬁciency due to b—tagging is not included in the tagged case.

As part of the optimization studies, the effect of b—tagging was also investigated.
Table 8.2 shows the pairing purity and efficiency for single-tagged and pretagged
(before b—tagging) dilepton events. At ﬁrst glance it looks like b—tagging does not
effect the performance since the 6D2 values in Table 8.2 are very close. However
directly comparing the 6D2 values in the table is not the right thing to do. For the
correct comparison between the tagged and pretagged samples, we need to consider
the effect of b—tagging on the pairing purity and also on the amount of background
in the sample. In the dilepton channel after the top charge cuts the background
fraction goes from 44% to 0% once one of the b-jets is tagged. Therefore even though

the pairing purity for the pretag is found to be 96% in the MC, it is diluted by the

166

background for which we have a purity of 0.5. In addition, to calculate 6.02 we must
also consider the b—tagging efﬁciency. Combining the effect of the M 523mm cut with
the b—tagging efﬁciency, we obtained an 602 of 0.185 for the single tight Sethx tagged
case. When no b—tagging is used the CD2 is 0.099, which is signiﬁcantly lower, so we

decided to use the single tight Sethx tagged events for the dilepton channel.

8.3 b Flavor Tagging

For ﬂavor tagging the I} jets we used the same momentum weighted jet charge method
as described for lepton+jets in Section 4.4.2.2. The same selections as listed in Section
4.5 were used. The results for the efﬁciency and purity of the jet charge algorithm

with and without b-tagging are given in Table 8.3.

 

 

# of 0 tags CJQ PJQ
0 0.767 :1: 0.002 0.598 :1: 0.003
1 0.863 :1: 0.002 0.61 :1: 0.003

 

 

 

 

 

Table 8.3. Purity (PJQ) of the momentum weighted jet charge along with the efﬁciency
(am) using the dilepton events from tf MC.

8.4 Backgrounds

The expected number of events for the backgrounds in the dilepton channel were
already calculated for the CDF top cross-section measurement [42] and are given in
Table 8.4 for 955 pb‘1 of data. Remember that for the top charge measurement we
also need to know if any of the backgrounds favor one hypothesis (Standard Model
or exotic model) over the other.

As we did in the lepton+jets channel, for each dilepton background we measured
the background purity (Pb) deﬁned as the number of events that look like Standard

Model over the total number of events (see Equation 6.2). A purity of 0.5 implies the

167

 

 

 

 

 

 

background DIII a prediction Nb

Drell-Yan 0.38ﬁ8;§§ 0 + 0.38
Fakes 0817:3313 0 + 0.81
Diboson 0.0 :t 0.1 0 + 0.1
Total 1.19i539 0 + 0.9

 

 

 

 

Table 8.4. Table of expected background events in the dilepton (DIL) charmel for 955
pb'1 of data. The second column gives the prediction for each background taken from the
CDF dilepton cross-section (a) measurement where one of the b—jets is tight Sethx tagged.
After the top charge analysis cuts, the expected number of background events (N b) is 0.

background is SM like 50% of the time and exotic model like 50% of the time. There

are three backgrounds in the dilepton channel which are described below:

0 Drell-Yan

()ne of the dominant background processes in the dilepton channel are Drell-Yan
events where a Z boson decays to two leptons. We used ALPGEN+HERWIG
samples that include Z,’y —+ If and within the poor statistics obtained after

cuts, we calculated a jet charge purity of 0.47 :l: 0.03.

o Fakes

These are the type of events where one or more of the jets are misidentiﬁed as
leptons in the detector, called fakes. We ran the top charge dilepton analysis
code on W+3 jets MC samples and obtained a purity of 0.49 :l: 0.08, meaning

no charge asymmetry was seen within its uncertainty.

0 Diboson (lI'VlV, 1V Z)

WW and WZ events can pass the dilepton selection cuts if both bosons decay
leptonically and the leptons are chosen as the two leptons in the dilepton top
event. When the dilepton top charge selection cuts were applied to WZ MC
events, no events were left. In order to gain more events, we dropped the

requirement of removing Z boson events and obtained a purity of 0.50 :l: 0.02.

168

Using a WW MC sample, we found a purity of 0.48 d: 0.02. These results are

consistent with 0.5 conﬁrming that there is no charge asymmetry.

Table 8.5 summarizes the charge asynnnetry study on the dilepton background

events. No charge asymmetry is found.

 

Table 8.5. Jet charge purity (P JQ) for dilepton backgrounds and the efﬁciency for accepting
each background.

8.5 Systematics

The sources of systematic uncertainties in the dilepton channel are the same (except
for one) as in the lepton+jets channel and are calculated in the same way. The
error on the event predictions obtained from the dilepton cross-section analysis [42]
include an uncertainty due to acceptance effects. Apart from the effect of systematic
uncertainties on the dilepton acceptance, we studied how the systematic uncertainties
affected the Wb pairing and jet charge efﬁciencies and purities.

There is one additional source of uncertainty in the dilepton channel compared to
the lepton+jets channel. This is due to the polarization of the W boson which refers
to the direction of the spin of the W boson with respect to its direction of motion.
The angle (6*) between the lepton in the W rest frame and the W direction in the
top rest frame is used for the W polarization studies. The relation of 6* with different
W polarization states is depicted in Figure 8.3 where the bold blue arrows represent
the spins of fermions and the bold red arrow represents the spin of the W boson.
The angle 6* is a function of the invariant mass of the E and b (filth) and since we used

Mg) to pick the correct lb pair, we need to assign an uncertainty due to different W

169

 

 

1/2 I 1+ 1/2 ”I" I”
If . ,, ;\\C.-\ .. 7 7m?
7 + "r - negative
W\ V I W direction

I 1

Longitudinally polarized Left handed nght handed

Figure 8.3. 6* for different W polarization states.

 

 

 

Systematics (in %) 61,81,ng Ppairing €JQ P JQ
ISR/FSR 4.6 1.0 1.2 1.9

MC generator 0 0 1.0 -

J ES 4.2 0. 8 ' 0.4 0

PDF ’ 4.1 0. 3 0 0

top mass 7 2 0 0

W polarization 1.5 0 0 0
total 10.3 2.4 T6 T9

 

 

 

 

 

 

 

Table 8.6. Summary of systematics uncertainties (in %) in Dilepton channel.

polarizations. In the Standard Model, the W is expected to be longitudinally polar-
ized 70% of the time and left-handed 30% of the time. We varied the fraction of the
longitudinally polarized Ws from 70% down to 65% and also up to 75% in the tf MC
and checked the effect on the pairing purity and efﬁciency. Varying the longitudinal
polarization fraction by 5% caused a 1.5% increase in the pairing efﬁciency and did
not affect the purity.

The summary of the systematic uncertainties in the dilepton channel is given
in Table 8.6 and corresponds to the systematics discussed in Chapter 7. The total
systematic uncertainties on Cpairingi Ppairinga em and PJQ are 10.3%, 2.4%, 1.6%
and 1.9% respectively. How these are used in the ﬁnal top charge result is explained

in Chapter 9.

170

CHAPTER 9

Signal and Background Estimates

Knowledge is to comprehend knowledge
Comprehension is to know yourself

if you don’t know yourself

What is the point of your studies?

Yunus Emre (1238-1320), a Turkish Poet.

9.1 Expected Number of Events

This chapter describes how we calculate the expected number of signal (NS) and
background events (Nb) that will be used for the top charge result as well as how we
calculate the total signal purity (PS) and total background purity (Pb).

Using 955 pb‘1 of data for the dilepton channel and 695 pb’1 of data for the
lepton+jets channel, we calculated the number of signal and background events we
expect for the top charge analysis. These are calculated by multiplying the predicted
number of events in each channel obtained from the 0 analyses [29, 42] by the total
efficiency (Etotal) which is the product of the pairing and jet charge efficiencies. The
expected number of events for each background was already presented in Chapter 6 for
the lepton+jets channel and Chapter 8 for the dilepton channel. Here we summarize
them again along with the expected number of signal events in Table 9.1. We expect

35.4 :i: 0.4(stat):l:7.9(sys) lepton+jets events and 10.3 :1: 0.4(stat)i1.7(sys) dilepton

171

events, for a total of 45.7 :i:0.6(stat)i8.1(sys) events for the top charge measurement.
In addition we expect to have 1.40 + 0.96 — 0.34 background events, all of which are
coming from the lepton+jets channel since the background is reduced to zero in the
dilepton channel after requiring one b—tag. The error on the background prediction
is statistical only. Since the amount of background is so small and does not affect
the top charge result we did not calculate the systematic uncertainties on it. The
second column in Table 9.1 shows the predictions from the 0 analysis for the number
of background and signal events. The third column is the efﬁciency for accepting
background events due to the top charge analysis cuts. The numbers in the fourth
column show the expected number of events for the backgrounds (Nb) and signal

(NS) obtained by multiplying the second and third columns.

9.2 Calculating Signal Purity

The calculation of the signal purity (P3) is not as straightforward as calculating the
number of signal events. The starting point is to multiply the pairing and jet charge
purities (Ppairing - P JQ) to get a combined purity. However, this product gives the
fraction of events with the correct top charge only if the methods used for Wb pairing
and b-jet ﬂavor tagging are both correct for the event. If one of the methods fails we
get an incorrect top charge. However if both methods fail, we actually get the correct
top charge. For example, assume we have a Standard Model tf event, so t —> W+b
and f —+ W—b. If our pairing method incorrectly matches W+ to the b but then the
ﬂavor tagging method assigns the wrong ﬂavor, declaring the b a b instead, we actually
get the same result (+2/ 3) as expected for the Standard Model case. So considering
the case where a correct result is obtained, one can write PS as the combination of

two pieces, the ﬁrst for when both methods (pairing and jet charge) are correct and

172

Signal

Drell-Yan
Fakes

Total
Signal

Total 1 .
Total Signal 45.

 

Table 9.1. Table of expected signal and background events. The second column shows
the predicted number of events that are taken from the cross-section measurements. The
lepton+jets predictions include the efﬁciency of the lepton+jets event selection with both b-
jets tagged with the loose Sethx algorithm. The dilepton predictions include the efﬁciency
of the dilepton event selection with one of the b—jets tagged with the tight Sethx algorithm.

173

the second for when both methods are incorrect, as shown in Equation 9.1.

P9 = Ppairing ' PJQ +(1— Ppairing)'(1"’ PJQ) (91)

Yet Equation 9.1 is neither complete nor correct. Even though we used b—tags in
the events, we still have events where the selected b—jets are not actually coming from
b quarks. There are only a few of these events but even so we must consider their
effect on the purity. Deﬁning fnonb as the fraction of events where one or more of the

jets tagged as b’s are not actually matched to b quarks, PS can be expressed as

P8 : fnonb ' 0'5 +(1_ fnonb) ' (Ppairing ' PJQ +(1— Ppairing) ' (1 — PJQ» (9-2)

Note that only the events for which the jets are real b—jets contribute to the PS in
Equation 9.1. The non-b jets are incorrect pairings and have no sign correlation with
the associated lepton, so they contribute to PS with a purity of 0.5 as shown in the
ﬁrst term of Equation 9.2. The second term is from Equation 9.1 but multiplied by
the fraction of real b events (1 — fmmb).

Equation 9.2 now has all the pieces but is still not accurate. Remember that we
do not rely on the MC to give us the correct b and non-b fractions. In Chapter 7, we
discussed the uncertainty introduced due to b—tagging and calculated a non-b scale
factor, S Fnonb' To get the correct fraction of non-b events (fnonb) we must multiply

it by the Smeb as in Equation 9.3.

P3 = fnonb ' SFnonb - 0-5 + (1 - f nonb ' S Fnonb) ' (Ppairing - PJQ + (1 - Ppairing) ° (1 - PJQ ))

(9.3)
In addition we do not rely on the jet charge purity from MC but instead did a
calibration study in data as described in Chapter 5. This resulted in a scale factor for
the jet charge method of S F JQ = 1.03 i 0.02(stat):l:0.04(sys). We must also correct
the jet charge purity (P JQ) by the scale factor S F JQ which causes Equation 9.3 to

become:

174

 

 

 

 

 

Dilepton Lepton+jets
f nb 0075 i71001 0.055 :l: 0.0771
s nonb 1.05 :l: 0.05 1.05 :l: 0.05
pairing 0.959 :t 0.003(stat) :l: 0.013(sys) 0.844 :l: 0.003(stat) :l: 0.024(sys)
PJQ < 0.603 :l: 0.005(stat) :t 0.011(sys) 0.608 :1: 0.003(stat) :l: 0.009(sys)
SF JQ 1.03 a: 0.02(stat) :t 0.04(sys) 1.03 i 0.02(stat) :l: 0.04(sys)

 

 

Table 9.2. All of the ingredients, fraction of pairs with no b—jets (fnonb), correction due
to the mistag rate difference between MC and data (S Fnonb)’ purity of pairing (Ppairing),
purity of jet charge (ij) and its scale factor (SF 1(3). to correct the PJQ obtained from
MC for the dilepton and lepton+jets channels.

 

 

 

 

 

Channel PS ' N+ N.
. i0.01(stat) i0.4(stat) i0.3(stat)
Lepton+jets 05810.02 8%)) 20'6i4.7((sys[ 14.8i3'4((8ys]
. i001 stat i0.3 stat :l:0.2 stat
Dllept‘m 0'60i0.02(sys) 6'2i1.0(sys) 4'1i0.7(sys)
:t0.01(stat) :l:0.5(stat) :tG4(stat)
Total 0'59i0.02(sys) 26'8:l:4.8(sys) 18"9:123.4(sys)

 

 

 

 

 

Table 9.3. Signal purity for each channel separately and both channels combined (total)
and the number of SM like (N+) and exotic model like (N_) events.

PS : fnonb ' SFnonb ' 0-5 + (1 _ fnonb ' SFnonb) ' (Ppairing ° PJQ ' SFJQ+

(1_ Ppaii'ing)'(1—PJQ ' SFJQ»

(9.4)

Putting all the ingredients from Table 9.2 into Equation 9.4, we measure the

signal purity (P5) to be 0.58 :l: 0.01(stat):l:0.02(sys) for the lepton+jets channel and

0.60 :l: 0.01(stat):l:0.02(sys) for the dilepton channel. Combining both channels and

taking into account the number of events from each channel, the total signal purity

is R, = 0.59 :l: 0.01(stat):l:0.02(sys). Knowing the signal purity and expected number

of signal events we can further calculate how many Standard Model like events (N +)

and how many exotic quark like events (N_) are expected. We expect a total of

N+ = 26.8 :1: 0.5(stat):l:4.8(sys) and N- = 18.9 :l: 0.4(stat)i3.4(sys) events. These

results are shown in Table 9.3.

bac ' und
n+Jets 695

+
QCD fakes

II

   

  
 

 
  
 
    

o . .
Total 0.52_ '
ton 955 b—
an . . + .
+ . +
+ . + .
1 0+097| 0+09 |

0.73 :l: 0.18 0.68 :l: 0.16

1 II

[nma 1 05400

   

 

 

 

I Total Background ] 0.52 :t 0.01(stat) [ 0.7:“33 [ 0.7:“83 I

 

Table 9.4. Background purity for each charmel separately and both channels combined
and the number of SM like (N +) and exotic model like (N_) events expected.

9.3 Calculating Background Purity

We have already presented the purity for each background in the lepton+jets channel
in Chapter 6. For the dilepton channel we have no background left after the top charge
selection cuts and none of the backgrounds showed a charge asymmetry towards SM or
exotic model events, so we use a total purity of 0.5 :l:0.0 for the dilepton backgrounds.
In this section we will describe how we combine the background purities for the
lepton+jets channel.

The total background purity (Pb,tot.al) can be calculated by summing the N+
values for each background and dividing the result by the total number of events as .

shown in Equation 9.5 where the sum is taken over all backgrounds.

P = Zi(N+)i
Ib,total 21(N+)i + Ei(N_)i

We can not directly use Equation 9.5 because there are two asymmetric backgrounds

 

(am

that have a purity higher than 0.5. These are the QCD and single top backgrounds
as can be seen in Table 9.4. For the backgrounds which we did not expect any charge.

asymmetry and the measured Pb agreed with 0.5 within its uncertainty, we use a Pb

176

 

 

 

NS 91.3 :i: 1.1(stat)i16.2(sys)

Nb 2.8 :l: 1.9(stat)

PS 0.59 :l: 0.01(stat):l:0.02(sys)
Pb,total 0.52 :l: 0.01(stat)

 

 

Table 9.5. Expected number of background and signal pairs together with the corre—
sponding purities.Since the amount of background is so small and does not affect the top
charge result the effect of systemmatic uncertainties were not checked on backgrounds. The
uncertainty on Nb and Pb are statistical only.

of 0.5 i 0.0 when calculating Pb,total- In order to ﬁnd Pb,t0ta.l we need an equation
that combines the asymmetric and symmetric parts of the backgrounds correctly. Let
N1 and N2 represent the amount of the two asymmetric backgrounds (QCD, single
top) and N3 the total amount of the symmetric backgrounds ((W+HF) + Diboson

+ Mistag). Pb.total can then be expressed as in Equation 9.6.

P ___N1-f1+N2-f2+N3-f3
b,total N1 + N2 + N3

 

(9.6)

where f1, f2 and f3 are the fractions of Standard Model like events for QCD, single
top and the symmetric backgrounds respectively. Using Equation 9.6 we measure the

total background purity (Pb,total) as 0.52 :t 0.01(stat).

9.4 Summary

Table 9.5 shows the total signal and background estimates for the top charge mea-
surement. Note that the estimates in Table 9.5 are twice of what was shown in Table
9.1. This is because we have two top charge measurements per tf event, one from
the t decay side and another from the f decay side. The calculation of the combined
signal purity (P5) was more complicated. While obtaining PS we considered that if
the pairing is wrong and if the jet charge is also wrong we still get the same answer
as having everything correct. There is also a small probability that the b-jets were
misidentiﬁed, in which case they will have a random charge correlation with the lep—

ton. The jet charge purity was also corrected by a scale factor obtained from data.

177

The calculation of the total background purity (Pb,total) was based on combining the
charge symmetric and asymmetric parts of the background correctly where 0.5 :l: 0.0
was used for the purity of the charge symmetric backgrounds. The results for PS and
Pb,total are srunmarized in Table 9.5. We expect 91.3 :l: 1.1(stat):l:16.2(sys) signal
events and 2.8 :i: 1.9(stat) background events. We expect to classify the signal events
(as SM or exotic model like) correctly 59 :l: 1(stat):l:2(sys)% of the time. In addition

we expect the background events to look like SM top events 52 i 1% of the time.

178

CHAPTER 10

Statistical Treatment

The null hypothesis is never proved or established, but
is possibly disproved, in the course of experimentation.
Every experiment may be said to exist only to give the facts
a chance of disproving the null hypothesis.

R. A. Fisher (1890-1962), an English statistician.

For the measurement of the top quarks charge, we count the number of Wb pairs
that support the Standard Model (SM) and those that support the exotic model
(XM). A positive lepton combined With a I} jet or a negative lepton combined with a
b—jet are assigned as a SM—like pair, whereas a positive lepton combined with a b—jet
or a negative lepton combined with a b—jet are assigned as a XM-like pair. The total
number of pairs that are SM-like is deﬁned as N+ while the total number of pairs
that support the XM is deﬁned as N... Once we obtain N4. and N- from the data,
we can compare the measurement with the Standard Model expectation and quantify
the degree of evidence in favor of the SM over the XM. In this pursuit, we would like
to use a parameter of interest that has quite different probability density functions
between the two hypotheses. We have chosen the fraction (f+) of events following

the SM as our parameter of interest and it is expressed as in Equation 10.1.

N4

= W (IO-1)

f+

179

In our MC, f+ should be equal to 1 since the MC was generated according to the
SM. However, due to the limitations in our methods for pairing and b-ﬂavor tagging
this is not always the case, but we still expect f+ to be close to 1 if the result is
consistent with the SM given the performance of our methods (refer to Section 4.2
for more details).

If we had an inﬁnite amount of statistics our result would be the measured value
of f+. However with ﬁnite statistics we can just ﬁnd the best estimation for f+ and
compare it with the SM expectation. In order to do this, the Particle Data Book [43]
advocates two approaches: the Bayesian and frequentist. We have exploited both

approaches for this result and they are described below.

10.1 Proﬁle Likelihood '

A common method used in high energy physics to ﬁnd the most likely value of a
parameter of interest is a maximum likelihood approach [44, 45] that selects the
hypothesis (H) which maximizes the conditional probability of a set of observations
X assuming H is true P(X [H ) The maximum likelihood is calculated based on the

distribution of the parameter of interest, in our case f+, as shown in Equation 10.2

I1

L(f+|X) = 1] Poem) (10.2)

i=1
where we have n independent observations X = (X 1,X 2, ..,X n). The top charge

measurement, like most other measurements, involves not only a parameter of interest
but also nuisance parameters that are incompletely known and add to the uncertainty

of the parameter of interest. In our case, we have 4 nuisance parameters:

NS: Number of signal events
PS: Purity of the signal
Nb: Number of background events

Pb: Purity of the background

180

With the nuisance parameters, 6=(NS, PS, Nb, 1],), the likelihood function can be
written as in Equation 10.3 where the maximum occurs when the unknown nuisance

parameters are replaced by their maximum likelihood estimates.

H

X) = II P(Xi|f+,0) (10.3)

i=1

L(f+,0

 

If the likelihood function is calculated at speciﬁc values of f+ = f+0 and then
divided by the maximum likelihood where f+ is not restricted to a speciﬁc value
we get a likelihood ratio (Equation 10.4). The maximum likelihood estimates are
substituted for both f+ and the nuisance parameters for the denominator. In the
context of nuisance parameters the function A is also called the “proﬁle likelihood”

[46].

 

_ mar(L(f+0,6|X);6)
“mm ‘ max<L<f+,6|X>;f+.e

Note that the denominator is just a number obtained by ﬁtting f+ along with all the

(10.4)

nuisance parameters. The advantage of a proﬁle likelihood is that all the nuisance
parameters are eliminated from the likelihood function and the likelihood is just a
function of f+. Further taking —2Ln/\ corresponds to a X2 distribution [46]. Larger
As correspond to smaller X23. So the minimum point of the —2Ln)\ distribution with
respect to f+ (see Figure 10.1 as an example) gives the best value of f+ for which the
nuisance parameters have their best estimates. For more details on proﬁle likelihood

see reference [46].

10. 1 . 1 Nuisance Parameters

As mentioned earlier, we have 4 nuisance parameters: the number of signal events
(N3), the purity of the signal (PS), the number of background events (Nb) and the

purity of the background (Pb). We have already given the. expected number for each

181

of these nuisance parameters in Table 9.5. Here I will remind you how each of these
parameters is calculated and show the relation of the nuisance parameters with our
parameter of interest (f+) which is the fraction of SM-like Wb pairs.

The number of expected signal events (N5) is the number of events left after the
Wb pairing (PR) and ﬂavor tagging (FT) criteria are applied. So NS includes the
efﬁciency of the PR and FT methods in it. Nb is the amount of all the backgrounds
added together and it also has the effect of the efﬁciency of the PR and FT methods
included in it. PS is the signal purity calculated as described in Section 9.2. Pb
is the probability that all the backgrounds look like the Standard Model, so it is a
combination of all the individual purities from the individual backgrounds. This is

all summarized in the following table.

 

NS expected number of signal events after PR and FT

Nb expected number of total background events after PR and FT
PS expected purity of the PR and FT methods on the signal

Pb expected charge asymmetry for the background

 

 

 

 

The f+ shown in Equation 10.1 can now be written as a function of these nuisance
parameters. This is illustrated in the following equations where < N+ > and < N- >

are the means of the Poisson distributed N+ and N...

< N+ > = N+f+ + N“(1 — f+) + N; (10.5)
<N_ > = N‘f++N+(1—f+)+Nb‘ (10.6)
where : (10.7)
N+ = PSNS (10.8)
N— : (1—PS)NS (10.9)
N; = PbNb (10.10)
A7,: = (1 — Pb)Nb (10.11)

182

10.1.2 Likelihood Expression

Our likelihood expression has ﬁve terms:
L : LS ' Lb ' L03 ' LPS ' L121) (10.12)

A signal part (Ls) which is Poisson distributed, the background (Lb) which is Gaus—
sian distributed, a term related to the uncertainty on the number of signal events
(L03) which is also Gaussian distributed, plus purities for the signal (L p3) and back-
ground (L pb) which are Gaussian distributed. The signal term (LS) can be expressed

8.82

:r+ (—<N+>) N r— (—<N_>)
LS=LS+-LS_=<N+> e .< _> e

 

 

33+! N (10.13)

where 17+ and :l:- are the number of events following the +2 / 3 and -4 / 3 hypotheses
in the data, respectively.
The second term in Equation 10.12 deals with the background component and can

be written as:

20
Lb = ———e Nb (10.14)

where Nb and UNb are the number of background and its uncertainty from the back-
ground prediction studies. yb is chosen from a Gaussian distribution whose mean is

Nb. The third term of Equation 10.12 considers the uncertainty on the signal:

ills—"N92

1 7 I 20
L09 _ 6 NS

‘ — ONSV27T

where NS and CNS are the expected numbers for the number of signal and its uncer-

(10.15)

tainty respectively. ys is chosen from a Gaussian distribution whose mean is NS.
The fourth and ﬁfth parts in Equation 10.12 are the the purity terms for signal and

background respectively:

183

 

(z -P')
1 — ZUPQS
L _, ' 10.16
P3 0P3 T77? S ( )
_(zrj 4%)2
1 20
L =.______ P5 10.17
P1. 0,..me ( l

where PS (Pb) and Ups (apb) are the measured signal (background) purity and the

error on it. Zps (sz) is chosen from a Gaussian distribution whose mean is PS (Pb).

10.1.3 Calculation of the Proﬁle Likelihood

To solve for f+, we must ﬁnd the minimum of the total likelihood expression given in
Equation 10.12 which is the product of all the likelihood expressions from Equation
10.13 to 10.19. To do this, we take the partial derivatives of the total likelihood
expression with respect to each nuisance parameter and set that equation equal to

zero acquiring a system of nonlinear equations.

 

 

 

 

(f ['68 = 0 (10.18)
g}: = 0 (10.19)
00165 = 0 (10.20)
g}: = 0 (10.21)

Since the computations are difﬁcult to perform by hand, appropriate software has
been implemented within the MIN UIT package[31], which is a widely used parameter
ﬁtting program in high energy physics.

As mentioned earlier, the likelihood curve (the numerator of Equation 10.4) is
calculated by scanning through different values of f+ and at each value we let MI-

NUIT minimize the likelihood for all the nuisance parameters. Figure 10.1 shows

184

 

‘2
llllllll'l'lllllllllTl'l'

 

4670
4675
4680

 

.1....|....1....1....1LL..LL..rni.
-‘I -0.5 0 0.5 ‘I ‘I .5 2
0"

Figure 10.1. The —2LnA curve obtained from one pseudo-experiment assuming the SM
is true.

the —2L71.)\ curve assuming the SM is true obtained from one pseudo-experiment. A
pseudo-experiment is constructed by randomly generating N+, N- and the nuisance
parameters given the expected values obtained for each from MC studies. In other
words, we generate fake data based on our predictions. Below is the list of variables

and how we simulate them in pseudo-experiments:

30+: draw a random number from a Poisson distribution whose mean is N1".

33': draw a random number from a Poisson distribution whose mean is N‘.

yb: draw a random number from a Gaussian distribution whose mean and 0 are
the expected number of background events (Nb) and its error (aNb).

ys: draw a random number from a Gaussian distribution whose mean and a are
the expected number of signal events (NS) and its error (0N3)

zps: draw a random number from a Gaussian distribution whose mean and a are
the expected signal purity (PS) and its error (UPS).

.2}: : draw a random number from a Gaussian distribution whose mean and a are

b
the expected background purity (Pb) and its error (Opb).

If we repeat the above procedure 100,000 times and pick the minimum of the like-
lihood curve as f+ and make a distribution of these values, we get the red curve
in Figure 10.2. This is the f+ curve assuming the SM is true and it peaks at 1 as

expected. The black curve is generated in the same way but assuming the XM is true

(f+ = 0)-

10.2 Extracting a Limit

Once we have obtained the N+ and N_ values from our data and used them to draw

the —2Ln)\ curve, the minimum of the curve is the maximum likelihood estimator

186

 

 

 

 

13 :
5W:
E :
t i—
am:-
i t

mono-_—
‘a’ I xu SM
31m:—
0- :

1m:—

mo}—

=_ lllllll lllllLl nilrlili
-0.5 0 0.5 1 1.5

Figure 10.2. f+ distributions for the Standard Model (SM) and exotic model (XM)
hypothesis obtained from 100,000 pseudo-experiments.

for f+. If we had a large amount of data, this would be our result. However given
our small data sample, we instead followed a hypothesis testing procedure which is
a common frequentist method. The hypothesis test [44, 45] is a statistical test that
rejects or accepts a null hypothesis (H0) given a data sample with two kinds of events

corresponding to hypotheses H0 or H1.

10.2.1 Hypothesis Test

The theory of hypothesis tests is based on the frequency interpretation of probability
and allows the rejection or non-rejection of the null hypothesis based on the proba-
bility of mistakenly inferring that the data support the other hypothesis more. Here
we will brieﬂy describe the theory of hypothesis. tests.

One starts by choosing a test statistic (X) that is a variable which provides some

discrimination between the two hypothesis H0 and H1. In a hypothesis test, before

187

making a measurement of X, one should identify a critical region or rejection region
(R) that is a set of values of the test statistic for which the null hypothesis is rejected
in a hypothesis test. The rejection region includes the values in an area which is

calculated as:

Xcut
o = / [(XIH0)dX (10.22)

—00

where f (X IHO) is the probability density of X given H 0 and X cut is the value of X at
the decision boundary that separates the rejection region from the rest of the region
(see Figure 10.3 as an example).

Given the data point corresponding to the observed value of X (X data), the deci-
sion can be made depending on whether the X data lies within the rejection region R
( X data 6 R) or outside R (Xdata Q’R). This gives us four possible outcomes as shown
in Table 10.1. If Xdam falls in R then H1 is true (case A). If it does not fall within
R then H0 is true (case C). But there is still some probability to fall within R and
be wrong meaning H0 is the true hypothesis(case B). There is also some probability

to be outside of R and be wrong meaning H1 is the true hypothesis (case D).

 

 

Case position of X data chosen hypofhesis
A Xdata E R H1
B Xdata E R H0
C Xdata ¢ R H 0
D X data g R ‘Hl

 

 

 

 

 

Table 10.1. The four different possible outcomes from a hypothesis test.

 

DECISION
Reject H0 Don’t reject HO
HO Type 1 Error (B) Right Decision (C)
TRUTH H1 Right Decision (A) Type II Error (D)

 

 

 

 

 

 

 

Table 10.2. Different decisions in a hypothesis test and the corresponding case from
Table10.1 in the parenthesis.

If the decision is A or C, we have chosen the correct hypothesis. If it is B or D, we

have the wrong conclusion. In the ease of a wrong conclusion: case B is called a

188

f(X)

Figure 10.3. An example with the parameter of interest X for two hypotheses, H 0 and
H1. The ﬁlled area under H0 is the chosen rejection region. If the observed X falls ill this

1.5

0.5

 

 

 

 

 

 

 

 

region H0 is rejected otherwise H0 is accepted.

189

XCUI
reject H0 ~';_i,---------'5-'s— accept H0
f(X|H,)
f(XlHo)
rejection
region (R?
1 2 3 4

 

“mistake of the ﬁrst kind”, while case D is called a “mistake of the second kind” (see
Table 10.2). The probability to reject H0 if H0 is true (case B or an error of the ﬁrst
kind) is given by Equation 10.22. The probability to accept 110 if H1 is true (Case D
or an error of the second kind) is calculated as:
[3: /Xoof f(X I Ill) (10.23)
cht
where f (X |Hl) is the probability density of X given H1. In statistical terms, a is

called the signiﬁcance of the test, while 1 — ,6 is called the power of test.

 

    
     
 
 

 

 

 

 

 

 

 

 

‘ :
acou—
» :
rm.—
1
l E XM
3 1am:—

I. ; rejection
moo: region
ME—

0

 

-o.5 0/ ‘ 'o.5' I 1 "‘1.5' f
f+.cut=0'2 +

Figure 10.4. f+ distributions obtained from pseudo—experiments assuming the Standard
Model (SM) or exotic model (XM). The ﬁlled red area is the a priori 1% for a that corre
sponds to a f+ of 0.2.

190

10.2.2 The Null Hypothesis and Test Statistic for the Top Charge Anal-

ysis:

In the top charge analysis, we need to choose the Standard Model (SM) or exotic
model (XM) as our null hypothesis. The null hypothesis should be chosen as the one
for which errors of the ﬁrst kind are more important than errors of the second kind.
The reason for this is that a (the error of the ﬁrst kind) is chosen by the experimenter
and then the rejection region is based on (1. Considering the experimental support
in favor of the SM, incorrectly rejecting the SM is more important than incorrectly
accepting it. Therefore, we take the SM as our null hypothesis.

Our test statistic is the parameter of interest (f+) that was introduced at the be-
ginning of the chapter. If we perform pseudo-experiments using the proﬁle likelihood
and our nuisance parameters, we get a f+ distribution peaking at 1 for the SM and

a distribution peaking at 0 for the XM as shown in Figure 10.4.

10.2.3 Choice of a for the Top Charge Analysis and the Calculation of
1 — B

As we have already mentioned, a is an a priori value chosen by the experimenter and
once a is determined, )6 is also determined. For this analysis, we chose or = 0.01,
meaning the probability of incorrectly rejecting the SM is 1%. This implies that the
rejection region covers 1% of the area under the SM distribution (see Figure 10.4).
For an a = 0.01, the corresponding boundary of the rejection region is 0.2.

To ﬁnd the relationship between a and B we performed pseudo—experiments. We
scanned the XM curve in Figure 10.4 by throwing random f+ values. We calculated
the area under the SM curve as given in Equation 10.24 for each f+ value. In other

words, we calculated the following integral

 

f+PE ,_
y: / f(X SM)dX (10.24)

00

191

where f+pE represents the f+ value chosen for a speciﬁc pseudo—experiment. The
resulting distribution is shown in Figure 10.5. The dashed line in the ﬁgure is located
at our a priori chosen a value of 0.01 and the area to the left of it corresponds to
1 — ,8. We can see now how the 1 — [3 increases as we choose (shift the dashed line
to) higher or values. The area to the left of a = 0.01 is 81% of the whole area and is

the level of rejecting the XM if SM is true.

p—vefucs fer Sill if )131 true

 

 

 

 

 

 

 

3
500 “=19
I CDF Runll Preliminary, L==955plr1
400:-
: (I = 0.01
3003 1"3 = 0.81
200:-
100}
n: 1 — F‘ l _L _ ._ A . l
'0 0. 01 0.02 0.03 0.04 0.0 5
p-valuos

Figure 10.5. The p—value distribution for the SM assuming the XM is true. The dashed
blue line represents the a priori a value of 1% (probability of incorrectly rejecting the SM
if SM is true) and its corresponding 1 — {i value or Power of Test (probability of rejecting
the SM if XM is true).

10.2.4 p-value

In high energy physics, we often report a p—value instead of a as the signiﬁcance of

the test. The p—value is defined as:

f+data _
p —— value = / f(X|H0)dX (10.25)

00

192

The p—value deﬁnition is equivalent to that for a. but the integral is evaluated at
the measured f+ value (f+data) rather than at an a priori chosen value. The p—value
can be interpreted as the probability of getting a result as extreme or more extreme
than the one we observed if the proposed null hypothesis is correct. A small p—value
provides evidence against the null hypothesis. If the p—value is less than a, we reject

the null hypothesis; otherwise, we accept the null hypothesis.

10.2.5 Interpretation of the Possible outcomes

When we perform our top charge analysis on data, we will calculate a p—value. As
explained above, if the p—value is greater than a = 1%, meaning outside of the
rejection region, the measurement will be therefore consistent with the SM (null-
hypothesis). The signiﬁcance level of the test would be the a value, i.e. 1%, while the
power of the test or the probability that the test will reject a false null hypothesis is
given by 1 — ,13. In our case, it corresponds to the probability to reject the SM if the
XM is true. This probability is calculated as 81% in Section 10.2.3. So if our p—value
is greater than a, we will reject the XM with an 81% CL, but if the p-value is smaller

than a, we will reject the SM with 99% conﬁdence.

10.3 Bayesian Treatment

Besides the frequentist approach, we also tried a Bayesian treatment which reﬂects the
degree of belief for a given hypothesis, while the frequentist approach tells more about
the conﬁdence of accepting or rejecting the hypothesis. Since there is no direct analogy
to the p-value from the frequentist treatment in the Bayesian framework, we can not
directly compare results obtained from the different treatments. In the Bayesian
structure instead of generating pseudo-experiments based on our expectations, we
require prior probabilities for the SM and XM. Even though we believe more strongly

in the SM due to the great amount of experimental evidence we give the SM and XM

193

equal probabilities to be true. In other words, f+ = 1 or 0 are equally probable. The
Bayesian result will tell us how much our prior beliefs change in the light of observed
data (a posteriori). Below is the Bayes’ theorem written considering SM and XM as

the two hypotheses.

P(SMlX) _ P(X|SA.I)*P(SM)
P(XMIX) _ P(X|XM) * P(XM)

 

(10.26)

where the individual terms are described below:

P SM |X )2 posterior probability of the Standard model (f+ = 1)
P X M IX ): posterior probability of the exotic model (f+ = 0)
P XISM): likelihood at f+ = 1

(

(

(

P(XlXM): likelihood at f+ = 0

P (S 1): prior probability of the Standard model
(

P X M): prior probability of the exotic model

 

 

 

2Ln(BF) Strength of Evidence
0-2 Not worth more than a bare mention
2—6 Positive
6—10 Strong
> 10 Very Strong

 

 

 

Table 10.3. Standard scale for the Bayes factor [47].

From Equation 10.28 we deﬁne the Bayes factor (BF) as the ratio of posterior
odds divided by the ratio of prior odds.

P(XISM)

BF : _—
P(X|XM)

(10.27)

Assuming P(SM) and P(XM) in Equation 10.28 to be 1 for both hypotheses and given
no systematic uncertainties, the Bayes factor reduces to a simple likelihood ratio. In

our case, we just evaluate the likelihood at X = 1 and X = 0 and take the ratio.

194

To include systematics we integrate separately the numerator and denominator over
the nuisance parameters. The BF is commonly quoted as 2Ln(BF) and the measured
value compared to the standard BF scale given in Table 10.3. The higher the value

the stronger the degree of evidence for the Standard Model.

10.4 Summary

In this chapter two different statistical approaches that will be used for quoting our
top charge result were presented. The ﬁrst approach is frequentist for which we used
a proﬁle likelihood along with a hypothesis test. From data we will measure the
fraction of SM—like events (f+) and report a p—value. We chose the probability of
incorrectly rejecting the SM if the SM is true to be a = 1%. We also calculated the
probability of rejecting the SM if the XM is true as 81%. Accepting or rejecting the
SM will depend on our p—value being larger or smaller than the chosen a = 1%. The
second approach is Bayesian. For the Bayesian result, we will calculate the Bayes

factor (BF) and quote 2Ln(BF).

195

CHAPTER 11

Summary and Results

Experimental confirmation of a prediction is a
measurement, but an experiment disproving a prediction is
a discovery.

Enrico Fermi (1901—1954), an Italian physicist.

We have completed the ﬁrst measurement of the top quark’s charge from CDF
using both the lepton+jets channel and the dilepton channel. We used CDF data with
an integrated luminosity of around 1 fb‘1 for the measurement. In the Standard
Model (SM) the top quark is expected to have a charge of 2/ 3 but an alternative
theory (XM) has been proposed with the charge being 4/ 3. To determine the top’s
charge we needed three components: the charge of the W boson, the ﬂavor of the b
quark and the correct pairing between the W boson and b quark. We use the charge
of the lepton (electron or muon) from the leptonically decaying W to determine the
W ’3 charge. The ﬂavor of the b—jet is assigned using a momentum weighted jet charge
algorithm. In the lepton+jets channel (t? —> ll/I—ijj) we kinematically reconstructed
the events using a X2 ﬁtting technique to get the correct Wb pairing. For the dilepton
channel tf —+ lull/(3b we used the invariant mass of the lepton plus b—jet.

After knowing the correct Wb pairing and the ﬂavor of the b—jets, we count and
assign each Wb pair to be Standard Model like (SM-like) or exotic model like (XM-

like). Using 695 pb"1 of data for the lepton+jets channel and 955 pb‘1 of data for

196

 

 

 

 

 

 

 

 

 

cl’lannel cuts [b pairing cuts jet charge cuts SM XM

Lepton+Jets 91 75) 48 51) 94 pairs 94 53 41
Dilepton 31 (33) 10 (11) 16 pairs 17) 9 7
Total 122 (108) 58 (6'2) 110 pairs (111) 62 48

 

 

Table 11.1. The observed number of Standard Model like (SM) and Exotic Model like
(XM) Wb pairs for each channel along with the expectations shown in parenthesis. The
second column shows the number of events after the lepton+jets/dilepton event selection
cuts. In the third column are the number of events left after pairing. The fourth column
gives the number of Wb pairs for which the b—jet charge was calculated using the momentum
weighted jet charge algorithm. Finally the last two columns show the number of SM and
XM-like pairs in our data.

the dilepton channel, a total of 110 Wb pairs were found. Out of the 110 Wb pairs,
62 had a SM signature with t —> W+1) or t —> W—f) resulting in a charge of 2/3 or
—2 / 3. The remaining 48 Wb pairs exhibited the XM signature resulting in a charge
of 4/ 3 or -4/3. Table 11.1 shows the ﬁnal data yields after each analysis cut. The
details of the lepton+jets and dilepton data yields can be found in Appendix B. We
used the number of SM-like events and XM-like events to measure various statistical
results that will be the topic of the next section. Figure 11.1 shows the data (points)
for the product of the W-charge and the associated b—jet charge for the lepton+jets
events compared to distributions obtained from MC for signal and backgrounds. Note
that W-chargexb—jet-charge is negative for SM—like events and positive for XM-like
events. A similar distribution for the dilepton events is shown in Figure 11.2. The
comparison of different kinematic distributions such as X2, number of tracks and the
PT of the tracks between the data and MC can be seen in Appendix C.

11. 1 Results

We decided to report our results using both a frequentist and a Bayesian approach.
For the frequentist method we used a proﬁle likelihood method to measure the fraction
(f+) of events that have a SM—like signature. Using 62 SM-like and 48 XM-like Wb

pairs as inputs for N+ and N- to the profile likelihood (A) we ﬁt for the fraction

197

CDF Run II prellmlnery L+J, mph-1
I Data

  
 
  
 
   

Standard Exotlc I Signal MC

25 Model - W+HF
-lee 060
20 - Dboeon
I Mistag

- elnglo Top

 

10
j 5
0
—1 —O.5 O 0.5 1
W Charge 8 Jet Charge

Figure 11.1. The W—chargexb—jet-charge points showing the number of SM—like and XM-
like data events (black squares) on top of the distributions obtained from signal and back-
ground MC sarnplas for the lepton+jets channel in 695 pb‘l.

, CDF Run II preliminary DIL. L=955 pt“
I Data
I Signal MC

    
 
  

Events

IOAMu-AOIQV

Exotic
Model-Like

 

   

—0.5 0 0.5 1

W Charge 8 Jet Chemo
Figure 11.2. The W—chargexb—jet—charge distribution showing the number of SM—like and
XM-like events in data (black squares) on top of the expected distributions obtained from

signal MC sample for the dilepton channel in 955 pb—l. There are no background events
for dilepton channel therefore no distribution for backgrounds.

198

(f+) of SM—like events and obtained 0.88 as the best ﬁt f+ value. Figure 11.3 shows
the —2.Ln/\ curve. For our f+ value of 0.88, we integrated the area under the SM
distribution and obtained a p-value of 0.35. Since our p-value is greater than our a
priori value of a = 0.01 (the probability of incorrectly rejecting SM), we exclude the
exotic quark hypothesis at an 81% conﬁdence level as explained in Section 10.1.2. We
also computed the Bayes factor as described in the previous chapter. For our Bayesian
approach, we calculated a Bayes Factor (BF) of 2.Ln(BF)=8.54 which translates into
the conclusion that the data strongly favors the Standard Model over the exotic

model.

CDF Runll Preliminary, LII9.">."iptr1

 

mo.)

«‘45
450

455

 

IIIIIII’]IIIIIIIITIIIFIIII
—+.
+
- II
9
CD
on

 

144111l1111‘l11111111 lLlllllllll

-05 0 0.5 1 1.5 2

k

 

0
‘

Figure 11.3. —2L-n/\ curve for the pairs observed. The best f+ found is 0.88.

This was the ﬁrst measurement of the top charge at CDF. The measurement was
done with close to 1 fb‘ 1 of data using the top decay products. We classiﬁed the data
events as SM-like or exotic-like depending on the charge of the b—jet and the associated
W boson. The data agree with the Standard Model expectation of a charge of 2 / 3

and excludes the exotic model case at an 81% conﬁdence level.

199

CDF Runll Preliminary, =955pb'1

 

8

E“
'3

-value =0.35

I llllllIIIIIIIITIIITIIIIIIIIIII

 

 

§aeu
i1“

 

 

Figure 11.4. f+ distributions for SM and XM. The red arrow indicates the observed f+
value of 0.88. The area to the left of 0.88 under the SM curve is 0.35.

200

APPENDIX A

Charge Bias

A bias was found for the jet charge algorithm between b and b—jets in MC. The purity
of the jet charge (J Q) algorithm obtained using only b—jets was different from the
purity obtained using only b—jets. To determine where the bias was coming from, we
ﬁrst looked at different track types. There are two types of tracks at CDF, offline
and secondary vertex. Secondary vertex tracks are chosen from offline tracks with
tighter cuts on the track momentum, silicon information and impact parameter. We
have checked if a similar asymmetry exists when ofﬂine tracks are used instead of
secondary vertex tracks. The discrepancy was worse with ofﬂine tracks. Using offline
tracks, the JQ purity is 0.616 3:: 0.005 and 0.643 :i: 0.005 for b and b—jets respectively.
The comparison for the jet charge distributions between b—jets and b—jets using offline
tracks (top plot) or using Sethx tracks (bottom plot) can be seen in Figure A.1. It
can be seen that the b—jet charge distribution is shifted more to the positive side than
the b—jet charge distribution is shifted to the negative side. The reason for this bias
was suspected to be an excess of positive charges in an event. Figure A.2 shows the
x and y coordinates of the primary particles coming from the interaction point that
are associated with negative (left plot) or positive (right plot) tracks. An excess of
positively charged particles is seen, notice there are more dots in the right-hand plot.
This is believed to be the result of interactions between particles from the collision

and the detector’s material which produces more proton (+) tracks than anti-proton

201

(-) tracks. Looking at the PT distribution of the positive and negative particles in
Figure A.3, we can also see the excess of positive particles at low PT. One other
possible source of charge bias is from errors made when assigning a charge to the
tracks at the reconstruction level. This has been conﬁrmed by comparing the number
of positively and negatively charged particles at MC generator level with the number
found at the detector reconstruction level. These studies are all done with the top
MC sample. We conﬁrmed that the inconsistency between b and b purity observed
in the MC also exists in data by looking at dijet data. The results are shown in
Table A.1. Refer to Chapter 5 for the explanation of how the jet charge purity is

measured in data.

 

Pb Pb
Ofﬂine tracks 0.530 :1: 0.006 0.565 :1: 0.006
Sethx tracks 0.547 :t 0.006 0.544 :1: 0.006

 

 

 

 

 

Table A.1. The jet charge purity Pb (P5) for b (b) jet candidates calculated with offline
tracks or with secondary vertex tracks using dijet data. Sethx tracks have less bias than
the offline tracks.

202

 

 

 

    

 

 

 

 

 

 

 

 

 

 

 

 

a
_. mam-nun
mf' pig-0.51s one»
399—
,_
zoo_.
100 l—. . .4
e:
-I

 

 

 

munch-en

—- bbar J0 dlsinbullon

ﬁlom “-0.0“
bnammmon

m - 0.634 61- am

 

Figure A.1. The jet charge distribution for b (black line) and b (red line) jets using ofﬂine
tracks (top plot) or using secondary vertex tracks (bottom plot).

203

 

 

 

 

     

-30 -20 -10 ll 10 an
obspVx
+ tracks
‘ it. 7

. ' -, I" " . ‘ :
J . " . 'trra‘1d.£‘ if

 

 

I I J I I I l l I I I I I J I L A I I I I I I I I I
40 40 -10 0 10 20 30
obspVx

Figure A.2. Vertex of the positive (right) and negative (left) tracks on the :r — y plane.

V3 (Vy) shows the a: (y) position of the vertex.

204

Anhn
'UUU

 

8000

7000

8000

5000

4000

Ill|||l|lllllllfllflllllllllllilllllllllllll

 

 

 

 

4 .5
PH

Figure A.3. PT distribution for the positive (red line) and negative (blue line) particles
that come from the interaction point.

205

APPENDIX B

Data Yield Details

The number of events in the lepton+jets channel after each analysis cut are given in
Table B.1. The events are separated into three categories depending on the detector
subsystem the lepton is observed in: CEM electron, CMUP muon or CMX muon.
For example, the 727 it— events with a CEM electron were reduced to 53 events after
tagging both of the b—jets. After the x2 cut, the number was reduced to 29 events of
which the leptonic b—jet charge was deﬁned for all, but the hadronic b—jet _charge was
defined for only 28.

 

 

L+J cuts >= 21.0.9 x2 cut leptonic b deﬁned hadronic b deﬁned
CEM 727 53 29 79 28
CMUP 310 28 13 13 12
CMX 91 10 6 6 6

 

 

 

 

 

 

 

 

Table B.1. The number of lepton+jets (L+J) events after the lepton+jets selection (col-
umn 2), requiring a double b—tag (column 3) and x2 cut(column 4). The last two columns
Show the number of measurements for the leptonic side and hadronic side respectively.

Remember that we have two top charge measurements for each event, one from
the leptonic side and one from the hadronic side, as long as the jet charge algorithm
can be applied on the tagged jets. A breakdown of how the events are divided between
the SM and XM cases are presented in Table B2 and Table B.3 for the leptonic and
hadronic sides respectively. The second column in these tables displays W charge

(WQ) and b—jet charge (J Q) signs. For example a “+-” indicates the charge of the VV

206

 

 

 

 

 

 

 

L +7 :Ieptonic side W'Q JQ electron muon total
SM - + 10 5 15
SM + — 9 4 13
XM — — 4 5 9
XM ++ 6 5 1 1

 

 

Table B.2. The results from the leptonic b—jet side of the lepton+jets events showing
the SM-like or XM-like Wb pairs depending on lepton type (electron or muon). The posi—
tive/ negative signs in the second column indicates the signs of the charge of the W boson
and the associated b—jet. For example a “+-” implies W' boson charge is + and the b—jet’s
charge is -.

 

 

L + J :hadronic side VVQ J Q electron muon total
SM —+ 9 I 10
SM +— 9 6 15
XM — — 6 9 15
XM ++ 4 2 6

 

 

 

 

 

 

 

Table B.3. The results from the hadronic b-jet side of the lepton+jets events showing
the SM-like or XM-like Wb pairs depending on lepton type (electron or muon). The posi-
tive/ negative signs in the second column indicates the signs of the charge of the W boson
and the associated b—jet. For example a “+-” implies W boson charge is + and the b-jet’s
charge is -.

boson was positive while the charge for the associated Sethx tagged jet was found to
be negative. Notice that the product of WQXJ Q is always negative in the case of the
SM and is always positive in the case of the XM. The third and fourth columns show
how the events are distributed based on lepton type, electron or muon. The dilepton

channel results for the W charge and b—jet charge (JQ) are shown in Table B.4.

 

 

Table B.4. Results from the dilepton events showing the W charge (WQ) and b—jet Charge
(JQ). The 1st b—jet column is the highest Err b—jet. The 2nd bjet column is the other b—jet

in the event.

 

Dilepton WQ JQ 131, b jet 2nd 6 jet
SM —+ I 3
SM +— 4 1
XM —— 3 2
XM ++ 2 0

 

 

 

 

 

207

APPENDIX C

Data MC Comparison Plots

The distributions for various kinematic variables in data are compared to the expec-
tations obtained from MC samples for signal and background. All of the MC plots

are normalized to the data area.

208

 

I M2Ib lager of the pair |

. Run II preliminary DII. L=955 pb"

 

   
  

10

- data

'signaIMC

o5
lillllllll‘r‘lITllii

h

 

 

 

       

' 10000 20000 30000

 

 

   
 

 

40000 50000 60000
uzib, eevz
mm larger of not the pair |
or sun ii preliminary DIL, L=955 pb"
- data

signalMC

    

 

 

10000 20000 30000 400mm 0000 80000 ammo
lillzlb, eevz

Figure C.1. At the top is the M 12b distribution of the Wb pair that has the larger M121,
value among the two correct Wb pairs. At the bottom is the M121) distribution of the Wb
pair that has larger M l2b value among the two wrong Wb pairs. The distributions include
the events after the dilepton event selection requirements.

209

 

M2Ib smaller of the pair I

 

cor Run ll preliminary DIL, L=955 pp“
- data

signalMC

 

 

 

 

  

 

50000
M2“), GeV2
M2ib smelter of not the Ir
cm= Run ll preliminary DIL, Lzeea p0"

‘2 - data
10 -

Sig nal MC
6
4
2;
°o *w' m ' ' m ‘ 40000 WWW“...

2

Figure 0.2. At the top is the M12!) distribution of the Wb pair that has the smaller M [2
value among the two correct Wb pairs. At the bottom is the M lib distribution of the Wb

pair that has the smaller M121) value among the two wrong Wb pairs. The distributions
include the events after the dilepton event selection requirements.

210

 

25 cos nun ll pram um. um: pl)" . m

 

 

45 50
mln 12

Figure 0.3. The x2 distribution after lepton+jets cuts and tagging the two b jets.

211

 

car it... ll mm. mp"

   
 

25

15

10

Tiiliiiiﬁiiiliiii'rriiilii

 

 

 

 

14 corn-nu ugmw‘

     
 
 

- data
.signalMC

12

10

 

Alllllllllllllll'll’TTTTTll

 

1
MO

Figure 0.4. The jet charge of b—jets that are used for the ﬁnal top charge measurement
for the lepton+jets (left) and dilepton (right) channels.

212

 

WMHWLN. was"

r
is

Elﬁllil-

 

 

—lllllllllllllllllllllllllll

        

1 ll
numdlnekelnm

 

In. urn-In“
- data

.signalMC

 

16 18 N
mu- ofrlcb h JetQ

Figure C.5. The distribution for the number of tracks used in the jet charge algorithm for
the lepton+jets (left) and dilepton (right) channels.

213

 

25 mmumw. Law. on" _ “a

 

   

140180130 200

 

      

 

 

WEIGOV]
25- .r
: CDF nllprellmlnary DIL, L2955pb
; - data
z)_
; DsignalMC
15."—
in?
5;
L'
oE .. ‘: =‘r .
o 20 40 so 80100120140160180200
PlGev

Figure C.6. Lepton PT distributions obtained after the lepton+jets (left) and dilepton
(right) selection cuts and b—tagging.

214

 

cor nun ll milrnm L+J. uses no"

r
3

DEBIUI-
an

 

 

25 an 35 u
ndhchlGoVIInJetQ

   
   

 

-r' CDF Run II preliminary DIL, L=955 pb“
- data

[:jslgnalMc

 

no
Pl, GeV

Figure C.7. The distribution for the PT of tracks used in the jet charge algorithm for the
lepton+jets (left) and dilepton (right) channels.

215

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