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This is to certify that the
dissertation entitled

MEASUREMENTS OF THE wz DI-BOSON
PRODUCTION CROSS SECTION AT «ls = 1.96 TeV
IN THE DIELECTRON AND DIMUON CHANNELS

presented by

Rahmi UNALAN

has been accepted towards fulfillment
of the requirements for the

PhD. degree in Physics

 

 

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5/08 KilPrqlAchres/CIRC/Dateoue indd

MEASUREMENTS OF THE WZ DI—BOSON PRODUCTION CROSS
SECTION AT \/E = 1.96 TeV IN THE DIELECTRON AND DIMUON
CHANNELS

By

Rahmi Unalan

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
A Physics
2009

ABSTRACT

MEASUREMENTS OF THE WZ/ZZ DI-BOSON PRODUCTION
CROSS SECTION AT \/§ 2 1.96 TeV IN THE DIELECTRON
AND DIMUON CHANNELS

By

Rahmi Unalan

The cross section measurements Of WZ and ZZ di-boson productions using proton-
antiproton collisions at \fs' = 1.96 TeV using the data collected with the DOdetector
at Fermilab is presented. Both the 66 + jets and up + jets final states are consid-
ered. with total luminosities 1044 pb‘1 and 948 pb‘1 respectively in each channel.
Both Of the leptons are decay products of a Z boson. This study uses a different
approach to simple likelihood method. The measured cross sections for the two
processes are :

O’WZ/ZZ—teejj = 2.67 :l: 1.90 pb

and

O'wz/szpm-j = 3.45 :i: 3.51 pb

To my parents
Nurcan and Nafz'z UNALAN

with all my gratitude . ..

iii

ACKNOWLEDGEMENTS

Even a small size project usually is accomplished better with several people
working on different aspects of it. This work is no exception with all the weaknesses
and short comings which are all due to myself. There are a lot of people who helped
me reach this point. I cannot possibly name all of them lest there won’t be any
space for the actual work.

However I’d like to share with the reader some of the names who deserves at
least a hint. ‘

First and foremost my respects and gratitudes go to my parents, Nurcan and
Nafiz Unalan, who never doubted me and always encouraged me not only in this
work but everything in my life, and for my life in general. I’d like tO thank to
my wife Zeynep whose help was mostly behind the curtains. I appreciated my son
Tank’s effort to keep me on track.

Reaching to the safest shore never easy and requires one to place one’s faith in
one’s guide. I thank to my adviser Harry Weerts for being so patient with me.

People in MSU experimental high energy group were extremely helpful, I’d like
to acknowledge especially Reiner Hauser, and James Kraus for their help whenever
I needed.

I wish to express my thanks to DiBoson Group,whose comments were very
helpful to shape this work and everyone in DC without them, this work and others
could not exist.

I think, this work would be useless and a wasted effort if there were no one to
read and think about it. Thus I thank the reader for honoring this work and me
by reading it.

Finally

iv

TABLE OF CONTENTS

LIST OF TABLES vi
LIST OF FIGURES viii
Introduction 1
1 Theory 4
1.1 Standard Model ............................. 4
1.1.1 Particles, Short History ..................... 4

1.1.2 Standard Model ......................... 6

1.2 Di-Boson Physics ........... . ................ 16
1.2.1 Electroweak Theory ....... h ................ 16

1.2.2 Di-Boson Interactions ...................... 17

2 Experimental Apparatus 22
2.1 Fermilab ................................. 22
2.2 Particle Accelerators .......................... 24
2.2.1 Proton Source .......................... 26

2.2.2 Anti-proton Source ....................... 29

2.2.3 Main Injector .......................... 30

2.2.4 Tevatron ............................. 31

2.2.5 Recycler ............................. 35

2.3 DC Detector ............................... 35
2.3.1 DO Coordinate System ..................... 37

2.3.2 DO Luminosity Monitor .................... 40

2.3.3 DO Tracking Detectors ..................... 41

I 2.3.4 DO Pre—shower Detectors ........ . ........... 45

2.3.5 DO Calorimeter ......................... 47

2.3.6 DO Muon Detectors ...................... 53

2.3.7 DO Trigger System ....................... 54

3 Event Reconstruction and Object Identification 61
3.1 Introduction ............................... 61
3.2 Tracks .................................. 62
3.3 Primary Vertex ............................. 63
3.4 Electromagnetic Objects ........................ 64

3.5 Hadronic Objects, Jets .........................
3.6 Missing Transverse Energy, MET ...................
3.7 Muons ..................................
4 Data Samples
4.1 Data Set .................................
4.2 Data Quality ..............................
4.3 Monte Carlo ...............................
5 Cross Section Measurement
5.1 Introduction ...............................
5.2 Objects Identification ..........................
5.2.1 Lepton Identification: Electrons ................
5.2.2 Lepton Identification: Muons .................
5.2.3 Jet Identification . . . .4 ....................
5.2.4 Missing Transverse Energy, MET ...............
5.2.5 Other Objects Identifications .................
5.2.6 Constructing the Vector Boson: Z Boson .......... h .
5.2.7 Object Identification Efficiencies ................
5.2.8 Trigger Efficiency ........................
5.3 Backgrounds ...............................
5.3.1 jet Backgrounds ........................
5.3.2 top-antttop Backgrounds ....................
5.3.3 Z + jets Backgrounds .....................
5.4 Corrections ...............................
5.5 Technique ................................
5.5.1 W2 and ZZ Event Selection ..................
5.5.2 Likelihood Method .......................
6 Results
6.1 Likelihood Results ...........................
6.1.1 Systematic Errors ........................
6.2 Conclusion ............................... ‘.
Bibliography

vi

67
70
70

74
74
76
78

79
79
80
80
81
83
86
87
88
91
93
94
95
98
101
103
107
107
114

165
165
171
172

173

1.1

1.2

1.3

4.1

4.2

5.1

5.2
5.3

LIST OF TABLES

Three families of leptons, their masses and electric charges. Anti-
particles of these have the same properties except the charge which
should be negated. All of these particles have spins 1 / 2. ...... 8

Three families of quarks, their masses and electric charges. Anti-particles
of these have the same properties except the charge which should
be negated. Besides electric charge quarks carry another type Of
charge: Color. There can only be three states of color charge which
are red, blue and green. Previous rule (negation) applies on color
charge too if one wants to get anti-particle counter-part of a quark.
For explanation Of the color see the tex. All of these particle have
spins 1 / 2. ................................ 9

Four forces, their masses and electric charges of their carrier particles.
All of these particles are observed except graviton. Anti-particles
Of these have the same properties except the charge which Should
be negated. However since gluon carries another charge, color, its
antiparticle is not itself as in 7 or Z but its anti-colored gluon. All
of these particle have spins 1 except graviton which should have spin
2 ...................................... 11

The integrated luminosity Of the RunIIa period is shown in this table
for the 2EMHighPt data sample. The run ranges include test runs
also but those runs are not included in the luminosity calculation
as well as those runs that are excluded due to bad data quality
tags. An uncertainty of 6.5% is associated to the luminosity result,
because of the way luminosities are measured at DC. ........ 77

The integrated luminosity of the RunIIa period is shown in this table
for the 2MUhighpt data sample. The run ranges include test runs
also but those runs are not included in the luminosity calculation
as well as those runs that are excluded due to bad data quality
tags. An uncertainty Of 6.5% is associated to the luminosity result,
because Of the way luminosities are measured at DC. ........ 77

The division of regions with respect to the distance between the two
highest pT jets in the events ....................... 113

The di-jet mass cut is kept constant over the regions. .......... 113

77jet1*77jet2 cuts are shown in different regions of AR for both electrons
and muons ................................ 113

vii

5.4

5.5
5.6
6.1

6.2
6.3
6.4

6.5

17%} vs pg? cuts are shown in different regions of AR for both electrons
and muons. The numbers given here are the intersection points of

a line with pig} and p512 plane ...................... 114
The names of the variables are given in their region ........... 123
The names of the variables are given in their region ........... 124

Number of estimated events in the RunIIa data using the MC discrim—

inant distributions as templates ..................... 169
Table of luminosity values for RunIIa run period. ............ 170
Table of overall efficiencies for WZ/ZZ event selection. ......... 170

Table of measured cross sections for electron and muon channels for
both WZ and ZZ processes. The measurement uses almost 1 f m’1
of data collected by DOdetector in both channels. .......... 171

Table showing the systematic uncertainties of the different sources. . . 171

viii

LIST OF FIGURES

1.1 The elementary particles that are predicted by the SM. The left most
column Shows the Observed gauge bosons carriers of three forces
out of four observed in the Nature. There are eight different type
of gluons (g) carrying color-anticolor charge. 7 and Z have anti-
particles identical with themselves, W+ is anti-particle Of W' and
anti-particles Of the gluons are elements of the same set. Quarks
carry electroweak and color charges. Next two columns Show isospin
doublets. Three different color charges are shown in the same area
to emphasize that actually there are three different quarks. u, e,t
quarks have +2/ 3 fractional charge, d, s, b quarks have —1/3 frac-
tional charge. The unobserved and and most sought after Higgs
boson is shown in the right most column ................

1.2 The leading order Feynman diagrams for WZ process. The left one on
top is for t-channel process, and the right one on top is for u-channel
process. The bottom picture shows s—channel process. The decay
products reflect that this analysis is interested in only: two leptons
and two jets final states. ........................

1.3 The leading order Feynman diagrams for Z Z process. The left one for
t—charmel process, and the one on the right is for u—channel process.
The decay products reflect that this analysis covers only two leptons
and two jets final states. ........................

2.1 An aerial View Of Fermilab facility at village of Weston, 40 miles west
Of ChicagO,IL. Timnels of Main Injector, Tevatron and fixed target
experiments can be seen. In the photo, one could see the north—east
side of the Fermilab in the distance ...................

2.2 l A schematic diagram Of Fermilab’s accelerator complex is Shown in the
figure. Drawings are smoothed at some points. The drawing is not
scaled. ..................................

2.3 A detailed schematic diagram of Pre Accelerator. On the left side a
part Of the high voltage dome is shown. H ‘ has leaves from the
pre-accelerator from the right side with an energy of 750 keV.

2.4 A picture of Fermilab’s Linac. On the left is shown the drift tube Linac
whereas on the right is shown the high energy part of the Linac.
Both of the components make up the Linac. H ‘ ions enters the
Linac at the drift tube Side of the Linac. ...............

2.5 A schematic diagram of Fermilab’s Booster. All the major components
are shown as well as the locations Of the RF cavities. ........

ix

15

19

21

23

26

2.6 A schematic diagram Of Fermilab’s nickel target for anti-proton pro-
duction. It consists Of alternating disks Of target (Ni) and cooling
disks (Al). The target is rotated after a period Of usage in order tO
preserve the targets shape ........................

2.7 A schematic diagram of Fermilab's Debuncher and Accumulator. Pro-
tons with 120 GeV energy are hit on the target producing 133. They
are collected via a lithium lens and sent to Debuncher. Then they
are transferred to accumulator (smaller triangular ring). Being a
small ring, accumulator cannot store all the 15s, therefore 13 are sent
to Recycler via transfer lines. .....................

2.8 A schematic diagram Of Fermilab’s Main Injector, and its connections
to its adjacent accelerator facilities. It is used for storing protons for
further usage such as 15 creation, neutrino creation, proton studies,
Tevatron stores and the like .......................

2.9 A schematic diagram of Fermilab’s Tevatron showing the relative lO-
cations Of the beams inside it.There are three “trains” of twelve
bunches. The bunch to bunch spacing is 396 ns = 21 RF buckets.
The abort gap between the trains of 2.617 psec buckets. Different
bunches in a train encounter the opposing beam at different places
around the ring. ............................

2.10 The schematic view Of the cross section of the DO detector. The fig-
ure is sealed. The beam pipe carrying proton anti-proton beams
passes through the center of the detector. The direction Of the pro—
ton beam is assigned to positive 2 direction. From the center Of
the detector in radial direction the following detectors are located:
Central Tracker (Silicon Microstrip Tracker, Central Fiber Tracker,
Solenoid), Preshowers, Calorimeters Inter Cryostat Detectors, Lu-
minosity Detectors, Muon Detectors. .................

2.11 The orientation of right handed coordinate system of the DO detector.
The direction of the movement of proton beam is accepted as pos-
itive z—direction; negative z-direction is assigned to the direction Of
anti-proton beam. y-axis is Chosen skywards and x-axis points in
the Opposite direction of the center Of the Tevatron ring. ......

30

32

2.12 The schematics of the DO detector’s tracking system. Silicon Microstrip
Tracker (SMT) is surrounded by Central Fiber Tracker (CFT). Dur-
ing the RunII upgrade phase, another tracking detector is placed in
the region between the beam pipe and SMT, layer-0 detector, which
has increased the resolution of the beam spot and the tracks. The
coverage of the tracker is up to 77 D = 2. Since the central tracking
system sits inside a 2 T magnetic field providing solenoid magnet,
it is possible to measure the momentum of the particles from the
curvature of the tracks. ........................ 42

2.13 A nice picture showing the DO detector’s silicon micro-strip tracking
system (SMT). It has six barrel shaped detector components laid in
the direction of beam pipe. The barrels have four layers. 8 disks are
dispersed between the six barrels and another four are further away
from the center. The disks are placed perpendicular to the beam pipe. 43

2.14 The picture showing the cross sectional view Of the DO detector’s sili-
con micro-strip tracking system (SMT). The SMT barrels and their
support structure are shown. Four double sided layers are placed
consecutively. ............. 7 ................. 44

2.15 The picture showing the DO detector’s central fiber tracker system
(CFT). Eight layers of scintillating fibers are used to get an accurate
measurement of momentum measurement of the charged particles
passing through the CFT. The solenoid is placed between CPS layer
and the eighth layer of CFT, but is not shown in this figure. . . . . 45

2.16 Figure showing the forward preshower detector system (CFT). These
detectors is placed between the central calorimeter and the end-cap
calorimeters ................................ 46

2.17 The figure Showing the DO detector’s central pre—shower detector and
forward pre-shower detector geometry. The geometry shows a little
difference between the two detector systems, but in both of the de-
tectors triangular scintillating fibers with a waveguide in the center
are used to transfer light wave for position measurement. ...... 47

2.18 The DC calorimeter. The regions shown yellow and dark blue are built
by depleted uranium to contain showers Of the particles in a small
volume. The rest is built with steel and copper. The calorime-
ter is cryogenic . The region between the layers of metals is filled
with liquid argon as active media. The calorimeter has three parts:
North End—cap Calorimeter, Central Calorimeter and South End-
cap Calorimeter. The cylindrical hollow region in the center houses
the tracking system of the DO detector. ............... 48

2.19 A nice picture showing the unit of the calorimeter cell of the DO detec-
tor. The thickness of the uranium absorbing plates differs depending
on which layer it is locatedBetween the plates resides the liquid ar-
gon as the active ionizing medium. .................. 50

2.20 The cross sectional view of calorimeter quadrant. In this picture the
calorimeter towers are shown as differing colors centered at the cen—
ter of the calorimeter. For trigger system two of these towers are
combined together and an approximate energy measurement is done
for fast response times .......................... 52

2.21 The schematics of the calorimeter readout chain. Every cell can be
thought of as being a big capacitance charged according to the en-
ergy of the incoming particles. At the end of this chain the energies
of the particles are digitized ....................... 53

2.22 The schematic picture of the muon drift chambers are shown in all the
layers. Due to the presence of the detector support, the bottom side
of the detector coverage is partial .................... 55

2.23 The schematic picture of the muon scintillators are shown in all the
layers. Due to the presence Of the detector support, the bottom
side of the detector coverage is partial. ................ 56

2.24 The data flow diagram Of the Level-1 and Level-2 trigger systems. SMT
is not used in the first level because of the time constraint on this
system. Trigger framework is the decision maker and the messenger
between the different detector components and read-out crates. . . . 58

3.1 The figure showing the development of the jets in the calorimeter, hence
the procedure to follow to reconstruct jets based on the information ,
collected by the calorimeter. ...................... 68

3.2 Figure showing the calculation Of the momentum of the muon locally by
the muon detector. The toroid affects the path of the muon passing
through it by deflecting it by certain angle which depends on the
charge and the momentum of the muon. The magnetic field in the
toroid is a known parameter of the calculation ............. 72

3.3 Figure showing construction of a muon track segment in drift tubes.
The drift wires are perpendicular to the plane defined by the paper.
Blue line is the constructed muon path according to the drift circles
which are shown in red. ........................ 73

5.1 Di-electron mass distribution for the RunIIa Data‘set after preselection.
All the events contributing to this histogram have two good quality
electrons with pT > 15 GeV and one good quality jet with pT > 20
GeV ................................... 89

xii

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

Di—muon mass distribution for RunIIa Data set after preselection. All
the events contributing to this histogram have two good quality
muons with pT > 15 GeV and one good quality jet with pT > 20
GeV .- ..................................

Figure Show a typical trigger turn on curve. This is produced by using
the CEM(1,11) trigger. It requires an electron with a transverse
momentum of 11 GeV in the event. As it is seen from the figure
selecting with this trigger is not quite efficient unless the Object has
at least 20 GeV transverse momentum. ................

The figure shows (a) the Z mass distribution for the QCD events and
the fit before the application of cuts; (b) same distribution after
the cuts; the number Of expected events in different bins before
normalization for (c) electron and (d) muon channels .........

The figure shows MET distributions for the electron (left column) and
the muon (right column) channels for Monte Carlo events. The
effect of MET cut can be seen on the second row. ..........

The figure shows di-lepton mass distributions for the electron (left col-
) umn) and the muon (right column) channels for tt events. In the
same panel is shown before (in black) and after (in blue) the missing
transverse energy cuts. While the first row shows whole mass range,

94

97

the second row shows only Z mass window region. ......... 100

The di-jet mass distributions for signal (left hand side) and background
(right hand side) Monte Carlo events for electron (first raw) and
muon (second raw) channels. To preserve the relative strengths of

the distributions, they are not normalized one. ........... 102

The figure shows the discrepancy between the Monte Carlo events and
data for 17 1, 77 Q and AR 1) j2 distributions (from top to bottom).
On the le is shown the e ectron channel, and on the right is shown
the muon channel. Since our result will heavily depend on these

distribution, a correction factor is assigned as a weight to every event. 104

The figure shows the fits that are used for correcting event weights
of the Monte Carlo events for 7731, 173-2 and Ale, j2 distributions
(from top to bottom). Since our result will heavily depend on these
distribution, a correction factor is assigned as a weight to every
event.Left column is for electron channel and right column is for

muon channel ............................... 105

5.10 The figure shows distributions of "jlv 773-2 and Ale, 32 (from top to

bottom) after corrections are applied.Left column is for electron

channel and right column is for muon channel ...... . ....... 106

xiii

5.11

5.12

5.13

5.14
A 5.15

5.16
5.17
5.18
5.19
5.20
5.21
5.22
5.23
5.24

5.25

The di-jet mass distributions for signal (left hand side) and background
(right hand side) Monte Carlo events for electron (first raw) and
muon (second raw) channels. TO preserve the relative strengths of
the distributions, they are not normalized one. ........... 110

The distributions for njetl x "jet2- The one on the left is obtained
by using only the signal Monte Carlo events. The one on the right
side is for the background Monte Carlo events. There is an obvious
skewness towards right in the signal distribution, which is expected. 111

The distributions for 1):]qu vs pa? . The left column is for electron channel
and the right column is for muon channel. The lines Show a probable
cut on these two variable together. It is Obvious from the plots that
background events are mostly below the line .............. 112

An example distributions showing the color codes used in this thesis. . 118

The distributions for di-jet mass for electron channel in first and second
regions for likelihood discriminant input. .............. 125

The distributions for di-jet mass for electron channel in third and fourth
regions for likelihood discriminant input. .............. 126

The distributions for di-jet mass for muon channel in first and second
regions for likelihood discriminant input. .............. 127

The distributions for di—jet mass for muon channel in third and fourth
regions for likelihood discriminant input. .............. 128

The distributions for leading jet pT for electron channel in first and
second regions. ............................. 129

The distributions for leading jet pT for electron channel in third and
fourth regions. ............................. 130

The distributions for leading jet pT for-muon channel in first and second
regions. ................................. 131

The distributions for leading jet pT for muon channel in third and
fourth regions ............................... 132

The distributions for second jet pT for electron channel in first and
second regions. ............................. 133

The distributions for second jet pT for electron channel in third and
fourth regions. ............................. 134

The distributions for second jet pT for muon channel in first and second
regions. ................................. 135

5.26 The distributions for second jet pT for muon channel in third and fourth
regions. ................................. 136

5.27 The distributions for Z rapidity in the center Of mass frame of W/ Z (di-
jet) and Z (di—lepton) frame for electron channel in first and second
regions. ................................. 137

5.28 The distributions for Z rapidity in the center Of mass frame Of W/ Z
(di-jet) and Z (di—lepton) frame for electron channel in third and
fourth regions. ............................. 138

5.29 The distributions for Z rapidity in the center Of mass frame Of W / Z (di—
jet) and Z (di-lepton) frame for muon channel in first and second
regions. ................................. 139

5.30 The distributions for Z rapidity in the center of mass frame of W / Z (di—
jet) and Z (di-lepton) frame for muon channel in third and fourth
regions. ............... , .................. 140

5.31 The distributions Of the angle between reconstructed Z Object and the
center of mass frame of W/ Z (di-jet) and Z (di-lepton) Objects for
electron channel in the first and second regions. ........... 141

5.32 The distributions of the angle between reconstructed Z object and the
center of mass frame of W/ Z (di-jet) and Z (di-lepton) objects for
electron channel in the third and fourth regions. .......... 142

5.33 The distributions Of the angle between reconstructed Z Object and the
center of mass frame of W/ Z (di-jet) and Z (di-lepton) Objects for
muon channel in the first and second regions. ............ 143

5.34 The distributions Of the angle between reconstructed Z Object and the
center of mass frame of W/ Z (di-jet) and Z (di—lepton) objects for
muon channel in the third and fourth regions. ............ 144

5.35 The distributions for pr difference of W/ Z (di—jet) and Z (di-lepton)
for electron channel in first and second regions. ........... 145

5.36 The distributions for pT difference of W/ Z (di—jet) and Z (di—lepton)
for electron channel in third and fourth regions. ........... 146

5.37 The distributions for pT difference Of W/ Z (di—jet) and Z (di—lepton)
for muon channel in first and second regions. ............ 147

5.38 The distributions for PT difference of W/ Z (di—jet) and Z (di-lepton)
for muon channel in third and fourth regions. ............ 148

539 The distributions for di-jet pT for electron channel in first and second
regions Of likelihood. .......................... 149

XV

5.40 The distributions for di—jet pT for electron channel in third and fourth
regions of likelihood. .......................... 150

5.41 The distributions for di-jet pT for muon Channel in first and second
regions Of likelihood. .......................... 151

5.42 The distributions for di-jet pT for muon channel in third and fourth
regions of likelihood. ........................... 152

5.43 The distributions for the pT of the center Of mass system for di—jet and
di-lepton Objects for electron channel in first and second regions. . 153

5.44 The distributions for the pT of the center Of mass system for di—jet and
di-lepton Objects for electron channel in third and fourth regions. . 154

5.45 The distributions for the pT of the center Of mass system for di-jet and
di-lepton objects for muon channel in first and second regions. . . 155

5.46 The distributions for the pT' of the center of mass system for di-jet and
di-lepton Objects for muon Channel in third and fourth regions. . . 156

5.47 The distributions for the cosine of the angle between highest pT jet and
second highest pT jet for electron channel in first and second regions. 157

5.48 The distributions for the cosine Of the angle between highest pT jet and
second highest pT jet for electron channel in first and second regions. 158

5.49 The distributions for the cosine of the angle between highest pT jet and
second highest pT jet for muon Channel in first and second regions. 159

5.50 The distributions for the cosine of the angle between highest pT jet and
second highest pT jet for muon channel in third and fourth regions. 160

5.51 The distributions for the cosine of the angle between the highest pT jet
and the Z (di-lepton) Object for electron in first and second regions. 161

5.52 The distributions for the cosine of the angle between the highest pT jet
and the Z (di-lepton) Object for electron in third and fourth regions. 162

5.53 The distributions for the cosine of the angle between the highest pT jet
and the Z (di-lepton) object for muon in first and second regions. . 163

5.54 The distributions for the cosine Of the angle between the highest pT jet
and the Z (di—lepton) object for muon in third and fourth regions. 164

XVI

 

6.1

6.2

6.3

6.4

The distributions of likelihood discriminant for em channel. The left
hand side shows signal and background Monte Carlo events discrim-
inant distribution. These distributions are normalized to 1, so that
their shape could be seen easily. The right hand side shows the
discriminant for RunIIa events passing all the cuts previously men-
tioned. Total number Of RunIIa data shown in this figure (right
hand side) is 475 events. ........................ 166

The distributions of likelihood discriminant for muon channel.The left
hand side shows signal and background Monte Carlo events discrim—
inant distribution. These distributions are normalized to 1, so that
their shape could be seen easily. The right hand side shows the
discriminant for RunIIa events passing all the cuts previously men-
tioned. Total number Of RunIIa data shown in this figure (left hand
side) is 381 events. ........................... 167

Likelihood discriminants and their fits to data for electron channel.
The points are for RunIIa data, the fit result is overlayed on them
represents data as signal (red) and background (blue) contributions. 168

Likelihood discriminants and their fits to data for muon channel.The
points are for RunIIa data, the fit result is overlayed on them rep-
resents data as signal (red) and background (blue) contributions. . 169

Images in this thesis/ dissertation are presented in color

xvii

Introduction

“. . .I had this feeling that I’d never
get to the other side of the street. ”[1]
JD. Salinger

”What is it?” asked the boy. ”Open and see for yourself.” answered his mother.
He was nervous. It could be anything, he would like or dislike. He hesitated but
his curiosity overcame his hesitancy and he found himself trying to find what was
beneath of all this beautiful covers.

This is our story. In front Of us there lies this beautiful nature perfectly bal-
anced, without any waste or luxury.

From the first human until now people always acknowledge their lack Of knowl-
edge and tried to know everything about themselves and their surroundings as
much as they can. This is accomplished mostly inheriting knowledge from the pre-
decessors. Last century witnessed the discovery Of plenty of facts about ourselves
and our environment. With them we understood that we still have innumerable
things to uncover and learn.

Last century noticed blooming Of atom like a rosebud. Thanks to Rutherford,
Thompson and all the pioneers, we now know that not just atoms are composite
Objects even the bulk Of their constituents are themselves composites. We learned
that it is possible to break even the smallest things, and understood that their

interactions between themselves are keys to answering questions such as ‘why’ or

‘hOw’.

This work is also one Of the many works by which the best working theory of
all the littlest things, Standard Model, is tested against.
Chapter 1 gives a basic introduction to the Standard Model (SM) and puts some
emphasis on theory Of diboson productions. The SM Of particles is the most
comprehensive (and provable by experiment) theory scientists could conjure up to
today. In this chapter the motivations for di—boson cross section measurements are
also is discussed.
Chapter 2 portrays the experimental apparatus used to collect data, explicitly the
DO detector and the Tevatron p15 collider located at the Fermi National Laboratory
(FermiLab). The DC detector was built during the 19803 as a hermetic high energy
particle physics detector in order to measure very precisely particle energies and
momenta. It has gone through three extensive upgrades, the last being in 2006.
The accelerator complex and the Tevatron is used to accelerate protons and anti-
protons to 980 GeV energies. During this writing the Tevatron is the highest
energr machine in the world.
Chapter 3 explains the data collection and reconstruction procedures and how
physics objects are identified. The collected data in its raw format is not very user
friendly and lacks many corrections. The procedures for building useful physics
Objects for analysis out of energy bits are explained.
Chapter 4 In this chapter data samples used in the analysis are explained and
the total number of events are given in terms of integrated luminosity.
Chapter 5 is the first place to look at for those who have very limited time. It
presents a measurement of diboson cross section measurement in the
WZ (Z Z ) ——> jets + leptons channel. Definitions of objects used in this analysis,
selection criteria specific to this analysis, efficiencies of the Objects and methods
are explained. Both the electron channel and the muon channel are mentioned in

this chapter.

Chapter 6 is the summary of the results of the analyses.

Chapter 1

Theory

“Yam, zerre kimin ise, gezdigvi b'z'itiin yerler de ommdur. ” l[2]

Bediiizzaman Said Nursi

The first part Of this chapter presents a very short overview Of particle physics
and the Standard Model. The second part focuses on di—boson physics. This

Cha.I)ter should provide the reader with a basic understanding for the rest of the

WOrk.

1 ~ 1 Standard Model

1 - 1.1 Particles, Short History

For a long time, it was known to humans that by bombarding it is possible to get
past closed doors, but it is fairly new to use this technique for Opening the door of
the unknown behind the matter. In a sense, this is the technique widely used in
particle accelerators in order to see what’s beyond the veil.

Discoveries of several particles at the very end of 19th century caused a lot
Of enthusiasm among physicists. X—rays, [3 and a radiations are among the very

I‘Tlrst of those. Before a new century’s helix started curling up; we knew that “the

\

1That is to say, whoever owns a particle must also own all the places it enters.

carriers of negative electricity are bodies having a mass very much smaller than
that of the atom of any known elemen ” [3] which are now called electrons instead

of “corpuscles” [3].
The electron’s discovery had led to a description Of the atom2 which was proved
to be wrong by shooting a particles (He+2 ions) at a thin foil of gold. Nowadays
even in elementary schools the atom’s Structure is taught as resembling to the solar
system. The disturbance of this metaphor in the physics community was calmed
“in 1 913 by the rules of quantization with help from the quantum theory(1900)” [4].
The photoelectric effect, wave nature of the electron and the concept that “only
cert ain preferred motions, quantized motions, are possible or at least stable, since
the energy can only assume values forming a discontinuous sequence” [5] forced
thSicist to adopt a new way Of thinking about the matter and the first half of
20t ’1 century witnessed the birth of quantum mechanics. The knowledge about the
atom, especially the hydrogen atom, was greatly increased with this new method.

While theorists were taking big steps in understanding how nature works, exper-
inlentalists were setting the spring of discoveries for the second half of the century.
Although new particles were discovered occasionally until the mid century there

WTire no signs of new particles that were proposed to explain some weird phenom-
9118 like the continuous energy distribution of electron as a result of 5 decay3 and
the like.

The second half of the century saw an explosion in the number of particles
discovered. Most of the earlier questions were answered but the excitement caused
by the new particles soon left its place to a little uneasiness. At earlier times those
Darticles were thought to be fundamental, however, their numbers were defying

that conception. Thus began a search for a new way Of combining the properties

2This description stated that atoms are made of positive bodies with negative charges
eInbedded in them

3 Energy was not conserved by the visible particles, electrons energy spectrum was
Continuous as opposed to being quantized if there were two decay products in the process.

of these particles, which eventually resulted in the standard model of particle

physiCs.

1 . 1.2 Standard Model

The abundance of observed new particles led physicists to the idea that there might

be structures to the newly discovered particles. Building symmetric groups by
newly found particles according to their properties, then, led to the idea of forming
Symmetry groups using point like constituents Of those new particles (quarks),
leptons and the go—between (bosons).

It is hard to explain the Standard Model (SM) thoroughly here since “it repre-
sent S an enormous body of knowledge of nature that can be seen as the culmination
of 400 years of physics” [6]. Although an essence Of it will be given here, for rigorous
treatments and explanations of SM the reader Should refer to textbooks written
011 the subject like [7, 8, 9, 10].

The SM is about the elementary particles that can be observed in nature and
the interactions between them. The term elementary in this context means that
this type of particles are not composite Objects, they are created and destroyed as
a Whole.

' In reality there are quite a few elementary particles known today. It is necessary
to group them so that the laws with which they are bound should emerge. The
grouping is done according to their one fundamental property namely their spins“.
0he refers to a point like object when one speaks about elementary particles. That
iS why it is not very meaningful to see the spin of a particle as a spin of a Spinning
top, but as an internal property that affects its behavior towards other particle
and forces, much like a will in humans. Yet this doesn’t prevent physicists to use

Spin in a classical sense where it is appropriate. For example depending on how

\‘

4Spin is a vectoral quantity and usually expressed by ‘5’

you look at a particle, it may be right-handed ( 3’? > 0 ) or left-handed ( 5’?
< 0 ); where ‘E’ and 79’ are spin vector and momentum vector respectively. This
is an important discrimination, because if a particle is massless then it is possible
to talk about a definite spin state5. Spin is a directional quantity, however, the

Classification is done according to the magnitude Of the particle’s spin. For all Of

the observed particles then, the classification6 is :
o S ' 1
pin 2
O spinl

Spin % particles, which are also called fermions since their statistical behavior
described by Fermi-Dirac statistics, Obey Pauli Exclusion Principle. According

to that principle one and only one fermion can occupy a given quantum state.

FerIltiions can be divided into leptons and quarks.

Fermions can be divided into leptons and quarks with respect to the role they
play in electrO-weak or strong interactions. While leptons feel the electro—weak
fOI‘ce, they have no sense of the strong force. On the other hand, quarks can

be attracted via the mediator of the strong force, they cannot interact with the

e1EctrO-weak force carrier bosons.

Although fermions are grouped according to their interactions, physicists group
1:hem in three families with respect to their weak-interaction counter—part. In
that respect there are three generations of fermions with the difference being only
their masses and all the other properties the same over families Leptons are
electron (e‘), electron neutrino (ye); muon (if), muon neutrino (12);); tau (7—),

tau neutrino (VT); and their respective antiparticles for which negative signs should

'\

5Massless particles move at the Speed of light regardless of the frame of reference.
Because of this a particle’s direction of momentum cannot change with respect to any
reference frame. This fact becomes especially more important in the case of neutrino,
Since Standard Model assumes that they have no mass.

6Here we did not consider a still not observed but suspected particle, graviton., which
is conceived to have a spin of 2.

 

 

 

 

 

 

 

 

 

 

 

Particle Name Mass (GeV/c2) Electric Charge
113 electron neutrino < 7 x 10‘9 0
e‘ electron 5.11 x 10—4 -1
up muon neutrino < 3 x 10‘4 0
if muon 1.06 x 10_1 —1
V7- tau neutrino < 3 x 10—2 0
T- tau 1.777 -1

 

 

 

 

 

 

 

 

rfriable 1.1: Three families of leptons, their masses and electric charges. Anti-
Darticles Of these have the same properties except the charge which should be
Ilegated. All of these particles have spins 1 / 2.

 

 

 

 

 

 

 

 

 

Particle Name Mass (GeV/c2) Electric Charge
2
up 0.002 + 3
down 0.005 — :1;
charm 1.25 + :2;
strange 0.095 — :1;
2
t top 175 + 3
, 1
b bottom 5 — 3

 

 

 

 

 

 

 

 

Table 1.2: Three families Of quarks, their masses and electric charges. Anti-
Darticles of these have the same properties except the charge which should be
Ilegated. Besides electric charge quarks carry another type Of charge: Color. There
Can only be three states of color charge which are red, blue and green. Previous
1‘Ille (negation) applies on color charge too if one wants to get anti-particle counter-

Dart of a quark. For explanation Of the color see the tex. All of these particle have
Spins 1 / 2.

be read positive. Quarks are up (rig), down (f5); charm (c+%), strange (3715‘);
top (5%), bottom (5%); and their respective antiparticles for which all the signs
for charges (both electrical and color) should be negated.

One striking feature of quarks is that their charges are fractional contrary to the
common assumption of the first half of the 20th century which stated that charge
is integer. Although there are some theories in which quarks are also composite
particles and their constituents have integer charges, they are out of the scope Of
this work.

The material in the universe is formed by bound states of the first family Of
these fermions (namely electron, its neutrino, u and d quarks), and probably their
antiparticles- In general the bound state Of quarks are called hadrons. All around
us, we don’t see a fractional charge carriers, which is a natural result Of another
striking feat Inc of quarks that they don’t have unbound states. They are observed
either as qci pairs (mesons) or in triplets of q’s and 6’s (baryons).

The inability to Observe quarks as singlets and observing particles made up Of
same the SIbin state and charge of quarks brought up two ideas, i) there was an
Other quantum state associated with quarks7, ii) some force was barring them from
being apart, from each other. The new “charge” was termed as color with its three
DOSSible Values (red, green, blue) and the force was named color confinement8[6].

Tir 91988 efforts of many physicists via high energy experiments produced many
bound States of quarks, but what remained unexplined was the assembling or

disassembling forces. What, then, is responsible for keeping the particles in atoms?

Quantlnn electro dynamics (QED) was very successful in recognizing a quantum

field 7 electro magnetic field — as the force; and its quanta - photons — as the carrier
we. QED was a gauge invariant theory, and by symmetry all the other

7

Pauli exclusion principle prevents two quarks (fermions) having been in the same
quantum State

8
There Can be no colored bound states or free colored particles.

10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

f Mediator of Mass (GeV/c2) Electric Charge
W" , Z weak nuclear force 81, 90 . —1,0
9 strong nuclear force 0 0
’7 electromagnetic force 0 0
97‘O—\’viton gravitational force 0 0

 

 

 

 

 

 

Table 1-3 I Four forces, their masses and electric charges of their carrier particles.
All Of these particles are Observed except graviton. Anti-particles of these have
the same properties except the charge which should be negated. However since
gluon carries another charge, color, its antiparticle is not itself as in 7 or Z but its

anti-colored gluon. All of these particle have spins 1 except graviton which should
have spin 2,

interactions between the particles were explained as gauge invariant field theoriesg.

The weak nuclear force is responsible for interactions like 6 decay via mediators
like Wi Z , and the strong nuclear force is responsible for holding the nucleus of the
atoms via. gluon, electromagnetic force is responsible for keeping electron around
the atom via photon.

The definitiOn Of the three forces (electro—magnetic, weak and strong) are done
in SHCh a. Way that they are gauge invariant.

All the mediator particles are bosons and obey Bose-Einstein statistics, which
states that there can be as many particles as possible in a single quantum state.

AS it is seen from the table 1.3 the symmetry Of the boson masses is not

reser . . .
p Ved for weak nuclear force carriers. The same can be seen in fermions where

the ObserVed mass difference is on the order Of 109 eV. This assymmetry problem

 

9 .
GraVltation is yet to be explained as a gauge invariant field.

11

was overcomed by proposing that the symmetry which would be observed in very
high energy events is broken at the energy levels of our reach in high energy
experiments. As its consequence another — yet to be observed — particle (whose
spin should be 0) was introduced, Higgs particle.

The Standard Model combines three of these forces (weak, strong, electromag-
netic) in a single Lagrangian and explains how elementary particles are coupled
to each other. “Standard Model is a quantum field theory that is based on the
gauge SYIIlmetry SU(3)C x SU(2)L x U(1)Y” [11]. SU(3)C part of this group
corresponds to strong interactions with 8 gluon mediators, S U (2) L x U (1)Y corre—
sponds to electro-weak interactions with four mediators 7, Wit and Z0. Although
gluons don’t carry electric charge, they carry color charge which allows them to
interact With both quarks and themselves alike. Gluons cannot couple to other
fermions (leptons) due to lack of electric charge. Weak bosons carry electroweak
charge and they can interact with themselves[11] also; upon which we’ll talk about
more in the next section. The Standard Model is very succesful in its predictions
up to this day. It was successful] in passing all the tests with which it was chal-
lenged_ rI‘here is only one challenge which still needs to be answered: where is the
Higgs particle? This thesis doesn’t answer this question.

Before ending this section we would like to write the full lagrangian of standard

model and the fundamental particles it foresees. The Lagrangian:
flagrv=£0+£em+£e+£q+£H (1.1)

Where the first term is free Lagrangian and

£0:

1 2
—- A

4( W)

1

2
__ B
l( ,uu)

12

 

+ Z{[7(z'7“8# - mew + fig-i’yuauz/g}
3

+ ZMUWEM — mq)(1}
q

+ Zfi'mwt - quM’} (12)
q/

the second term is electromagnetic part of the SM Lagrangian and defined as

_ 2 _ 1 - ,
Eem = dszfl - 3 quq + 3- Zq’wq M“ (1.3)
r q q,

the tllird term is the weak leptonic sector of the SM Lagrangian and defined as

: §{%§[€—7A(1 + 75)V€lV/\ + h.C.]

g _ » _ A
+4cos8W WM“ + 75W — ”NOV + itVlZ } (1.4)

the fOUI‘th term is the weak quark sector of the SM Lagrangian and defined as

=Zq{ -97[q7,\( (1+ qI,L—,)qu,q'wA + h.c.]

+mé—[qvn CV + 75M - q WMCV + 75))131ZA} (1-5)

the last term is Higgs sector of the the SM Lagrangian and defined as

1 2 2 2 3 h 4

2

9 ’r 1
+Z(W#W“ +

w l1 2 2
QCOSQBWmZHZ )(A +2AH+H)

+ Z( (m—l’iimm —qq+ mqq‘q'm (1.6)
gqq, .\ A

where . . .
h'C- stands for ‘hermltian cOJugate’ and

13

 

6 : (6,11, 7') (electron,muon,tau)
q = (u,c,t) (up, charm, top)
q’ = (61,3, 5) (down, strange, bottom)
Auu = B/JAI/ - all/Au + giA/J X AVl
B M, = eta, _ 31.3,,
A'i‘ + iAg = fiwu
A“ = cosGW - Z!” — sinGW - Aft
B“ = sin 9W - Z“ + cosGW' - A”

6W iS the weak mixing angle and

WA 3 W; 2 charged intermediate boson field
AA = photon field
Z A 2 neutral intermediate boson field
6 = gsinGW = g’cosew
CV =1— 4sin2 eW
Ci/ =1-g-sin26W
f/ 21— gsingew
sin2 9w = 0.23 i 0.01
CI 3103 3133
5 clc233 — 82036316 (1-7)
6

U = ”3102 c10203 + $2838i
_3132 €132c3 — 0233676 618283 + 026362.

With Ci “Q cos 8,- and s, = sin 9,- and z' = 1,2, 3. Particles:
See Figure 1.1. In the Standard Model there are 17 free parameters such as

the masses of the particles. These free parameters are not predicted in the SM ,

bUt need to be measured. This is the reason behind all the experiments.

14

 

Figure 1.1: The elementary particles that are predicted by the SM. The left most
C01u1nn shows the observed gauge bosons carriers of three forces out of four ob—
served in the Nature. There are eight different type of gluons (g) carrying color—
antiCOIOI‘ Charge. 7 and Z have anti—particles identical with themselves, W + is
anti‘pa’rtiCle of W‘ and anti-particles of the gluons are elements of the same set.
Quarks carry electroweak and color charges. Next two columns show isospin dou—
blets Three different color charges are shown in the same area to emphasize that
actually there are three different quarks. u, e,t quarks have +2 / 3 fractional chargCa
d,s,b qua’I‘ks have —1/3 fractional charge. The unobserved and and most sought
after Higgs boson is shown in the right most column.

 

1.2 Di- Boson Physics

1.2.1 Electroweak Theory

The Standard Model (SM) is based on group theory. It is part of the SU (3) x
SU(2)L X U (1)31. group. The SU(2)L x U(1)Y symmetry group is the part that
defines gauge interactions of electroweak bosons with fermions. The gauge fields
introduced by this theory are Wit, (where 2' can take only three values) for S U (2) L
and B” for U(1)Y'

The SM requires massless neutrinos, and neutrinos only occur with one handed-
ness, they are always in left-handed spin state, that’s why electroweak interactions
do not CCNilserve parity. Conservation of parity means that the identical interaction
happening for aleft-handed neutrino‘should occur for right-handed one which do
not exist [15]. Due to the fact that electroweak interactions don’t conserve par-
ity, fermions coupling via electroweak force are called left-handed fermion fields,
they can be observed-But their right-handed counter-part fermion fields are never

observed. The left-handed fermion fields are shown as isospin doublets
(1.8)

Where 2' 2 (e,p,T), k = (u,c, t) and k' = (d, 3,b); and right handed fermion fields

are Shown as isospin singlets

(o a) , ‘

Where i Q (er/1'27)? k, = ('u, d, c, s, t, b). The electroweak doublets transform under

j : 1/2 of SU(2) and singlets transform under j = O representaiOIl 0f 311(2)-

AS in Quantum electro dynamics (QED), electroweak theory has an interaction

16

 

term of the form :

Jé‘VEAKWH, (1.10)

with

_ 1 _ ,
JiLVEAK = if’aLlfl'lf’bL = germ“ — WWW, (1.11)

J5, E A K Contains only left handed particles and has the vector — axial vector
(V ‘ A) form. Since the particles a and b can be different particles with different

charge, the carrier of the field must carry charge too. '

1.2-2 Di—Boson Interactions

The di“b()son interactions are predicted by the Standard Model. This study is
about the Simultaneous production of massive electro—weak bosons (WW, WZ, ZZ).

The Lagr angian describing these interactions is contained in the free lagrangian

£,.

1 1
-;(Aiw)2 + guy/1,, — alarms/1A”
2

= glAu X AplaflAu + %{(A),AV)(AVA#) — (Au/WP} (1-12)

The first term in the above equation is the trilinear coupling term. The effective

Lagrangian of the process then becomes

 

C .
WWV _ - V ’r u 1/ 71' 4w - 1 av
— 29 (W VW V —W VVW )+mVW WVV
,\
+z'——‘2/—W( Wfi‘vV" —— gXW’LWI/(Bf‘VV + BVV”)
M n
W
+gge/WP0(W,L‘5,,WV)VQ + vikVWLWVV/w

 

AV ..
+z' W1 WWW 1.13
Mgv A), 1/ ( )

17

The differential cross section for reaction

and

(liq—j —> ZOZO

averaged over quark colors is given by [12]. VViZO expression contains four terms
one for each channel (u, t, s) and one for their interference. Depending on which
part of the phase space one looks at the contributions coming from each of these
diagrams change. 3 channel has more dependence on the available energy, thus as
the center of mass energy increases its contribution decreases. However with the
a‘lllalriolous couplings one should expect to see, an increase in the contribution to
Cross section from s channel.[13] Z OZ 0 expression contains only two terms one for
eaCh Charmel (u,t) since in the SM there is no 3 channel production mechanism
for it- Both of these channels contribute equally to the total cross section of this
DI‘OCeSS_

The search in this analysis is for those cases where one boson decays leptonically
Wh ereas the other decays hadronically. Due to the nature of the final particles in the
prc)Ctess, there may be two different di-boson production mechanism: simultaneous
I)r()(1uction of W and Z bosons or simultaneous production of two Z bosons; with a

decaying leptonically in both of the processes and the remaining boson decaying

hadronically.

W 2 Production

The simultaneous production of WZ bosons is described by three Feynman dia-
grams in the leading order as shown in the Figure 1.2. The most clean channel

Would be all lepton channel, and second to this is the two charged leptons and

18

.1

\LChannel production u-Channel Production
(1

 

 

 

 

s-Channel Production

Flglne 1.2: The leading order Feynman diagrams for WZ process. The left one

on top is for t-channel process, and the right one on top is for u-channel process.
The bottom picture shows s—channel process. The decay products reflect that this
a‘Ilalysis is interested in only: two leptons and two jets final states.

19

two jets Channel, where jets are decaying from IV boson and charged leptons are
decaying from Z boson. This work is devoted on this semi-leptonic decay channel
where leptons are the decay products of the Z boson.

The 1eD’tons coming from the Z boson should be charged, so neutrino final states
are exehlded. Since 7' particles decay to lighter leptons, they are also excluded from
the Signal acceptance. Thus as our signal signature of the two possible final states
for WZ decay are eej j and ppjj. For years it has been easy to construct a Z
particle from its lepton signature due to the very cleaniness of the signature the Z
leaves in the detector. But it is always hard to separate the two jets of the boson
decay from jets of the remnants of the proton—proton interaction. Therefore this
Challtlel suffers most from the simultaneous production of jets along with a W or
Z boson.

The theoretical production cross section for W Z production at the Tevatron
is 3-68 pb[14]. To have an idea of how small the probability of producing WZ
events, the reader should refer to the production cross section of ti (the heaviest
two particles known) events which is around 7 pb, doubling the rate of di-boson
eVellts. Including the detector effects such as the phase space coverage deficiencies,
detection inefficiencies and the like, one could expect to see around 50 events in

beth electron and muon channels separately, for the whole RunIIa data taking

period.

2 2 Production

The simultaneous production of Z Z s is somewhat different than simultaneous pro-
ClIlction of WZ. Although there may be an interaction vertex of WW(Z/7) (trilin— '
ear) or WW(Z/'y)(Z/’y) (quartic), the SM does not allow for the same vertices for
2 pairs, namely there is no trilinear Z Z (Z / 7) or quartic Z Z ( Z / 7)(Z / 7) couplings.

Because of this the Z Z interaction cannot be described by s-channel interactions.

20

 

 

(I
t-Channel Production u-Channel Production

Figul‘e 1.3: The leading order Feynman diagrams for Z Z process. The left one for
t‘cha-Itmel process, and the one on the right is for u-channel process. The decay
pr 0dLlcts reflect that this analysis covers only two leptons and two jets final states.

For the leading order Feynman diagrams please see Figure 1.3.

The leptons are required to have charges ~excluding 7' final states~. Therefore
the possible two final states for this process is eej j and ,upj j. Although it is
r elatively easy to construct Z from leptons, it is a big challenge to construct Z
fr 0111 jets due to large volume of backgrounds. These channels suffer most from
the simultaneous production of jets along with a Z boson.

rThe theoretical calculations of the cross section for Z Z production in the Teva-
tron is 1.46 pb[14]. As it is evident, this signal is very feeble and it is not expected

t0 See more than 10 events for the whole RunIIa data taking period.

21

Chapter 2

Experimental Apparatus

“The moment Hayy realized that

all exists is His work, he saw things
in a new and difierent light. ”[16]
Ibn Tufayl

The previous chapter builds some interest in di-boson physics. In order to
Check and correct our theories we need experiments. Understanding the detector,
its Capacities and pitfalls, plays an important role in what type of physics can
be tested. This chapter gives a minimal description of the accelerator facility,

TeVatron and the DQ detector used for collecting data.

2 - 1 Fermilab

Chicago, the Windy City, is one of the most renowned and sought after cities in
the world with its skyscrapers, beautiful location near the Great Lakes,and one of
the attraction centers in the world by being “an American cultural capital” [17]. To
a particle physicist however, it is the city which hosts the World’s highest energy
Ihachine, the Tevatron at Fermilab, in one of its suburbs.
Originally named as the National Accelerator Laboratory, Fermilab was com—

missioned by US. Atomic Energy Commission on November 21, 1967; built and has

22

 

Figure 2.1: An aerial view of Fermilab facility at village of Weston, 40 miles west
Of CJ'l'licagoJL. Tunnels of Main Injector, Tevatron and fixed target experiments
(ii-1n be seen. In the photo, one could see the north-east side of the F ermilab in the
dlstallce.

been operated by Universities Research Association since its founding. Renamed
in hOnor of Enrico Fermi, on May 11, 1974 [18]; Fermilab defines its mission as
“advancing the understanding of fundamental nature of matter and energy by pro-
viding leadership and resources for qualified researchers to conduct basic research
at the frontiers of high energy physics and related disciplines” [19].

From the day with the first beam of 200 GeV energy (March 1977) to this
(133’, Fermilab had many discoveries, among them bottom quark in 1977 and top
quark in 1995 [20], merited many praises, among them International Mechanical
1Engineering Landmark from ASME [18]; all of which were possible with the accel-

erators(Main Ring —now Main Injector-,Tevatron) and the detectors(fixed target
detectors, CDF, DG) it is home to.
Not only is Fermilab one of the fore runners of advanced physics, but also it

makes available the technologies developed there to the public. The connection

23

between Public and Fermilab is on all levels. The prairie conservation site and the

American bisons keep its prairie connections alive and provides the local commu-
nity With environmental richness .

Science is not just making elegant calculation for its devotees, it has an artistic

side to it. It is very easy to grasp that by just visiting the site and seeing the

CulptureS made by sc1ent1sts who genuinely combined art and sc1ence in their

work.

2'2 Particle ACcelerators

Chal‘ged particles can be accelerated by means of electro—magnetic fields, and with
Sufli(:ient energies it is possible to observe “interesting things happen”, which usu—
ally means the creation of new particles that were absent before, by colliding a
beam of charged particles with some targets.

ITermilab uses proton and anti-proton beams that are accelerated to kinetic
energies of 980 GeV1 in opposite directions to get a center of mass energy nearng
to 2 TeV. In order to prepare these beams and give them the necessary energy,

SeVeral different accelerator systems are utilized:
O Proton Source which is composed of Pre—accelerator, Linac and Booster,
9 Anti-prOton Source, which comprises Debuncher and Accumulator,
0 Main Injector,
o Tevatron,

o Recycler.

\
1One eV (electron volt) is the amount of energy a particle of charge of an electron

Can get by crossing a potential difference of one volt. Thus one GeV equals 109 eV or
1.602177x10—1O J of energy.

24

—.‘T"r{Switchyard

   
 

an
“(if d
g E ' <\‘o U
c 4.; m
j m C o
38 e 0.3
790 H ‘
" Q)
8 E I—
m g 8
m.
C
O
O
E
.E
E
6

Figure 2.2: A schematic diagram of F ermilab’s accelerator complex is shown in the
fig‘ure. Drawings are smoothed at some points. The drawing is not scaled.

WAter Resistor Insulator Pit Wall
[ Spark Gap HV Lead

 

 

 

 

bime|\[®[ rots. [I] fgzi
saw I Ejijzzé‘: w;—
r...rif¥—--f—-uwl 7 .
[JAKE _Ion
\./ . . :Q 3'". \.Q Pump

Gas at 2 atm Pressure Vessel

Figul‘e 2.3: A detailed schematic diagram of Pre Accelerator. On the left side a
part Of the high voltage dome is shown. H _ has leaves from the pre-accelerator
fr 0111 the right side with an energy of 750 keV.

2~2- 1 Proton Source

Protons are essentially the nucleus of hydrogen atoms. So, as the easiest logical
Step hydrogen atoms are used in producing protons. Here it is described very
briefly how.

The Pre-accelerator (Preacc) is the first accelerator in Fermilab’s accelerator
Chains. It consists of a source -which converts hydrogen gas (H2) to ionized hydro-
gen gas (H_)- resided in an electrically charged dome see Figure 2.3. The dome
is Charged to —750 kV. The ionized hydrogen gas is allowed to accelerate through
a Column from the charged dome to a grounded wall, therefore at the end of this

Drooess ions gain an energy of 750 keV. With a period of 66 ms, preacc can ac-
QElerate beams. After exiting the accelerating column, the beam is conveyed via a
tI‘ansfer line to the Linac.

The Linear Accelerator (Linac) increases the energy of the H_ beam that is

26

 

 

 

Flg‘lre 2.4: A picture of Fermilab’s Linac. On the left is shown the drift tube
“lac whereas on the right is shown the high energy part of the Linac. Both of the

components make up the Linac. H ‘ ions enters the Linac at the drift tube side of
e Linac.

delivered to it, from 750 keV to 400 MeV. It consists of two main sections, the low
energy drift tube Linac and the high energy side coupled cavity Linac. In theory
Linac also can accelerate H- beam with a period of 66 ms, but this cannot be
sustained for a long period of time without compromising safety. H‘ ions may be
transferred to one of two locations, based on the needs of that day: Booster which
is last leg of proton source, or Linac dump, which is a large concrete block. The
Linac is operated in three modes: High Energy Physics (HEP) mode referring to
Booster transfer; Neutron Therapy Facility (NTF), for cancer treatment facility
in this mode H_ are accelerated up to 66 MeV, and studies, dumps for various
tune—ups or diagnostics. ,
The Booster, see Figure 2.5, is the last step to convert H 2 gas into 8 GeV pro-
tons. It takes H‘ ions that are accelerated to 400 MeV from the Linac, strips off
their electrons by means of a carbon filter, and accelerates the remaining protons

to 8 GeV. [It is the first synchrotron2 in the chain of accelerators that a proton

 

2A 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

27

 

 

 

 

i
5‘ RF
1.2

    
     

\
I
s

Figure 2.5: A schematic diagram of Fermilab’s Booster. All the major components
are shown as well as the locations of the RF cavities.

28

passes through at Fermilab. It consists of a series of magnets that are dispersed
throughout of a 475 m circumference (75 m radius) circle, with 18 RF (radio fre-
quency) cavities 3 interspersed. The Booster has a period of 66 ms for accelerating
beams. As in the Linac the boosted proton beams can be guided to two different
designated places according to the need: the MI-8 transfer line (Main Injector
line carrying 8 GeV particles), or beam dump. Beams leaving the Booster via the
MI—8 line can be used either in HEP mode or sent to MiniBooNE (Mini Booster
Neutrino Experiment) for producing the neutrino beam aimed at the MiniBooNE

detector.

2.2.2 Anti-proton Source

We live in a world made up of matter, therefore in contrast to the production of
protons we basically have no easy access to anti-protons. Production of antimatter
is rather cumbersome and in our case it is very inefficient too“. Anti-protons are
created by striking 120 GeV protons from the Main Injector onto a nickel target
see Figure 2.6. This process creates a lot of secondary particles some of which
are anti-protons. By means of magnets anti-protons with an energy distribution
averaging at 8 GeV are selected and transported to the Debuncher.

The Debuncher is a synchrotron which has a shape similar to a rounded triangle
with an average radius of 90 m. It is designed to accept pulses of anti-protons at
8 GeV from the target station and to reduce their momentum spread by means of
RF bunch rotation and adiabatic stochastic cooling while maintaining them at 8

GeV. There are two additional cooling systems which are used to reduce the beam

 

region are synchronized to the beam momentum and revolution frequency.
3An RF cavity is basically a gap placed into the beam pipe across which an electric

field is applied. They are electrically resonant structures with a natural frequency of
radio frequency range. [21]

4The efficiency of this process is very low; 105 protons is needed to create one or two
anti-proton.

29

  
 
 
 
 
 
  
 

A: 3‘? " .Aluminum
[:[Copper cooling disk
INickel target
DTarget Housing

1: Thin targets
3: Thin targets

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

“ " ‘ Air Channel

Figure 2.6: A schematic diagram of Fermilab’s nickel target for anti-proton pro-
duction. It consists of alternating disks of target (Ni) and cooling disks (A1). The
target is rotated after a period of usage in order to preserve the targets shape.

spread in the horizontal and vertical directions.

The second synchrotron in the anti-proton source is the Accumulator which is
also shaped like a rounded triangle with an average radius of 75 m. This system’s
purpose is to store anti—protons by stacking consecutive pulses of anti-protons from
the Debuncher over a long time (several hours) until enough anti-protons are gen-
erated.The Accumulator has also several cooling systems: stack-tail momentum,
core momentum, and core transverse. When enough 13’s are produced they are sent

to Main Injector see Figure 2.7.

2.2.3 Main Injector

Protons and anti—protons are produced at a mean energy of 8 GeV, however the
Tevatron is designed to accept beams of protons and anti-protons at energies of 150
GeV. During the RunI, the Tevatron was sharing its tunnel with the Main Ring
which was responsible for accelerating protons and anti—protons to 120 GeV or
150 GeV depending on the need of the time. Due to complications of running the
Main Ring and Tevatron at the same time in the same enclosure forced Fermilab
to decommission the Main Ring and establish the Main Injector (MI) which is a

smaller, faster and more efficient version of the Main Ring. The Main Injector

30

    

"Debuncher

Figure 2.7: A schematic diagram of Fermilab’s Debuncher and Accumulator. Pro-
tons with 120 GeV energy are hit on the target producing ps. They are collected
via a lithium lens and sent to Debuncher. Then they are transferred to accumula-
tor (smaller triangular ring). Being a small ring, accumulator cannot store all the
ps, therefore 13 are sent to Recycler via transfer lines.

is the second circular synchrotron in the accelerator chains of Fermilab after the
Booster. See Figure 2.8. With its 18 accelerating RF cavities the Main Injector can
accelerate 8 GeV protons from the Booster to 120 GeV for anti-proton production
or 150 GeV for injection into the Tevatron. 120 GeV protons are utilized for fixed
target experiments and neutrino experiments as well. The Main Injector is also
used for transferring anti—protons from the Accumulator to the Recycler for further
cooling and storing.

For more information please look at [21, 22]

2.2.4 Tevatron

The Tevatron is the largest most energetic synchrotron at Fermilab5. It has 8
accelerating RF cavities to increase the energy of the beams from 150 GeV to 980

GeV. The Tevatron is primarily a storage ring that’s why beams are kept in it for

 

5The energy provided to the beams by the Tevatron is 980 GeV and its circumference
is about 4 miles

31

       
  
 

'5
gr
2:
3a
ch
5.:
IUa‘
moi-V
L'F“
39.3
=.rn
.-
.4
a.
o
H
m
e
o
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Phar Rings

MiniBooNE

Ml-20

Main Injector
Ml-50

  
   

Ah o rt
Du mp

3
E

MI-32
Nil-40

Figure 2.8: A schematic diagram of Fermilab’s Main Injector, and its connections
to its adjacent accelerator facilities. It is used for storing protons for further usage
such as 15 creation, neutrino creation, proton studies, Tevatron stores and the like.

32

r—Tfl

hours until their quality degrades to a point where it is not efficient to keep beams,
due to collisions at detector centers. It is the only cryogenically cooled (at 4 K)
accelerator at Fermilab with about 1000 superconducting magnets which provide
a field of 4.2 Tesla to keep the beams in orbit.

There are two modes of operation for the Tevatron, collider mode and studies
mode. In collider mode protons and anti—protons are injected into the Tevatron
from the Main Injector at 150 GeV energy respectively. These two beams of
particles form a double helix around each other. The protons circle through the
beam pipe clock-wise and anti-protons counter clock-wise. The proton and anti-
proton beams are divided into 3 trains (super-bunch) and each train contains 12
bunches. The bunches in a super bunch are separated by 396 ns from each other.
The time between any two super bunches is 2.65 us. When the Tevatron is filled
with 36 bunches of the two beams, the energies of the beams are ramped up to
980 GeV, giving rise to p13 collisions at the center of mass energy of \/§ 2 1.96
TeV every 396 ns. Please refer to the Figure 2.9 for the relative locations of the
bunches of the proton and anti-proton beams.

The Tevatron is divided into 6 sections labeled ‘A’ through ‘F’. Each section
has 5 buildings labeled ‘0’ through ‘4’. Each ‘0’ location has a straight section
with a special purpose. The CDF detector and collision hall is located at the B0
straight section and the DO detector and collision hall is located at the D0 straight
section. At these two locations proton and anti—proton beams are squeezed and
steered towards each other and forced to collide with each other. The duration of
these collisions are called a ‘store’ which lasts about a day if no problems occur.

For more information about the TeVatron please see[21, 23].

33

Train

 

\

L
139 buckets

N.
1113 RWM ,/'

buckets Abort Gap
total BO c0

 
  
 

protons

Collision Areas —-e-

  
 

A0 DO

3 "Trains" of 12 bunches

  
    

F0 50

Figure 2.9: A schematic diagram of Fermilab’s Tevatron showing the relative loca—
tions of the beams inside it.There are three “trains” of twelve bunches. The bunch
to bunch spacing is 396 ns = 21 RF buckets. The abort gap between the trains of
2.617 psec buckets. Different bunches in a train encounter the opposing beam at
different places around the ring.

34

2.2.5 Recycler

The Recycler shares the same tunnel and is located just above the Main Injec—
tor. The primary purpose for building this machine was to reduce the time to
have enough anti-protons by re—cycling anti-protons from the previous store. Due
to technical difficulties, nowadays the Recycler is used only to store anti-protons
for longer hours and to cool them down beyond the capabilities of the Accumu-
lator. Stochastic cooling and electron cooling techniques are employed to cool
anti-protons to the desired level of intensity. The Recycler has only permanent
magnets.

For more information about the Tevatron please see[21, 24].

2.3 DO Detector

As stated previously proton and anti—proton collisions happen at two points in the
Tevatron tunnel, B0 and D0. In this section we will explain the detector which
resides at D0 section of the Tevatron.

The D0 detectOr, see Figure 2.10, is a general purpose hermetic detector with
a solid angle coverage of nearly 47r. It is designed to study particles that are
remnants of hard scatter collisions of pp. The detector itself is built from inside—
out in a layered fashion so that short lived particles are detected and measured

first. The detector’s components can be listed radially outward as:

tracking system

pre—shower detectors

calorimeter and inner cryostat detectors

muon detector

35

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The

section of the D0 detector.

figure is sealed. The beam pipe carrying proton anti—proton beams passes through
the center of the detector. The direction of the proton beam is assigned to posi-

Figure 2.10: The schematic view of the cross

tive z direction. From the center of the detector in radial direction the following
detectors are located: Central Tracker (Silicon Microstrip Tracker, Central Fiber
Tracker, Solenoid), Preshowers, Calorimeters Inter Cryostat Detectors, Luminosity

Detectors, Muon Detectors.

36

Besides these components, the DO detector has its own luminosity measuring
detectors. Another important part of the detector is the trigger system which is not
used for particle detection but used for selecting interesting events as most of the
collisions between p15 beam are not capable of producing hard scatter events. This
is due to the fact that momentum carried by a proton or anti-proton is distributed
between the valance partons in the hadron. Thus many of the collisions produce
stray particles going in the direction of the beam pipe. Even when a hard scatter
occurs, from the signatures the particles leave behind, one can discriminate against
uninteresting events (not containing weak bosons, or heavy quarks) by means of a
trigger system.

Before going into detector components an introductory information about the

detector’s coordinate system will be given.

2.3. 1 D0 Coordinate System

Choosing a reference point is necessary for every measurement, and the measure-
ments done at the D0 are not different. The definition of a coordinate system
for DO is as following (see Figure2.11): The origin of the right handed Cartesian
coordinate system (x=0,y=0,z=0) coincides with the central point of the D0 de-
tector.The +z axis of this coordinate system is along the beam line in the direction
of proton beam (clockwise in the Tevatron). +x axis points away from the center
of the Tevatron ring and + y axis is pointing upwards.

In experimental high energy, one often finds oneself in need of transforming
quantities such as speed or momentum from one frame to another. This process is

not so simple requiring to make Lorentz transformations of the form

, __ BL-fiv

flL _1—BLfiv

(2.1)

37

 

 

 

Figure 2.11: The orientation of right handed coordinate system of the D0 detector.
The direction of the movement of proton beam is accepted as positive z-direction;
negative z-direction is assigned to the direction of anti-proton beam. y-axis is
chosen skywards and x-axis points in the opposite direction of the center of the
Tevatron ring.

38

By making 6 L = tanhy parametrization this equation becomes

31' = 9L — 212) (2.2)

and boosts along the movement become additive changes to this new parameter.

This parameter is called rapidity and is defined as

1 E
yz—ln +191“

2 E _ 19L (2.3)

 

where L stands for ‘longitudinal’ (along the beam direction). For massless particles
or very energetic ones one can approximate E = p and p L = p cos 6 ,so that rapidity
depends only on the direction. The resulting expression is used for massive particles
as well since measuring 0 is easier, then it is called as ‘pseudo—rapidity’ and defined

as

1 1+cosl9 _

=_1_____
77 2 nl—cos6

— 1n tan 2 (2.4)
and it is a very good approximation when the particles are moving close to the
speed of light.

It is practically impossible to account for every particle produced by the colli-
sion since some of them escape through the beam pipe, which results in the inability
of using momentum conservation, yet one can still use momentum conservation in

the plane perpendicular to the beams movement, the transverse plane. To do this

effectively several variables are defined.

 

 

E
E = E ° = .
T S111 6 COSh 77 (2 5)
2 2 - P P1? Py _
pT pa; + py 1) sm 6 cosh n cos ()5 sin 45 ( 6)

39

Finally there is one other important relation which is used quite often

 

AR = W.- — 27,-)? — (as.- — 453-)2 (27)

th th

This relation defines the separation between i coordinate from j coordinate
in a Lorentz invariant fashion. This variable lets us to discuss separation of the
particles without referring to the frame of reference.

Although in the Tevatron, most of the time there is only one collision per bunch,
due to the widths of the beams, the collision doesn’t take place at the center of
the detector all the time. Because of this fact, unless it is stated otherwise, the
center of the coordinate system used for defining previous variables is taken to be
the interaction point, which has a spread of about 25 cm around the detector’s

center. Thus, 1') calculated with respect to detector center is called detector eta,

17D, whereas 77 calculated with respect to event vertex is called physics eta, 77.

2.3.2 DO Luminosity Monitor

“The rate of interaction within a detector is given by
R = aintL (2.8)

where L is the luminosity and “int is the cross-section of the interaction. The
luminosity is a measure of the density of the particles in both beams.” [23]
Accurate measurement of the luminosity is very important since many mea-
surable quantities depend on it. ] DO’S luminosity measurement is done by its
luminosity monitor detectors placed at z 2 i135 cm from the detectors center.
They have a coverage of 2.7 < [77] < 4.4. These monitors are made up of twenty
four wedge shaped scintillating tiles which have a thickness of 1.6 cm and length of

15 cm. The monitors provide and acceptance of about 98% for inelastic collision

40

detection,see Figure 2.12.

Another important quantity is the integrated luminosity which is a measure
of collected data, f Ldt where L is instantaneous luminosity. In particle physics
its unit is usually expressed in inverse barns bn—ls—‘l. The definition of the

production cross section of any given process is given by

_ dN/dt
_ L

 

0'

(am

where N is the expected number of events and L is the instantaneous luminosity.

Therefore one can write cross section as

NzafLa. (2w)

2.3.3 D0 Tracking Detectors

Tracking detectors are used for the measurements of the momentum of the charged
particless. The idea is to form a path for every particle from the traces they leave
behind, then to calculate the curvature of the paths to evaluate the momentums.
For this purpose a light media should be used in order to decrease energy loss due
to interactions between the media and the particles.

The tracking system was renewed completely for RunlI. It covers a range of
[n] g 3. The tracking system at DO resides inside a 2 Tesla super conducting
solenoid magnet. The magnetic field it produces is in the beam direction, z-
axis. The magnetic field both helps to measure the charge of the particle and
the momentum of the particle by bending the particle in the tracking system.

Measurements of positions of primary and secondary vertexes, in the event are

also done by the tracking system.

 

6Neutral particles do not interact with magnetic fields, thus they do not curve in the
presence of a magnetic field.

41

Intercryostal
Detector

Gama Fiber Tracker

 

Figure 2.12: The schematics of the DO detector’s tracking system. Silicon Mi-
crostrip Tracker (SMT) is surrounded by Central Fiber Tracker (CFT). During the
RunII upgrade phase, another tracking detector is placed in the region between the
beam pipe and SMT, layer-0 detector, which has increased the resolution of the
beam spot and the tracks. The coverage of the tracker is up to n D = 2. Since the
central tracking system sits inside a 2 T magnetic field providing solenoid magnet,
it is possible to measure the momentum of the particles from the curvature of the
tracks.

_ The tracking system of the DO has 2 sub-detectors, Silicon Microstrip Tracker
(SMT), and Central Fiber Tracker (CFT), see Figure 2.12

Silicon Microstrip 'Ikacker (SMT)

This was the closest detector to the beam pipe during RunIIa7. The SMT is

designed to have a very high position resolution so that it is possible to examine

 

7During the upgrade in 2006 Another detector ‘Layer 0’ is placed between SMT and
beryllium beam pipe to regain the lost SMT sensitivity due to radiation coming off of

the beams.

42

z = O 12 F-Dlsks

  
 
 

 

4 H-Disks ;.
section/modules

Figure 2.13: A nice picture showing the DO detector’s silicon micro—strip tracking
system (SMT). It has six barrel shaped detector components laid in the direction
of beam pipe. The barrels have four layers. 8 disks are dispersed between the six
barrels and another four are further away from the center. The disks are placed
Perpendicular to the beam pipe.

the region closest to interaction points. See Figure 2.13.

The S MT is built from silicon wafers in two different shapes, rectangular ones
forms concentric cylinders, ‘barrels’, running parallel along the beam pipe, wedge
shaped Ones are put into circular disks perpendicular to the beam pipe and dis—
persed aal’tnong the barrels. There are six barrels and 16 disks (12 ‘F’ disks, 4 ‘H’
disks).

Barrels are 12 cm long and occupy the central region,hence they are used to
identify particles with small 77. Every barrel has four layers with both sides covered
With Silicon strips, see Figure 2.14.

On the other hand F-type disks stretch out radially from 2.5 to 9.8 cm from

the beam pipe at the positions [z] = 12.5, 25.3, 38.2, 43.1 and 48.1 cm. They are
made of double sided silicon strips. The H—type disks are located at |z| = 100.4

and 121.0 cm. H-type disks are built from single sided silicon strips.

43

 

Carbon

9 fiber
support
structure
l\\
‘ i

° Water
a“ manifolds

 
 
 

 

Fignre 2- 14: The picture showing the cross sectional view of the DO detector’s
silicon micro-strip tracking system (SMT). The SMT barrels and their support
Structure are shown. Four double sided layers are placed consecutively.

Central Fiber Tracker (CFT)

The CF T is the next detector for a particle to visit after its journey through
the SMT- It covers the SMT completely with its eight equidistant super layers of
scintillating fibers, see Figure 2.15 Its outer six layers are 2.5 m long whereas its
inner two layers are only 1.7 m long in order to give room to the H-type disks of
the SMT- The CFT’S detection range is [eta] _<_ 2. Radially the CFT occupies a
region from r = 20 cm to r = 51 cm with 76,800 fibers. Every super layer has one
axial dOUblet layer(along z axis, x layer) and one stereo doublet layer (i30 from
Z axis, u/ V iayers). The axial layer is used for measuring go and stereo layers are
used for Ineasuring n. The resolution of the fiber doublets are about 100 micron.
Compared to SMT, CFT is better for determining the transverse momentum (197*)
Of the Particles due to the long range of radial coverage. The photons created by the
passage 0f particles through the fibers are read by a Visible Light Photon Counter

44

CFT Axial Layers

“AVAVAV'A

 

CPS Axial Layer

one 4.5° sector
(enlarged view above)

Figure 2.15: The picture showing the DO detector’s central fiber tracker system
( CF T). Eight layers of scintillating fibers are used to get an accurate measurement
0f momentum measurement of the charged particles passing through the CFT.
The solenoid is placed between CPS layer and the eighth layer of CF T, but is not

Shown in this figure.
(VLPC), a kind of photomultiplier. At their optimal operation temperature of

90K the photon detection efficiency of the VLPC is about 80%.

2.3.4 DO Pre-shower Detectors

The placement of the solenoid at the center of the DO detector degraded the
calorimeter resolution, as it is uninstrumented. In order to regain it and improve
separation of photons from electrons, DO has another detector, the Pre-shower.

There are three Pre-shower detectors, one for every calorimeter part, one central

and two fOI‘Ward.

The part that sits between the tracking system and the Central Calorimeter
is called the Central Pre-shower Detector (CPS) and has a coverage of n D < 1.2.
It is a CyliI1C1rical detector having a length of 2.73 m and a radius of 72 cm and
cramped into a 5 cm gap. The CPS has three layers of scintillating strips of fibers.

The central layer is axial whereas the outer two layers are situated with an offset

45

 

Support Arc

Figure 2. 16: Figure showing the forward preshower detector system (CFT). These
detectors is placed between the central calorimeter and the end-cap calorimeters.
angle of 3:22.50 with z axis.

TWO other detectors having the same constructional properties are located in
front of the End-cap calorimeters. They are called Forward Pre-shower Detectors.
Unlike the CPS they have four layers of scintillating fibers two 11 and two v type
stereo laKat‘s. The main purpose of these are to improve electron photon separation
power.

Every layer in these detectors is composed of triangles of scintillating fiber with
a 11016 in the middle to accommodate wave-shifting fibers which carry the signal

to waveguides which eventually transport signals to VLPCs. See Figure 2.16, 2.17.

There are Cl‘Dse to 23680 read-out channels for the pre—shower detectors.

46

b) CPS GEOMET RY

/\ 60.00
AWLS Fiber \

a) SCINTILLATOR GEOMETRY 2 Layer of My.”

    

       

Figure 2. 17: The figure showing the DO detector’s central pre—shower detector and

fOl‘Ward pre-shower detector geometry. The geometry shows a little difference be-
tWeen the two detector systems, but in both of the detectors triangular scintillating

fibers with a waveguide in the center are used to transfer light wave for position

measurement.

2.3.5 DO Calorimeter

The DO calorimeter is one of the major parts of the detector. Because of that the
DO detector has such a big coverage in rapidity. Although there were some changes
to the read-out system, the detector itself is the same as in the RunI period. It is
designed to measure the energies of the jets of particles precisely.

The DQ calorimeter system is a sampling calorimeter system which uses de-
pleted u"cadmium (U 238) as the absorbing material and liquid argon at 900K as the
sampling medium (active medium). It consists of three separate cryostats, one in
the central region with an'eta range of l’7Dl < 1.2 and one on either side of central
cryostat, Closing the detector from each side with an eta range of 1.4 < lilDl < 4.2.
For a depiction of the calorimeter see the Figure 2.18. The one in the center is
called Central Calorimeter (CC), and the others are appropriately called End—cap

Calorimeters (EC). The Central Calorimeter (CC) is composed of three sections,

47

  
 
 
 

CENTRAL
CALORIMETER
Electromagnetic
Fine Hadronic

Coarse Hadronic

  
   
             

END CALORIMETER
Outer Hadronic
(Coarse)
Middle Hadronic
Electromagnetic

(Fine 8: Coarse)
Inner Hadronic
(Fine & Coarse)

F Igur e 2-18 I The DO calorimeter. The regions shown yellow and dark blue are built
.by depleted uranium to contain showers of the particles in a small volume. The rest
‘3 bmlt With steel and copper. The calorimeter is cryogenic . The region between
the layers Of metals is filled with liquid argon as active media. The calorimeter
has three parts: North End-cap Calorimeter, Central Calorimeter and South End-
cap calorimeter. The cylindrical hollow region in the center houses the tracking
system 0f the DO detector.

48

electro-magnetic (EM), fine hadronic (FH), and coarse hadronic(CH). In the radial
direction the CC is made up_ of 4 EM layers, 3 PH layers and 1 CH layer. The
absorbing plates are 3 mm thick uranium plates in the EM layers whereas in the
PH they are made of 6 mm uranium-niobium alloys. The CH has 46.5 mm copper
plates as absorbing material. The End—cap Calorimeters (EC) are composed of the
same sections but their orientation is slightly different. The EM layers are placed
closest to the interaction point after them comes the fine hadronic layers, depend-
ing on the closeness to the beam pipe, they are called either inner, or middle. The
CH layers come after the PH layers and are named inner, middle, and outer with
respect to their proximity to the beam pipe. The EM layers and the PH layers
Of the EC have the same properties with the CC’s EM and FH layers but its CH
133/em are built with 46.5 cm stainless steel instead of copper.

The Choice of the thickness of the absorber plates and the depth of the layers is
Optimized according to the type of interaction. EM objects, electrons and photons
interact With the uranium via two processes: bremsstrahlung and pair production.
The energy of an electron with initial energy of E0, after traveling through 1:

amount of material is

E(:1:) = EOe_$/X0 (2.11)

where x is the distance traveled in the material and X 0 is the radiation length
for the material. X0 is defined as the average distance over which a high energy
electron loses 63.21% of its energy (1 -— 1/e); and for photons as 7/ 9 of the mean
free path for pair production. It is 3.2 mm for uranium. Hadrons interact with
the uranium via the strong force. Secondary particles created by the interaction
are mostly neutral pions, no, that decay to photons without delay. The rest
Of the secondary particles continue interacting strongly, and this results in the
spread 0f the hadronic showers. The equation is similar to equation 2.11 with the

replacement of X0 with A0 nuclear radiation length.

49

\

’----

 

|«—1 Unit Cell —>|

Figure 2.19: A nice picture showing the unit of the calorimeter cell of the DO
detector. The thickness of the uranium absorbing plates differs depending on
Which layer it is located.Between the plates resides the liquid argon as the active

ionizing medium.

The energy measurement of the incoming particle is done by the charge col-
lected in the fimdamental unit of calorimeter, the gap. For a schematic drawing of
this unit see Figure 2.19. Secondary particles (electrons, pions) from the shower,
ionize liquid Argon. These electrons move under the influence of the high voltage
electric field and accumulate on the signal board. The drift time for electrons to
reach the signal board is 450 us at most. From the signal board the charge is sent
to pr e‘3»1111)1ifiers. Earlier we mentioned that the calorimeter is built in layers like
an onion. Every layer have several (not necessarily the same number of) gaps in
them. In 77 x 45 surface, every layer is divided into cells which have dimensions of

0'1 X 0-1 (A77 x A45) with one exception in third EM layer which has more fine
segmentation 0.05 x 0.05 (An x A¢).The reason for this finer partition is that this
layer corresp ends to the maximum of an EM shower. Although this was correct
in the RunI period, due to solenoid and pre-shower detectors the maximum of EM

showers happens between the second and the third layer of the EM calorimeter.For

50

schematic views of a calorimeter quadrant refer to Figure 2.20. Although cell sizes
don’t change in 17 x ()3 space, in the lab frame they change, as the second exception
, for high T) values (In Di > 3.2) the sizes of the cells are increased to 0.2 x 0.2 in all
layers. The total number of cells, or read-out channels is on the order of 50,000,
which are grouped into projective towers whose number is on the order of 5,000
see Figure 2.20.

The regions where ECs and CC meet are called ‘inter cryostat region’s (ICRs).
In order to reduce the ‘dead’ region in the detector, two additional types of detec—
tors are added to the calorimeters. The massless gap detectors are placed inside
the cryostat covering 0.6 < I17 Dl < 1.3. They are ring shaped in (15. They are simi-
lar to the gaps but don’t have absorber plates, that’s why they are called massless.
The second type of detector is the ‘inter cryostat detector’ (ICD), which is again
a ring in (13 covering 1.1 < lnDl < 1.5. Its structure is similar to the pre-shower
detectors.

The read-out chain for the calorimeter is shown in Figure 2.21. A charge
proportional to the lost energy of the particles passing through the cells is sent to
the read-out electronics. This charge is integrated in the preamplifier, and turned
into a voltage. These voltage pulses are carried to baseline subtracters (BLS),
which shape the signal and remove the offsets in the input voltages. The signal is
sampled at its peak at around 320 ns, which corresponds to only a portion of the
actual signal (2/3). These signals are, then, stored. in switched capacitor arrays
(SCAS) until a trigger accept decision is sent, otherwise they are discarded. The
trigger system is explained later. If the signal has high probability of containing
heavy particles , then it is digitized by analog to digital converters (ADCs) and
sent to the data acquisition system (DAQ). The read-out system is designed to
handle data input up to a levell rate of 10 kHz.

The. calorimeter design criteria for the energy resolution are given as below.

m

. c

V-c

“.0

0-0”:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

N V“? “l ".
o - '
(Q N (Y \_ \ \_ l
‘9 1-\ \. \‘i\\_\.\\l‘“lll|l
q: T: ‘\ \‘ \ i l lllulli .
‘— "\ \ "‘ ‘ .illi
0! \ \ “ \ -\i \‘Xilllni i
\ \ . .
O- I
P \\ ‘ I
\ a . I
ll ‘ ‘ l
°°- a
O\ -. \ ‘
\x i
\ l
\ \ 'l
‘0. \ ll
0 . ., .
\l . \ \ I
\\ ‘‘‘‘‘
<1- \\ - ‘\\\'\\\\\\il...
' \ \ \ \_..... .
O \l N x \ -‘ \'\\\\\ll. ill
\ \ ,\, A...“
\ \ \‘\\N‘ ,\-.'.:". ._l
\w\\ \\\ f; I‘ll”
N v N ‘ ,
d \I‘ \ \‘~ \\§ \ \ l
P\ Fish
\\ \‘:\\Q \ |
q .53.:
o .._._ _
ll
:'

Figure 2.20: The cross sectional view of calorimeter quadrant. In this picture
the calorimeter towers are shown as differing colors centered at the center of the
calorimeter. For trigger system two of these towers are combined together and an
approximate energy measurement is done for fast response times.

52

 

 

 

 

 

 

 

 

 

 

UN ‘30
Cell i”!
:1; . 5
Pulse f ‘ l
Input Fm" scars ADC

5MP" 4 in 2 banks

Figure 2.21: The schematics of the calorimeter readout chain. Every cell can be
thought of as being a big capacitance charged according to the energy of the in-
coming particles. At the end of this chain the energies of the particles are digitized.

For electromagnetic energy

0E 0.15
— = —— 2.12
E «E ( l

and for hadronic energy
”_E _ L50
E \/E

However, the new material in front of the calorimeter worsened these resolutions

(2.13)

in RunII.

2.3.6 DO Muon Detectors

The outermost sub-detector in the DO detector is the muon detector which is also
manufactured in layers like all the other systems explained until now.

The muon detector is a cubic detector having four layers one of which is the
muon toroid providing the necessary magnetic field to bend muons. The layers
are placed in the following order: A layer, toroid, B layer and C layer. Due to
being a cubic detector it has four sides running parallel to the beam pipe which
are called muon central (MUC); the other two sides which are perpendicular to

the beam pipe are called muon front (MUF). Being a rectangular detector MUC

covers approximately a range of |n| < 1 and MUF covers from that point until
approximately 77 < 2.0.

All the layers in both MUC and MUF contain wire chambers (drift tubes),
depending on the position they contain scintillators too. Drift tubes (PDTs in
MUC and MDTs in MUF) are used to measure position 2 and either x or y.
The scintillators are used for 43 measurements as well as timing for triggers and
background reduction.See Figures 2.22, 2.23 for inflated schematics of three layer
of MUC and MUF for both drift tubes and scintillators. As mentioned above
the toroid is located between A and B layers and provides a magnetic field of
1.8 Tesla. Drift tubes contain an ionizing gas and high voltage anodes(4.7 kV)
and cathodes(2.3 kV). When a particle enters, it ionizes the gas and electrons are
collected on the anode. From the drift time it, is possible to locate where the
particle hit in the tube with good precision ( 1mm for PDT, and 0.7 for MDT).
The drift times for PDTs and MDTs are 490 ns and 10 ns respectively.

MUC coverage is compromised at 4.25 < (.6 < 5.15 (can be seen in the Fig—
ures 2.22, 2.23) due to the fact that detector systems placed inside(calorimeter,
tracking system) and readout electronics need support. Besides this MUC and

MUF detectors have other gaps due to construction in (15 octants.

2.3.7 DO Trigger System

An other component of the DO detector, which is not used for measurements but
plays a rather important role in data taking is the DO trigger system. It is the
system that selects events that are worth to keep for further processing. It may
be tempting to analyze all data that is produced by the detector; however, this is
impossible with today’s technology. The collision rate at the Tevatron is 2.5 MHz,
which corresponds to approximately 425 GB of data per second. This amount of

data is impossible to write to tapes. Besides, most of the collisions happen in a

54

 

 

 

 

   
 

Proportional

 

 

Figure 2.22: The schematic picture of the muon drift chambers are shown in all
the layers. Due to the presence of the detector support, the bottom side of the
detector coverage is partial.

55

   

     
    

 

  
   

Nonh

   
   
 

  
  
 
   
 

      
   

 

       
  

   
    

 

' v ‘- ‘v- '1' . , y g
; «eav;.:IIIII///,"." N X
'o’vil'.llu’l”/I’ ’/ 5 .
6“ o" """00 ’6 [e
- - a , e c
(It'll;’,‘ ’6’? a o w
“in". 1 a
3 '3 E E ‘ o-
- g z: +0 Q
::_ :55: a ,
-::‘ . . . -.- L o
:;;; (I) := 4.. >5
5%,: \ O) H c + >~.
322122,, . :31, ., C 3 I
. ’ .70,’(,l,‘:ru.‘-‘-.';_>'..|“v .. a o—
v ééifill 'n ' \.l ‘ o
/ I [I II" c :

South

 

. a v ro,..0, ’
'IIIIII’,’ . 0.
”tall,” 1” - ‘
II I’ ’

  

 

M.
\\
\\ ‘

\\\\\\\\

;\\‘

\\\\\\
\\

“\u

0"”; '41:." ‘ I :'
"Iain“ “ t
(I

l

1 l
‘0 ‘..‘,. r

«“
213*

.3.
«“

   
 

 
     
 

’v'iuIII/i 6'?

  
  
  

    
  

,’ ,l72,':it=.-;;:55‘::;e.3
Ill: 0 l 0

'4’ Wit/llonnflgv’»;

”an”. ”a;

p"’

 
   
   

 
 

’/Illluu

   

Figure 2.23: The schematic picture of the muon scintillators are shown in all the
layers. Due to the presence of the detector support, the bottom side of the detector

coverage is partial.

way that doesn’t produce a head on collision which has the potential to produce
the particles related to the processes of interesting physics, such as W or Z bosons.

It is the responsibility of the trigger system to pick events with high probability
of containing interesting physics objects such as bosonsThe system consists of
three stages: The Level-1 (L1) trigger system which makes very fast decisions
by hardware level instructions, the Level-2 (L2) trigger system is a mixture of
hardware and software; and the Level-3 (L3) carries out selections by a software
system which takes the longest time between the three due to complexities of the

instructions.

The Level-1 Trigger

As shown in Figure 2.24 the decisions made by L1 trigger system are based on
information given by four sub-detector systems: the calorimeter, the central fiber
tracker, the muon and the forward proton detectorse. The L1 trigger decisions re—
lated with these detectors are made by their corresponding trigger systems. These
systems uses information collected by the detectors to feed L1 trigger framework
with an acceptance decision named as an AN D / OR term. Depending on the result
of the AN D / OR terms and the availability of the data acquisition system, the L1
Trigger System either issues an accept decision and sends the event to L1 Trigger
System or a reject decision and discards the event.

The Level-1 Calorimeter (L1Cal) trigger uses a special form of calorimeter tow-
ers which are constructed from four neighboring standard read-out towers grouped
together 2 x 2; which means every tower has a cross sectional area of 0.2 x 0.2
in (77, qfi) space. Totally, there are 1280 trigger towers for the calorimeter, (b D is
divided in 32 and n D is divided in 40 regions. The trigger towers are read sep-

arately as EM trigger towers and HAD trigger towers. The coarse hadronic part

 

8the forward proton detector was decommissioned at the beginning of the Rung

57

Detector Leve|1 Level2
CAL —> L1CAL r—H L2CAL

CPS l——— L2PS F
FPS L1 CTT-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l——> LZCTT -
CFT . +
SMT I , LZST'I'
MUO ’* '-1 MUD " L2MUO —

 

 

 

 

 

 

 

 

 

FPD L1 FPD —
v i

__*
- Trigger I: Global
Luml +lFramework * L2

Figure 2.24: The data flow diagram of the Level-1 and Level-2 trigger systems.
SMT is not used in the first level because of the time constraint on this system.
Trigger framework is the decision maker and the messenger between the different
detector components and read-out crates.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

58

of the calorimeter, the massless gaps and the ICD detectors are not used in the
triggering. The two parts of the trigger towers (EM and HAD) contain the sum
of the energies in the EM layers and the F H layers of the calorimeter respectively.
The energies in these towers are digitized in 8 bit numbers (ADC counts), and
then converted to transverse energies ( ET(EM) and ET(H AD) ). A low energy
cut (pedestal removal) is applied at this point to remove noise. After calculating
global ET of EM and HAD for the entire calorimeter, the number of EM towers
having an ET above a certain threshold is counted. Both of these informations
are used for making L1 Calorimeter decision.

The Level-1 Central Track Trigger (LICTT) reconstruct tracks by only using
CFT and CPS detector axial hits. The conditions for accepting an event is usually
the number of tracks above a pT threshold. The list of the tracks are passed
to Level-1 Muon Trigger (L1Muon) system and TWF. LlMuon employs tracks
consistent with a muon track pattern from the passed list and builds trigger objects
by using both tracks and muon scintillator hits. An L1Muon trigger condition can

be created by detector region, track quality and pr threshold.

The Level-2 Trigger

The L2 trigger system, builds physics objects by relating different components
of the L1 trigger system for events passing the L1 triggers. It has access to more
detector trigger systems.Its elements are shown in Figure 2.24. The L2 calorimeter
(L2Cal) trigger runs EM and jet algorithms to form em objects (electrons and
photons) and jets from EM and HAD trigger towers. 'The L2 Pre-shower (L2PS)
is used to improve the electron photon separation efficiency. All the layers of PS
detector are used to form track clusters. The L2 Central Track Trigger (L2CTT)
takes information from both the LlCTT and the L2 Silicon Track Trigger (L2STT).

It combines the LICTT tracks and sorts, calculates several isolation criteria which

help increase trigger capabilities and (to of the tracks with respect to beam axis.
Level-2 Muon (L2Muon) produce muon candidates by combining track segments
and layers of the detectors and sorts them in descending order of pr. Level-2 Pre-
shower (L2PS) is used in improving the detection efficiency of electrons. All the
information from level-2 preprocessors are combined in Level-2 Global (L2GBL)
which. makes a decision of acceptance depending on the AND / OR terms. Then
that decision is sent to TWF which eventually communicates with the read-out
crates about sending the event to Level—3 triggers in the case of acceptance or

discarding it in the case of rejection.

Level-3 Trigger

Accepting an event at L2 causes the trigger system to send the event to the next
and the final step Level-3 before writing the event to the tape for safekeeping. At
this SYStem all of the decisions are high-level (software). The trigger software is
a light Version of DO reconstruction algorithm. Each detector system passes the
readout information to the L3 farm nodes (high performance PCs). The events are
reconstructed and by means of filters to identify physics objects such as jets and
muons ,

trigger decision are made both on the objects and their inter-relations.

If an event passes an L3 trigger, it is sent to computing center to be recorded

on, tape -

60

Chapter 3

Event Reconstruction and Object

Identification

“The balance between the positive and the negative

helps make it a safer environment. In any event,
employ lots of data in the review. Because we’re a
creative organization, people tend to assume that

much of what we do can’t be measured or analyzed. ”[25]
Ed Catmull

3.1 Introduction

Every Collision passing trigger requirements is named as an event. Every event is
comp 0Seed of information from every active sub-detector system. At this stage an
event is not very useful for physics analysis since it consists of digitized readout
information for each channel of each sub-detector. These readouts are different for
every sub—detector. For the calorimeter and silicon, it is the amount of collected
Char ge, for the muon system it is time differences in the drift tubes and for scintil-
lators it is the light yields. The software collected under the name DOreco is used

t . .
0 Convert ‘raw’ data from each sub-detectors to physrcs objects such as muons or

e . . . . . .
lectTons. It also applies corrections from calibration and ahgnment studies.

61

3. 2 Tracks

The tracking system is built in such a way that a charged particle leaves traces
along its way through the SMT and the CFT detectors. By combining hits in the
consecutive layers of this system it is possible to visualize a path where a particle
has passed. Because of the presence of the magnetic field these paths are curved
allowing one to measure their momentum and charge.

D @reco starts building tracks from the data by first clustering hits in each layer
of the SMT and the CFT. It uses two different algorithms, which take the energy
weighted centroid of these clusters, in parallel. The two algorithms are called the
Histogram Track Finder (HTF) and the Alternative Algorithm (AA).

The HTF algorithm uses the fact that a curve can be parametrized by p, cur-
vature of the track, o the angular direction of the curve from the origin ,and do
the distance of the closest approach to the origin. Hits with the same do will pro-
duce a. line in a p x ab histogram. Then hits that belong to the same curve should
intersect at a point in p x (1) space, and the corresponding histogram will have a
local maximum at that point. Those hits which have the same (p, (p) values should
be on the same curve, then.

The AA algorithm finds track candidates by using the same technique in two
different directions, from inside to outside, and in the reverse direction. It starts
with seed clusters in SMT barrels or F—disks. Then tracks are built by searching
a Sechd cluster in any larger silicon layer within a window of |A¢>| < 0.08. This
proceSS continues until three clusters are found. Then they are fit to a curve. If
the Cillll‘ve has a do within 2.5 cm of the beam spot and its radius of curvature p
is greater then 30 cm (pT > 180 MeV) and X2 of the fit is less than 16, then it
is accepted. The same procedure is applied on the remaining layers Of SMT and

CFT in the order of increasing radius. If a multiplicity occurs due to getting the

s‘ .
(1th track from different clusters, then both of the candidates are passed to the

62

next level of acceptance. This process is followed in the reverse order to find tracks
with a few or no SMT hits.

After completion of both algorithms track candidates are eliminated by the
requirements on the number and type of missed hits along the candidate’s path.
The tracks are processed by a Kalman fit algorithm which simulates the effects
of the non-uniform magnetic field, interaction of particles with the material in
the tracking system and the beam pipe. Duplications due to processing twice are
removed.

Then the final list of the tracks are put into the event by the DQreco algorithm.
These tracks have properties like curvature and distance of the closest approach
(dca,d0) of the track with respect to beam spot, probable charge of the particle

and SO on,

3.3 Primary Vertex

The cellter of the coordinate system which is defined as the point where pp collision
happens and in principle the primary vertex, from which all objects originate. Its
DOSitiOII changes between events, with a spread of 40 pm in the x—y plane (0333/)
and 28 cm in the z-direction (oz).

Identifying the primary vertexes (PVs) is a two step process, the first primary
vertex finder algorithm approximates a position for beam position and PV candi-
dateS_ For this tracks with dca significance (dca/adca) less than 100 with respect
to detector center in (r, ab) coordinates are used. The position of the PV is found
iter a'tively calculating the fit value until its X2 is less than 10 otherwise removing
the track with the largest contribution. Then other vertex positions are found by
the t‘l‘acks’ not used in the previous steps. Finally, the selection of the hard collision

c . . . .
enter from these candidates comes from a log10 pT track dlstrlbution of Monte

63

Carlo simulation of minimum bias eventsl. A probability value for every track
1' n each vertex is calculated by using this distribution[29]. Then every vertex is
assigned a probability by multiplying the probabilities of the tracks in them. The

vertex having the lowest probability is chosen as PV.

3. 4: Electromagnetic Objects

ElVI object reconstruction starts with a generation of a list of candidate clusters
in the data produced by EM calorimeters citation. They are found with a simple
cone algorithm. This algorithm starts with sorting all the EM towers2 and selects

the most energetic one as the seed tower. If the total transverse energy of the

 

towers within a radius of r 2 AB = \/Ad>2 + A172 < 0.2 is greater than 1.5 GeV
(ET > 1.5GeV), then it is compared against EM variables.
The EM cluster should be isolated which is defined by the fz- so parameter.

_ Etotalmn = 0.4) — E E Mum = 0.2)

ft” _ EEM(AR = 0.2) (3'1)

 

Another variable is the em fraction f E M which is defined as

_ EEM(AR = 0.4)

 

(3.2)

Where Eton, is the energy in all of the layers and E E M is the energy in the four EM
layers and the first FH layer. The requirement on these variables are fiso < 0.2
and f EM > 0.9. Clusters passing these two criteria are subjected to search for a

Ina‘t'ciling track. For a track to be matched to a cluster the X2 of the fit between
1\

 

minimum bias event is a soft interaction, so most of the energy in the event is deposited
0 the beam pipe, high |77D|[28].

ters An EM tower is defined as the four EM layers accompanied by the first FH layer of calorime-
PV (ECN,CC,ECS) having a cross-sectional area of 0.1 x 0.1 in 17 x (b and originating from the

close t.

64

the track and the EM cluster is determined. It is defined as

 

X2_(_A£ 2+(_Ai)2+(ET/PT—1)2

_ (3.3)
0A¢ 0A2 GET/p71

where A45 and A2 are the azimuthal angle and 2 position difference between the
track and the EM cluster at the third EM layer; 045 and 02 are the corresponding
resolutions. The ratio of ET/pT is the ratio of the transverse energy of EM cluster
to transverse momentum of the track. This definition of X2 holds true only for
the central calorimeter region, for end-caps the last term is dropped. Fora track

to match to an EM cluster X2

should be greater than 0.01. A cluster passing the
fiso al'ld the fem criteria is assigned an EMID of 10 (photon). If it satisfies all
of the above conditions then it will be assigned an EMID of -11 for electrons and
+11 for positrons.

T0 diminish contamination from the hadronic decays additional selection cuts

can be applied to multivariate quantities such as the H-matrix and the electron

likelihOOd. The H-matrix is a X2 test. It has seven variables:
' tile fractions of the energies in the four layers of the EM calorimeter.
' the cluster size in the third layer of EM calorimeter.
° the 2 position for the PV.
. the logarithm of the cluster energy.

is calculated from the following equation:
X2 = Z Zea,- — ma]- — :r'flHij (3.4)
i j

w .
here as,- is the values of the ith variable of EM cluster, 372' IS the expected value

f . . .
or that variable from the test beam data and Monte Carlo sunulatlons. H .2; j 18 the

element of the inverse covariance matrix which is calculated from the test beam.
The electron likelihood [26] on the other hand, depends on the following vari-

ables:
o the EM fraction, f E [W-
o the H—matrix value.

2

a tile spatial track match X probability.

0 @712 the ratio of the calorimeter cluster energy to its matched track’s mo—

mentum.
o the distance of closest approach, (10.

0 the number of tracks in a cone of radius r2005 from the associated track,

inc: luding itself.

the Zz’ pan of the tracks in a cone of radius r= 0.4 from the associated track,

e>C(:luding itself.

To Calculate the value of the likelihood the following equation is used:

 

_ Psigm)
L(a:) -— Psiga) + Pbkglx) (3.5)
P5290: :HP sigh: (3'6)
13%ng :HPbkg( 5%) (3-7)

w

here :10 is a vector of afore mentioned variables; Psigtci) is the probability of
b

elng an electron, assigned to the EM cluster; Pbk g(517,-) is the probability of being
a

nBrthing else, assigned to the EM cluster. These probabilities are obtained from

he distributions of the variables entering the likehhood calculation.

66

3.5 Hadronic Objects, Jets

It was mentioned in the first chapter that quarks cannot be observed alone but
rather they quickly form bonds with other quarks which are created from the
vacuum. This process is known as hadronization. A high energy quark then
becomes a jet of hadronic particles, which are referred only as jets. Some of the
particles are charged whereas some are not. Thus instead. of measuring properties
of the quarks coming out of the interaction, one measures these jets’ properties.
See Figure 3.1

At DO jet reconstructions and hence their measurements are done according
to the information collected by the calorimeters. Although there is more than
one jet reconstruction algorithms, this analysis uses jets reconstructed with the
. ’Simple Cone Jet Algorithm’, therefore we will only speak about the simple cone
algorithm. The following steps are taken in order to reconstruct a jet: formation of
jet towers from the calorimeter cells, preclustering of the towers, proto—jet collection
0f prec1L‘lsters, finalizing jets by splitting or merging of the proto—jets.

For every cell in the calorimeter, the program called E—scheme calculates the
moment-11m four-vector assuming E of the cell equals the magnitude of the three-
mOmentnm (massless cell assumption). The direction of the momentum is defined
from the primary vertex to the centroid of the cell. Then the four-momentum of ,
the toVVer is calculated by adding four-momenta of all the cells in that tower. Once
all the active cells are placed in jets, the list of jets is transferred to the Simple
Cone Algorithm.

The Simple Cone Algorithm identifies preclusters from the jet towers as below.

It '
Selects the highest ET tower as seed and adds to that tower its neighboring

 

to .
We? in AR = \/An2 + A¢2 < 0.3 one by one starting from the highest ET

t , . .
Owen calculating the new center after each addition. When no tower 18 left, it

f1 - '
1t'el‘s out preclusters With only one tower or With pT < 1 GeV.

67

 

 

 

 

 

 

 

 

 

’-‘.b--- to- ..-+~.
CB1~~.-P-- ---#"
l
| I
*- ‘ 0
'2. ‘ ’ H
l-
3 J | '
E FH | '
‘ I
% i '
u ' E
EM 0
—————————— .‘—--
E.
2
0
E
I
9' I
———————————— +—
3
--u
5
i:
I
:-

 

 

Figure 3.1: The figure showing the development of the jets in the calorimeter, hence
the procedure to follow to reconstruct jets based on the information collected by
the calorimeter.

68

Generation of proto-jets is similar to preclustering in the sense that instead
of individual towers, preclusters are used. The difference Comes from the fact
that instead of using 17 (pseudo rapidity) to measure the distance from the center,
y (rapidity) is used in the AR calculation. Taking the highest pT precluster
as the first proto—jet seed, every precluster is consumed within a cone of radius
7‘ 2 AR = 0.5 by combining it with the seed via the E—scheme until the candidate
is stable. This procedure is repeated until all the preclusters are used.

The next step is to verify that, all of the proto—jets are unique and none of them
are sharing elements by the ‘Merging and Splitting Algorithm’. This algorithm
merges two proto—jets if the lower pT jet shares more than 50% of its pT with the
other. The one with the lower pT, then, is removed from the jets list. On the
other hand if the lower pT jet shares less than 50% of its pT then the two shared
towers are split. The final list is the jets list. They are required to have at least a
pT of 8.0 GeV.

Once all these steps are taken,quality cuts are applied to separate real jets from

fake ones. These requirements are:

c Electromagnetic fraction; 0.05 < f E M < 0.95
0 Coarse hadronic fraction; fC' H < 0.4

0 Hot Fraction < 10

o n90 > 1

The first one of these is to remove electron or photon like objects and against too
much hadronic activity. The second removes jets with very high coarse hadronic
content. CH layers shouldn’t have too much energy deposition, and they tend to
be noisy. The third cut means that the ratio of the energy in the most energetic cell
to the energy of the second most energetic cell cannot be more than 10. That is a

signature of a read-out problem. The forth one requires that the number of towers

69

with 90% of the energy of the jet be greater than 1. Besides these requirements,
there is one more important out which is the comparison between the energies of
the jets found by the Levell Trigger System and the DQreco system.

At this point it is said that the jet is reconstructed. However, in order to use
these jets in analyses, the energies of the jets are corrected. These corrections
account for the noise, calorimeter response, showering effects and the underlying
event. This type of correction is termed Jet Energy Scale (JES) corrections. With
JES it is aimed to get back the energies of the particles in the jet before they hit

the calorimeter. Then

Emeas _ O
EJESZ RXS (3.8)

 

where Emeas is the reconstructed energy, 0 is the offset of the energy due to elec-
tronic noise, uranium noise, energy pile-up or underlying event, R is the calorimeter

response and S is the fraction of shower leakage from the cone.

3.6 Missing Transverse Energy, MET

Unlike the other particles, neutrinos interact with the matter in very rare occasions.
The DO detector does not detect neutrinos directly. However, the presence of the
neutrino in the event manifests itself as an imbalance of the measured transverse
energy. The magnitude of MET is the magnitude of the transverse energies of the
calorimeter cells and its direction is the opposite in qfi so that it balances energies

in transverse plane.

3.7 Muons

Muon system is built to see the path of the particle, hence to measure its momen-

tum. Their reconstruction starts locally in the muon system. The hits in the drift

70

 

r-

u. j

chambers of the three layers are used to make local track segments in the muon
system. Hits from the scintillators are matched to the track segments. With the
help of the toroid it is possible to make a local transverse. momentum pT measure-
ment by measuring the deflection on the path of the muons, see Figure 3.2. The
resolution and the precision of this measurement is increased by matching these
tracks to the ones reconstructed by central tracking system.

The muon reconstruction algorithm starts building the tracks based on the
drift chamber hits in individual layers of detectors. This process considers only
one o octant at a time. The algorithm requires some restrictions on the track
segments deve10ped from the pairs of wire hits: i) no hit can lie on the same drift
circle ii) the separation of the hits along the y axis should be less than 20 cm iii)
hits should be on different wire planes unless they are from different neighboring
wires. These can be more easily visualised by looking at the Figure 3.3. Track
segment candidates are compared and connected together if they are compatible.
The scintillator hits are used to refine the timing of the hits, the tracks are fitted
to a line. The tracks with lowest XQ/th'ts are kept for each layer of an octant.
This process is repeated for every octant. Afterwards a search for a possible track
match in the central tracking system is done.

Depending on the number of hits a muon can have different quality which can
be tight, medium or loose. These qualities are based on the local muon information.

For a muon to be tight, it should have both A and B+C layer segments, at
least two wire hits and at least one scintillator hit in the A layer, at least three
wire hits and at least on scilliator hit in the B+C layers and the fit between A and
B+C layers should converge.

For a muon to be medium, there are a few different possible scenarios depending
on the number of layers a muon has a hit. It is an ’nseg3’ (number of layers in

the muon detector that are hit by this muon) medium if it has at least two wire

71

   

 

 

<

>~.

a:

, >5
*5 i
g) I
8 I
U I
m I

.e

 

 

x
xB

end toro
begin toro
xA

Figure 3.2: Figure showing the calculation of the momentum of the muon locally
by the muon detector. The toroid affects the path of the muon passing through it
by deflecting it by certain angle which depends on the charge and the momentum of
the muon. The magnetic field in the toroid is a known parameter of the calculation.

72

Wires: black x's '
MC track: blue “ ‘
Drm circles: red

 

 

 

 

 

Figure 3.3: Figure showing construction of a muon track segment in drift tubes.
The drift wires are perpendicular to the plane defined by the paper. Blue line is
the constructed muon path according to the drift circles which are shown in red.

hits and one scintillator hit in the A layer, at least two wire hits and either one
scintillator hit in the B+C layers or a central track is matched to it with less than
four hits in B+C layers. The muon is an ’nseg2’ medium if it has two wire hits
and one scintillator hit in the B+C layers with a central track match. The muon
is an ’nsegl’ medium if it has at least two wire hits and one scintillator hit in the
A layer with a central track match.

By dropping one of the requirements on the different type of medium muons,
one can get loose muon definitions.

Matching is done between a muon track in the muon detector and a central
track with at least pT > 1 GeV, if they are within |An| < 1 and |A¢| < 1 of each
other. The track must have a X2 x d.o. f < 1000. In the calculation of X2 the

position and momentum measurements are used. [27]

73

Chapter 4

Data Samples

“ ‘I had’ said he, ‘come to an entirely
erroneous conclusion which shows,

my dear Watson, how dangerous it always is
to reason from z'nsufiicz’ent data.’ ”[41]

Sir Arthur Conan Doyle

As mentioned in the previous chapters, it is virtually impossible to analyze
all the collisions happening in the detectors. Depending on the signature of the
process for which one looks, most of the time, it is unnecessary to analyze all
the recorded events as well. This chapter talks about data sets that are used in
this analysis and the quality requirements by which they are bound to produce a

scientific and unbiased result.

4.1 Data Set

This analysis uses data collected during the 2002-2006 physics runs. The versions
of DQreco to reconstruct the events in these runs are p17.09.03 and p17.09.06. The
term to refer to data just after reconstruction is ‘raw data’. The raw data from
this period was further processed by DQCORRECT in order to make corrections

on the properties of the physics objects such as EM, muon, jets and missing ET.

74

The Common Samples Group (CSG) established in D0 is responsible for pro—
viding analyzers with pre—processed data in order to . Pre-processed here only
means that a very first selection based on very loose criteria is done. For this

analysis the following data sets are used:
c CSG_CAF_2EMhighpt_PASSB_p17.09.03

CSG_CAFQEMhighth’ASSlpl7.09.06

CSG_CAFJEMhighpt_PASS3_p17.09.06b

CSG_CAF_2MUhighpt_PASSB_p17.09.03

CSG_CAF_2MUhighpt_PASSB_p17.09.06

o CSG_CAF_2MUhighpt_PASSB_pl7.09.06b ,

These samples are CAF trees1 produced by the Common Samples Group with the
p17.09.03 or p17.09.06 DQreco versions. They were created by selecting 2 high pT
leptons from all the data collected during RunIIa with the following requirements.
For the EM case there should be two simple cone objects with an EM ID of 10
(identification number for photon) or ill (identification number for electron ‘-’ or
positron ‘+’) having a pT greater than 12 GeV. For the MU case however, there
should be two ‘Loose’ muon objects with central tracks having at least a pT of 10
GeV. Producing these data sets beforehand helps analyzers by reducing the time
of running analysis code on the whole data.

Moreover the same data sets are used when measuring the QCD background,
which will be discussed in more detail in the next chapter. The reason for using

the same set is to avoid any biases.

1CAF trees are ROOT trees (a. data format readable by ROOT) specialized to keep
information about a collision event created by Common Samples Group (CSG).

 

75

 

 

 

A
i
s
“l7
M.
,1.
_v
i.
t
' 4
k
~

4.2 Data Quality

Although constant emphasis is put on and much care is given to the quality of
the data written to tape, complexity and the immensity of the system produces
occasional hiccups under such as a failing power supply or unreliable read-out
channel and so on. An analysis should be free of any of the problematic events in
order to secure its results’ reliability. For this reason there are several restraints
placed on the states in which an event can be. The first one of these is the run to
which this event belongs should be declared by the Data Quality Group as ‘good’
which means that for EM channels the SMT quality tag, CFT quality tag should be
‘REASONABLE’ or better and calorimeter quality tag should be ‘UNKNOWN’
or better; for MU channels SMT quality tag, CFT quality tag, MUON quality
tag should be ‘REASONABLE’ or better and calorimeter quality tag should be
‘UNKNOWN’ or better.

Bad luminosity blocks2 are also removed. Events with unphysical activity in
the calorimeter for example ‘ring of fire’ or ‘hot cells’ are also removed by removing
their corresponding luminosity blocks.

After removing all the bad quality events, it is possible to measure the lumi-
nosity of the data. As mentioned before in chapter 2, luminosity is a measure of
how much data is collected. Nevertheless a trigger system is in place before even
checking if the states of the detector components are fine, which weaves complexity
into the calculation of luminosity. For the total luminosities of different luminosity
epochs please see Tables 4.1, 4.2. An irreducible uncertainty of 6.5% is attached

to all of these numbers.

 

2luminosity block refers to a data collection period which is about 1 minute

76

 

 

Trigger Run Ranges Luminosity
Version (pb‘ 1)
U8 — 2211 160582 — 178721 118 i 8
1212 178722 — 194566 239 d: 15
v13 194567 — 208203 375 :l: 24
1214 208204 — 215670 337 d: 22
v8 — 2214 160582 — 215670 1068 :l: 69

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.1: The integrated luminosity of the RunIIa period is shown in this table
for the 2EMHighPt data sample. The run ranges include test runs also but those
runs are not included in the luminosity calculation as well as those runs that are
excluded due to bad data quality tags. An uncertainty of 6.5% is associated to the
luminosity result, because of the way luminosities are measured at DC.

 

 

Trigger Run Ranges Luminosity
Version (pb‘ 1 )
u8 — u11 160582 - 177283 52 :l: 3
v12 177284 — 194566 248 :t 16
2213 194567 -— 208203 342 j: 22
v14 208204 — 215670 292 :l: 19
v8 — 2114 160582 — 215670 944 i 61

 

 

 

 

 

 

 

 

 

 

 

 

Table 4-22 The integrated luminosity of the RunIIa period is shown in this table
for the 21\/IUhighpt data sample. The run ranges include test runs also but those
runs are not included in the luminosity calculation as well as those runs that are
excludeei due to bad data quality tags. An uncertainty of 6.5% is associated to the
lummoslty result, because of the way luminosities are measured at DC.

77

4-3 Monte Carlo

All of the measurements are done on the data collected by the DO detector. How-
ever not only to test the theory, but also to understand the detector response more
deeply, one essentially needs a way of simulating high energy collisions. This is
achieved through simulations of collisions and simulations of detector measure—
ments of those events. The collection of them is referred to Monte Carlo events.

The DO detector is modelled by a program named GEANT which has all the
structural information about the detector so that it can incorporate all the effects
of detector material (instrumented or uninstrumented) and the magnetic fields in
the bulk of the detector. This program models the ionization and the secondary
particle generations, as the particles move through the detector.

For this analysis the generation of the events the Pythia and AlpGen event
generation programs are used. The parton distribution function used in the gen-
eration process is CTEQ6L1. If an event is generated by AlpGen, it is further
Processed by Pythia to add the effects of parton showering and hadronization to
it.

To better approach and represent the real collision events, these Monte Carlo
events are laid over min-bias3 events. The program responsible for merging min—
biaS eVents with hard scatter events is called DOsim.

A“ the Monte Carlo generated events are required to pass all the above men-

tioned data quality requirements.

3 - '\.
A_m1n11num bias event is a soft interaction, so most of the energy in the event is
deposrted Close to the beam pipe, high l-nD|[28].

78

Chapter 5
Cross Section Measurement

“Haste still pays haste, and leisure answers leisure,

Like doth quit like, and measure still for measure. ”[42]
Shakespeare

In tlliS chapter a cross section measurement for the process WZ(ZZ) —> 2j + 21

is explained.

5.1 Introduction

W and Z bosons can decay into both leptons and quarks, which eventually form
jets of hadrons. We are interested in events where a Z boson decays to leptons
and a W boson decays to hadrons. The mass of the W is 80.41 GeV and the
mass 0f the Z boson is 91.19 GeV. The energy resolution of the DO calorimeter
for the jets is insufficient to distinguish a W decaying to jetsl from a Z boson
decaying to jets, since the uncertainty of the measurement (12.65 GeV) is greater
than the Inass difference of the bosons. Therefore it is practically impossible for
“S to distinguish Z and W bosons in the case where both of them decays to jets.

This led 118 to choose our analysis chain as being WZ and ZZ events producing two

 

1
Due to hadronization of the quarks as mentioned above

79

1eDtons and two jets. From now on whenever ‘signal’ is mentioned, it is expected

‘50 be understood as both kind of interactions.

5.2 Objects Identification

In order to centralize common tasks that are performed in every physics analysis,
such as finding objects in a consistent manner and applying similar cuts in a
consistent manner, a framework is established and it is called Comman Analysis
Format Environment (CAFé). The code for this analysis (WZ/ZZ cross section
measurement) is also a small part in the framework and utilizes the components
of the framework.

This analysis has a real Z decaying to leptons, therefore, it starts with identi—
fying a Z in the event, which is a relatively easy step. It consists of finding at least
two leptons consistent with decay products of a Z boson. Then it is required that
the event should have at least one jet excluding many events that have no interest
to our final state while keeping enough of them for the multivariate technique to

work.

5.2. 1 Lepton Identification: Electrons

There are several different electron definitions within DO. Depending on the need
of the analysis, one can select the electron type that best suits one’s analysis.
The definitions differ only in the quality cuts. In this analysis, Loose_trk type of
electrons are used. The following conditions must be met by EM objects to qualify

as a LOOSe_trk electron. The object should have

’ EM ID = 10 or 3211

0 Calorimeter isolation fiso
fiSO : Et0t(0'4) _ Eem(02)
Eem(0-2)

 

< 0.2

80

0 EM fraction fem
= ——Eem(0'4) > 0.9
Etotal(0'4)

O electron likelihood2

fem.

Zhoodem > 0.2
O the transverse momentum of the electron pT > 3 GeV

This concludes the definition of Loose_trk electrons. Any object passing these re-
quirements will be named as being at least a Loose_trk electron. However, because
electrons are decaying from a very heavy particle —Z boson—, they are expected
to have high transverse momentum. Due to this fact, the pT requirement on the
electrons are tightened by incrementing it to 15 GeV.

The region betWeen the Central Calorimeter (CC) and the Endcap Calorimeters
(ECS) “the inter cryostat region (ICR)— is not instrumented as well as the other
reglons. This results in very poor resolution for that region. Because of this,
electrons that are in the ICR are not used, and electron detector eta coverage is
limited to include only lnDl < 1.1 and 1.5 < l77Dl < 2.5 regions with the full
‘1’ range, Since the ultimate goal in identifying the leptons is to reconstruct a Z

b03011, it is necessary that the event have at least two electrons of the same quality.

52-2 Lepton Identification: Muons

AS in the case of electrons, muons have several different definitions depending on
the need of the analysis. The definitions of muons differ in the number of hits in
the chamb ers and tracking system. Different analysis use different definitions.
The definition of a muon includes three quantities: its quality from the local
muon SYStem (muon detector), its track quality from the central tracking system,

and Its iSOlation quality from both tracking system and the calorimeter. This anal-

235 defirled in the third chapter

 

81

ySiS uses Medium quality muons3, having a matching central track with medium
qUality and NPThight isolation (tight definition made by New Phenomena group
meeting their requirements). All these definitions are done centrally by the object-
id groups to be used by analyzers and can be found in muon ID note [27] but a
summary will be given here for convenience.

The quality of the muon object depends on the number of hits it'leaves behind
‘m the muon system. The nseg quantity gives the number of layers hit in the muon
detector. This quantity is negated if no track is found in the tracking matching
to the object. Against cosmic muon radiation there is a cosmic veto flag which
depends on the time difference between the scintillator hits of the track and the
event timing. The difference should be less than 10 ns otherwise the muon is
8«CCEptecl as a cosmic ray. The distance of closest approach (dca) of the muon
should be less than 0.02 mm or 0.2 mm depending on whether its track has an

SMT hit or not respectively. The tracker part of the isolation requires that the pT

sum of all of the tracks sharing the same vertex with the muon in a cone of radius

of 0.5 be less than 2.5 GeV. The calorimeter part, on the other hand, necessitates

that the energy sum of all the cells in a hollow cone defined by radii of 0.4 and 0.2

around the muon track be less than 2.5 GeV. To summarize all of them a muon
' having a medium quality with an ‘nseg’ parameter of nseg > 0

0 being inconsistent with a cosmic muon

' haVing an associated track with a dca parameter of [deal < 0.02 with SMT

hits and [deal < 0.2 without SMT hits
0 having a spatial track match of XQ/d-O-f S 4

° being isolated in the tracker by Ztracks pT(R < 0.5) < 2.5 GeV and in the
cal -
OI‘lmeter by :cells ETcell(0.2 < R < 0.4) < 2.5 GeV

 

3
for more explanations see chapter 3

82

SiIIce the ultimate goal in identifying the leptons is to reconstruct a Z boson, it is

necessary that the event have at least two muons of the same quality.

5.2.3 Jet Identification

Since this analysis searches for an event signature that has at least two leptons
and two jets; as a preliminary selection criteria at least the presence of one jet
is imposed on the events. The jet algorithm used in DO is the simple cone jet
algorithm. For this analysis, the construction of the jets is done as explained in
Chapter 4 with a radius of AR 2 0.5. The name of the algorithm type of jets is
“JCCB”. For this analysis, at the preselection level there should be at least one

good jet with the following properties“:

the electromagnetic energy fraction5 of the jet (fem) should be in the range

0. 05 < fem < 0.95

O the coarse hadronic energy fraction of the jet (fch) should be fch < 0.40

tlle Level-1 trigger system should confirm the presence of the jet

the detector eta (77 D) position of the jets should be 17 D < 2.5.

AS With the leptons, the jets (or more appropriately quarks) are coming from
heavy particles (either a W boson or a Z boson), they are expected to carry high
transverse momentum, given the fact that bosons are more or less created motion—
less. Because of this, at the pre—selection stage events are required to have at least
one good jet with pT > 20 GeV.

The 111 ain reason for having a cut at pT > 20 GeV stems from the following

reason: In order for us to make a healthy comparison between Monte Carlo events
\

4
The c‘ths listed here are generalized for the convenience of the reader. For more

“32W“: and accurate cuts the reader should refer to [30]
Its efinition is given above

83

and data events another set of corrections is done on Monte Carlo events. Those

are the re—weighting of the event with respect to the transverse momentum of the

Z boson (ZPtReweighting) and the number of jets in the event. There are actually
three ZPtReweighting procedures changing according to the complexity of the final
particles in the events. If one is only interested in the inclusive production of Z
particles, then it is not necessary to implement a re—weighting with respect to the
numb er of jets in the events, since the sheer number of Z events in the ‘zero’ jet
bin would drown all the others. The second one is optimized for the previous
run period (p14 version of the DOreco), which is old and cannot produce correct
results as there are many changes to the reconstruction of the objects. The third
has two branches depending on the Monte Carlo event generator, ALPGEN or
PYTHIA. Both of these branches implement the re—weighting both with respect to
the number of jets or without considering the number of jets in the event giving an
average correction over the jet multiplicity. Since eventually the event selection will
include at least two jets, this analysis uses ZPtReweighting with jet multiplicity
folded in for the PYTHIA generator. As its name suggests, the event should have a
Z boson generated. Although the signal (as mentioned earlier, WZ and ZZ events)
has also at least one Z boson in it, this re—weighting is not applied to signal events.
The measurement of the energies of the jets is affected by several factors as will

be explained and it is essential to know the energy carried away by the particle
jets to make an accurate measurement. The Jet Energy Scale (JES) is the bridge
to reach from measured jet energy Egg?“ to the particle jet energy Eptd The

jet '
relation between the two is

 

meas

ptcl_Ejet _EO

Eje, _ R s (5.1)
jet jet

where:

84

0 Offset Energy E0:
is defined as the energy that is not associated with the hard scattering. The
noise from the decay of the uranium absorber, the noise from the electronics,
additional pp events (underlying events) and the additional energy from the
previous crossings (pile-up) are the causes of. the presence of an offset in en-

ergy. To determine this contribution minimum bias events, events containing

no hard interaction, are used.

Calorimeter Response Rjeti

is the energy response of the calorimeter to particle jets. Jets are made up of
different kind of particles, which get different response from the calorimeter.
This number is smaller than unity due to energy lost before the calorimeter,
uninstrumented regions between the calorimeter modules and lower response
of the calorimeter to hadrons as compared to electrons and photons. The
inhomogeneities between the modules contributes as well. The calorimeter
response depends on the jet energy and the detector eta (n D). The radius
of the cone of the jet also affects it, since the particles near the center of the
cone have higher energies and therefore higher response. Rjet is measured
from the pT imbalance in the back-to—back ’y + jets events making use of the
electromagnetic energy scale for photon since it is known to a high accuracy

fr Om Z —+ ee events.

ShOVvering Correction S j eti

is the correction factor due to the inability to include only particles radiated
from the hard scatter and to exclude all else. Because of the energy deposited
011teide of the jet cone from the run-away particles of the jet and the energy
incllrded from the particles that don’t belong to the jet. Usually it is smaller

than unity and depends on the cone size of the jet and the detector eta. This

qualitity is measured from the jet energy profiles.

u

The total uncertainty of the JES contains systematical and statistical uncer-
tainties from both data and Monte Carlo. [31, 32, 33]

After the hadronization step and processing the events with the detector sim-
ulation, the Monte Carlo events have to go through jet corrections in order to
replicate ‘real data’. Jet Shifting, Smearing and Removal (JSSR) [34, 35] is the
one that comes after JES. The purpose of J SSR is to correct Monte Carlo events
in three classes: i) differences in the reconstruction and identification efficiency ii)
energy resolution iii) calorimeter responses. The corrections are calculated using
'7 + jets and Z + jets events and provided to analyses by the JES Group.

The measurements for the inter-cryostat region (ICR) are deemed‘unreliable.
If a selected jet’s position is in the ICR than that event is completely ignored. Less
than 0.05% of the events are rejected due to this requirement.

EM objects are usually reconstructed as jets with small radius of cone. The list
of EM objects and the list of jet objects are separate entities in the event. This has
a significant effect on event selection. One may find events where a jet is actually
an electron. This led us to correct our list of jets by comparing the locations of
EM objects and the locations of jet objects in the calorimeter. If an overlap occurs
between the two lists, the jet is removed from the good jets list. Double counting

of an em object as a jet is prevented this way.

5.2.4 Missing Transverse Energy, MET

In previous chapters, we mentioned that properties of neutrinos cannot be mea-
sured directly. They are rather identified indirectly as a transverse momentum
imbalance. By using momentum conservation in the transverse plane with re-
spect to the z-axis (beam pipe), and using every active cell in the calorimeter it is
possible to measure its transverse momentum. The transverse momentum of the

neutrino, then corresponds to the missing transverse energy in the event; because

86

the transverse momentum carried away must be zero and neutrinos do not interact

with matter.

METz— :3 ET]: (5.2)

visible

One problem of calculating MET indirectly is that even when neutrinos are
not present in the event, limited detector resolution may lead to calculate a finite
MET (fake). Another problem is that, there is no way of knowing how many
neutrino particles were in the event, since we could only see the vector sum of
their transverse momenta.

Because MET is derived from other quantities, the corrections made on them
such as JES corrections or EM scale corrections should be reflected on MET as
well. Furthermore, if an event contains a muon which interacts with the calorime-
ter minimally, one has to correct the value of MET with respect to transverse
momentum of the muon in the event.

Therefore, the final MET value includes summation of positive energy deposits

(raw energies), EM scale, JES and muon corrections; see below.

 

METCOT" = \/MET% + METg + AEM + AJES + A,” (5.3)

The final states of the signals do not include any neutrino. This actually gives
a good handle on the events against backgrounds including a neutrino in the event.

We will employ this fact to reduce tt events in the final selection.

5.2.5 Other Objects Identifications

The distribution of the z—coordinate of the primary vertex has a Gaussian shape
with a spread of approximately 30 cm. Therefore, it is required that the 2 position

of the reconstructed primary vertex of the event should fall between i60 cm of

87

the detector center. Having a jet and at least two charged leptons is translated
as a requirement of the number of tracks coming from the primary vertex. If the
number of tracks coming out of it is less than three the event is not accepted.

In a channel it is very unlikely to have another isolated high pt lepton of another
kind. This is dictated by the final state of the processes. Thus a veto mechanism
is active in the selection process which prevents events with two selected electrons

and a high pT isolated muon or vice versa.

5.2.6 Constructing the Vector Boson: Z Boson

The reconstruction of the Z boson is a two step process. The first is the selection
of leptons. If an event has at least two good quality leptons, it is considered for
having a Z candidate in it. The second step is the actual reconstruction of a
new object from the two leptons in the event and comparison of the new object’s
properties with the Z boson’s properties. One question that comes to mind is how
to select two leptons if more than two leptons are found in the event. The answer
for this question is the combination that has the closest invariant mass to 91.19
GeV (Z mass). Thus every combination is considered as a candidate.

For further selections we consider an invariant mass cut around 91 GeV, and
the points from where the leptons radiate out. As it is evident from the figures
5.1 and 5.2 there are slight changes in the observation of the Z boson. Therefore
the selection criteria shows little differences between the two channels.

For the electron channel, the mass window for Z candidates is set to be 70 <
M Z < 110 GeV. As can be seen from the Figure 5.1 this cut doesn’t compromise
our acceptance. Besides the mass cut on the Z candidate, it should have originated
within the probable spread of the primary interaction point. Moreover, since Z
particles decay almost instantaneously, the calculated primary interaction point

for the event should be within the 3 cm distance of the extrapolated position of

88

RunIIa Data afier preselection

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

: + massz data 1>0
— 10771
1600_— 1 87.05
I 17.06
I400: l
1200:—
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: 4
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L:
200: “f: 4‘ "
0:Lll ‘ fiffigllll‘h“““flméll 1111
0 25 50 75 100 125 150 175 200 225 250
electrons

dllepton mass for

Figure 5.1: Di-electron mass distribution for the RunIIa Data set after preselection.
All the events contributing to this histogram have two good quality electrons with
pT > 15 GeV and one good quality jet with pT > 20 GeV

the Z particle.

For the muon channel, the mass window cut for Z candidates is larger than
the one for electron channel, 50 < M Z < 130 GeV due to the fact that the muon
detector resolution is not as good as the calorimeter resolution for electrons. As
can be seen from the Figure 5.2 this cut, although allowing more backgrounds
than the one on the electron channel, still does a very good job. Besides the mass
cut on the Z candidate, it should have originated within the probable spread of
the primary interaction point. By the same reasoning as the electron channel,
the calculated primary interaction point of the event should be within the 3 cm

distance of the extrapolated position of the Z particle.

89

 

RunIIa Data after preselection

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

600:— l
500:— f
400‘—
: l l
300:— l +
: l 1
200:— 1 j
E l ,
100_— J J «a
_. 7
: “ll!“ “A W
0 l l l l A 1 LL 1 I ll 1 [IL I l I 1 MI I l l 1 L1 l l
o 25 50 75 100 125 150 175 200 225 250
dlIepton massformuons

Figure 5.2: Di-muon mass distribution for RunIIa Data set after preselection.
All the events contributing to this histogram have two good quality muons with
PT > 15 GeV and one good quality jet with pT > 20 GeV

90

5.2.7 Object Identification Efficiencies

Due to the difference observed in the reconstruction and identification efficiencies
between the Monte Carlo events and the data, correction factors are applied to the

Monte Carlo events. They are all referred here as object identification efficiencies.

Electron Efficiency

The efficiencies of selecting a single electron with given properties are determined
by the EM ID group [36]. The group uses a method named tag-and-pmbe [37, 38]
on a pure sample of Z ——» ee events. In the tag and probe method a tag electron is

first selected by a very tight cut:

0 EMID = 10 or :tll,

O fiSO < 0.2,

fem > 09,

either 77D < 1.1 and XffoY < 12, or 1.5 < 77D < 2.5 and Xf1Mx8 < 20,
9 ET > 25GeV,

o a track matched to EM object with E / p > 1 and number of SMT hits > 0,

the trigger object matched to EM object.

The remaining electron (probe) should pass the cuts. The efficincy is the ratio of

the number of events with a passing e1ectron(A) to the total number of events(T).
A

:. _ 5.4

e T < 1

If there is more than one electron qualifying as a tag electron in an event, then

that event is used for both electrons being as tag electrons. The efficiency is

91

parametrized with respect to 77 D and (DD. This is done both on data and Monte
Carlo (PYTHIA generated) events. Comparison of the two gives the correction
factors that should be applied on the Monte Carlo events. Thus after making the
corrections Monte Carlo events look more like real data. The efficiency is close to
90% in the central calorimeter (CC) and goes down to around 50% in the endcap
calorimeters (EC). There is also a dependency on the 77 value, and this dependence
is also taken into account. The correction factors are applied in the same way
through all the analyses: First an analyst applies the pre-selection efficiencies to
the selected events, afterwards the electron type efficiencies are applied by use of
‘.spc’ files, which keep binned efficiency factors with respect to different parameters

like 7} or (15.

Muon Efficiency

The efficiencies of selecting a single muon with given properties are determined
by the Muon ID group [27]. This group also uses the same method tag-and-probe
method to measure muon identification efiiciencies. Similarly, they use a sample
of pure Z -—> up events. The procedure for calculating efficiencies is the same as
explained above. Muon ID efficiencies include, muon identification in the muon

detector, track efficiencies and isolation efficiencies.

Jet Efficiency

The efficiencies of identifying and selecting jets with predetermined properties are
measured by the Jet-ID group [38, 39]. The efficiencies are provided collaboration—
wide by Jet-ID group to account for the inefficiencies when selecting jets in the
prescribed fashion. In order to be free of any trigger biases on the probe object
the tag jet is required to be capable of firing the level-1 level-2 and level-3 terms of

the trigger. This is done by matching the jet with the triggering object. The two

92

efficiencies can be summed up as reconstruction efficiencies and jet-id efficiencies.
For the calculation of the jet-ID efficiencies, a pure sample of back-to—back dijet
events which have an MET less than 40 GeV are used. The former is the fraction

of calorimeter jets in the probe region ( > 3.0) and the latter is the

A‘f’tag, probe
fraction of the jets passing jet-id cuts in the same region. The jet-id efficiencies
are very high, in the vicinity of 99%. The application of the efficiencies to correct
Monte Carlo events is done through the application of efficiency factors by loading

’.spc’ files. The efficiencies are parametrized in detector eta (77D) and transverse

momentum of the jet (17%?)

5.2.8 Trigger Efficiency

For any event to be recorded, it has to pass trigger requirements. As shown in
the Figure 5.3 unless the triggered object falls on the plateau region, there is an
inefficiency associated with the triggers. To better replicate the effects of imperfect
measuring media Monte Carlo events are weighted so that the trigger turn on curve
is reproduced.

For this analysis, instead of selecting some triggers, we employed a newly de-
veloped procedure: Trigger Super OR’ing. It can be explained as follows. This
analysis requires that there should be at least two charged leptons and two jets.
Depending on this final state, one can choose to select events with “di—lepton trig—
gers”, “single-lepton triggers”, “1epton+jets triggers” or “jet triggers”. It is not
wise to use just the last element of this set. Instead of selecting one element from
the set the union of the elements are used. For this single-lepton triggers are com-
bined with 1epton+jets triggers. If an event fires any of the unprescaled triggers
from single-lepton or 1epton+jets triggers it is accepted. This way the trigger ac—
ceptance and efficiency is increased. This gives a correction factor for the Monte

Carlo events on the order of 99%.

93

 

 

 

 

 

 

E 1;— “k‘v‘ ““1.“ fl
’9 t
.9
$08?
:: _
"I. 1-
30.6?
Ill 1—
O _
0.4—
0.2;
G—l llllllllllll
O 40 50 60
PT

Figure 5.3: Figure show a typical trigger turn on curve. This is produced by using
the CEM(1,11) trigger. It requires an electron with a transverse momentum of 11
GeV in the event. As it is seen from the figure selecting with this trigger is not
quite efficient unless the object has at least 20 GeV transverse momentum.

5.3 Backgrounds

Even though this term has been used in this study, it hasn’t been properly in-
troduced to the reader. In the dictionary it is defined as “the totality of effects
that tend to obscure a phenomenon under investigation and above which the phe-
nomenon must be detected” [40]. If we adapt this definition to this analysis, ‘every
interaction that produces the same final state particles, yet different from the
physics that is sought after’. Then any interaction that produces two leptons and
two jets other than WZ or ZZ events comprise the background for the WZ/ZZ

productions. Those are
c jet final states
0 top quark and anti-top quark production

0 Z+jets

94

5.3. 1 jet Backgrounds

This type of background is due to misidentification. One or both of the leptons
(e, p) are actually jet objects that are faking e or ,u. The origin of the jets may be
anything, a genuine jet coming from the hard scatter or a low energy jet or else an
instrumental hiccup making a jet appear as a lepton.

We make an estimation of the degree to which this analysis is susceptible to jet
background. The main feature of the estimation is a ratio test. The signal region
is two jets with a Z boson having a mass in the mass window range6. We assume
that outside of the mass window the number of signal events is negligibly small.

The di-lepton mass spectrum includes a Z mass peak at around 91 GeV laid on
top of continuous spectrum of Drell-Yan events. Drell-Yan events can be simulated
but jet events may not. The presence of the Z peak in the mass spectrum wouldn’t
change the shape of the Drell—Yan mass spectrum. Since jet events are due to
instrumental deficiency we can safely assume that at every mass interval those
events behave similar to Drell-Yan events. Because the number of Drell-Yan events
is several order larger than jet events, the shape of the distribution doesn’t change
anyway. Then it can be concluded that if one calculates the number of jet events
outside of the Z mass window, by extrapolation it should be fairly straightforward
to estimate the number of events inside the window.

For the purpose of counting the number of possible jet events, one changes the
selection criteria of the leptons. The final state contains two leptons which means
that either one of them or both of them may be faked by a jet. For the definition
of a fake lepton the isolation quality is reversed. For the electron channel it is the
likelihood and for the muons it is the combination of Ell—fab and 19573061“. Thus

for a jet “faking” a lepton, it is required that' the event has one good quality lepton

 

6For the sake of completeness the mass window for electron channel is 70 < M Z < 110
GeV and for muon channel 50 < M Z < 130 GeV.

95

and one bad quality, jet—like (fake) lepton; and for two “fakes” we require two bad
quality leptons.

The definition of the fake electron is the same as the good one’s, other than
likelihood. Its likelihood value should be in the range 0 < lhood < 0.2. If an
electron doesn’t have an associated track its likelihood is assigned a negative value
that’s why reversal of the likelihood cut is limited to positive values.

The definition of the fake muon is the same as the good one’s, except the
isolation requirement is completely removed along with events containing good
muons.

The comparison of Monte Carlo events with data events in the low di—lepton
mass region is done. The difference between the number of data events and the
number [of Monte Carlo events is the jet events in this region. The number of
possible jet events in the Z-mass region, can be found out by fitting this number
to the di-lepton mass distribution of fake electrons. See Figure 5.4(a). However,
after all the cuts, we didn’t even need to make the fit since the number of events in
Z—mass window was very low. See-Figure 5.4(b,c,d). From this one can conclude
that the number of jet events are negligibly small.

Thus, in this analysis the number of jet events is set to zero.

96‘

 

250

.1411.

200

150

Z mass for QCD
after cuts

 

   
   

 

 

 

 

 

 

 

. l ; :
LLLI lJllllllllllllllllllllll
(3

EE 3 .3.

 

(b)

 

 

Z mass for QCD

electrons

 

 

 

lLulllJlllllllllllllLLlllllllIll‘

38 N 8 8 3
v-O I—!

Figure 5.4: The figure shows (a) the Z mass distribution for the QCD events and
the fit before the application of cuts; (b) same distribution after the cuts; the
number of expected events in different bins before normalization for (c) electron
and (d) muon channels. -

97

5.3.2 top-antitop Backgrounds

Only when both of the W bosons in tf events decay to leptons (di—lepton channel)
the final particles of this process (it) are the same as the signal’s (WZ /Z Z ), two
leptons and two jets with one addition, neutrino. However, the presence of the
neutrinos in the tf events helps eliminate a big portion of these events by the MET
cut imposed on the events. Figure 5.6 shows the effect of MET cut on tt events.
In the electron channel the reduction of tf events is 90% (27.64 ——> 2.78) whereas
in the muon channel it is 75% (16.99 —+ 4.30) with the MET and Z mass window
cut. Horn this picture alone it is safe to infer that by this cut. alone we have a very
good handle on tf events. One other aspect of these events is that the two leptons
don’t have to be same kind for tt events, which also helps reduce the background
we get from these events.

The cut on the MET quantity is calculated by rounding off the cut removing
most top-antitop events and keeping the signal events. Thus in the electron channel
it is 45 GeV and in the muon channel it is 55 GeV. See Figure 5.5

The effect of MET cut on the events that are passing the Z-mass window cut
is shown in Figure 5.6. The number of events entering that region is small, and
by means of this cut the number of events gets even more smaller (less than 5 in

both of the channels for RunIIa period data of ~ 1 f m”1 data).

98

 

    

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Figure 5.5: The figure shows MET distributions for the electron (left column) and

the muon (right column) channels for Monte Carlo events. The effect of MET cut

can be seen on the second row.

99

 

 

G V
250
GeV

      
  
 
 

100 110 120 130 140

in Z mass window

8090

70

di-lepton mass in ttbar for muons

 

 

405060

   

0

0.35
0.30
0.25
0 20
0 IS
0 10
0.05

 

 

 

GeV
20

 

di-lepton mass in ttbar for electrons
in Z mass window
80 90 100 1 I0

70

 

 

60

 

   

Figure 5.6: The figure shows di-lepton mass distributions for the electron (left
column) and the muon (right column) channels for tf events. In the same panel
is shown before (in black) and after (in blue) the missing transverse energy cuts.
While the first row shows whole mass range, the second row shows only Z mass
window region.

100

5.3.3 Z + jets Backgrounds

The production of a Z boson accompanied with jets has the exact same signature
as our signal. The production mechanism, however, is entirely different. Initial or
final state gluon radiation can cause these events be created as well as jets from
soft interactions. The only remarkable difference between Z + jets and the signal
(W Z / Z Z ) is that while the di-jet mass spectrum of the former has an exponential
form, the latter has a sharp peak at the W mass region. See Figure 5.7

The number of events for a given luminosity is favoring Z + jets events by
one to two hundred. Thus, in order to separate signal from this background, we
have looked at several different methods, and decided that an ‘improved’ likelihood

method gives enough power to distinguish one from the other.

101

 

 

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suN n~ev~'-es'VN°

(pazuumou) nun: JO .Iaqumu (PWIIHOU) ”WAD Jo ”mm.

 

Figure 5.7: The di—jet mass distributions for signal (left hand side) and background
(right hand side) Monte Carlo events for electron (first raw) and muon (second
raw) channels. To preserve the relative strengths of the distributions, they are not
normalized one.

102

5.4 Corrections

Before proceeding any further, it should be stated that, recently another corrections
to the Monte Carlo generated (W/ Z) + jets events are proposed. The reason for
this correction is that Monte Carlo events generated by Pythia are not capable of
representing the distributions of the jets’ eta (77]) and of the distance between the
jets (Ale, 32) for boson (W/ Z) + jets events. This study is dependent on (17]),
(Ale, jg); therefore it is necessary to do those corrections on MC Z+jets events.
Although the reason is still not known fully, events generated with Pythia causes
the discrepancies as seen in the Figure 5.8.

The recipe for dealing with this is as following. Since the reason behind the
discrepancies are Pythia generated events, one should consider to correct those
events only, by differing their weights in the plots. For this study, tf events from
background events and all of the signal events (WZ/Z Z) are excluded from this
corrections because in their production Pythia was not used. Z + jets events,
however, are generated by Pythia and the correction factors are calculated by
using exclusive Z + jets events. Both of the channels (e and u) the correction
factors are calculated separately. At the pre-selection level, expected number of
events for signal and top—antitop events are subtracted from the RunIIa Data set
bin by bin in three different variables (’7j1: 77an ARj1,j2)- For every variable, a
bin-by-bin ratio histogram is obtained between“ the data and the Z + jets Monte
Carlo events. Then the ratio histograms are fitted to second degree polynomials
giving rise to small but crucial corrections in the afore mentioned variables. See
Figure 5.9, 5.10. The fit results are used as average corrections in the form of
an event weight for all the variables that are used in this analysis. Any further
cuts are applied after employing these corrections on every variable used in this

analysis.

103

 

 

 

 

 

 

  

 

    
  
  

  

160

120 Delta R 120

Delta R

    

4

Figure 5.8: The figure shows the discrepancy between the Monte Carlo events and
data for n -1, le2 and Ale j2 distributions (from top to bottom). On the-left
is shown t e electron channe , and on the right is shown the muon channel. Since
our result will heavily depend on these distribution, a correction factor is assigned
as a weight to every event.

104

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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3:" eta jetl 4 etajetl
' 3
2
1 +
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5 DeltaR 14;
4 ? DeltaR
3 10;
2 M 6;
1 2‘
o— 2?

 

 

Figure 5.9: The figure shows the fits that are used for correcting event weights
of the Monte Carlo events for 77 -1, le2 and Ally-1J2 distributions (from top to
bottom). Since our result will heavily depend on these distribution, a correction
factor is assigned as a weight to every event.Left colunm is for electron charmel
and right column is for muon channel.

105

electron muon

    

 

l
eta Jet]. i eta Jet].

     
 

 
  

    

o3

93—2—10123

[i

 

 

eta jetZ

     

 

 

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—

 

     

     

 

Delta R Delta R
160

12

 

 

Figure 5.10: The figure shows distributions of 17 -1, 17 -2 and Ale, -2 (from top to

bottom) after corrections are applied.Left column is for electron channel and right
column is for muon channel.

106

5.5 Technique

The rule of thumb “the simpler the better” has to be given up in some cases. This
analysis is one of them. The cross sections of the processes are very low (~35 pb
for WZ production and ~1.5 pb for ZZ production). As if this is not enough, the ‘
cross section of the most similar background is very high (~750 pb for Z+jets). If
one were to count the number of signal events that can be seen by just employing
square cuts, the uncertainty in the number of just this background could be on the
order of the total number of expected events from the signal7. Because of these
reasons one has to develop new methods, for this analysis I checked the feasibility of
the next two methods: the matrix element method and the random forest method.
While the former requires a through knowledge of the Z+jets matrix elements and
needs huge numbers of cpu cycles for the calculations; the latter does not provide
much difference in terms of significance than the method I developed. The method
used is a mixture of the likelihood method and decision tree in which selection of
the variables are not left to computer but done by the analyser.

Although a multivariate technique will be employed, pure samples will improve
our ability of discriminating signal from background. There are three obvious cuts

which will be explored in the next section.

5.5.1 WZ and ZZ Event Selection

A further selection of WZ and ZZ events following Z —> 6+6_ and Z —-> uflu‘
selection is done by requiring the following cuts.

The usual way for an analysis is to use square cuts and get a limited region
in which the number of events is comparable to or more than the number of

background events. For this analysis, however, after selecting objects one has to

 

7The expected number of events for WZ and ZZ processes for whole RunIIa period
(~ lfp‘l) is about 36 events.

107

use more complicated methods such as multivariate techniques since the properties
of the background differ from the signal only slightly. But in order to improve the
separation power of those techniques, some obvious cuts are employed. Those cuts

are :
o The di-jet mass window cut
0 The 77j’77j cut

0 The pT-pT cut

The di-jet mass window cut

Because we are interested in the cases where two jets decay from weak bosons,
the reconstructed W/ Z boson from the two jets should be in the vicinity of real
W/ Z mass (~80 GeV and ~90 GeV). While the signal Monte Carlo events have
a definite peak in this region, the background events show an exponential decay.

See Figure 5.11. The di—jet mass should be above 50 GeV and below 130 GeV.
SOGBV < Aljj < 130G6V (5.5)

See Table 5.2. In the case where an event has more than two jets, selection of the
jets are limited to the first and second jets. As mentioned before this is the correct
choice 90% of the time. It is possible to choose the combination that is giving the

mass closest to MW, we avoided that to not introduce an unknown bias.

The 77j‘77j cut

Decaying from a heavy particle causes the jets to be boosted. This results in the
jets being closer to each other in the signal Monte Carlo events compared to the
background Monte Carlo events. When one multiplies the physics 77 of the jets,

one expects that the distribution be skewed to the right for the signal and no

108

skewness for the background since in the latter the jets don’t originate from one
heavy particle but have random directions and origins. In Figure 5.12 this cut is

shown as 77j'77j > —1. For its values please see Table 5.3.

The pT-pT out

As mentioned earlier the momentum carried in transverse directions by jets should
be large due to momentum conservation. Although events are already required
to have a jet with a pT > 20 GeV there is still some room to go. Our region of
interest is events with a W/ Z decaying into jets. This means that the two jets are
strongly coupled together. Even by employing a very simple relation between the
two jets will help us recover lost events due to square cuts and removing events
sneaking in originating from background. Thus, a linear relation between first and
second jets pT’s are used. A triangular cut is employed on the two highest jets
vs ijet2' See Figure 5.13. As it is seen on the plots a definite peak exists

ijetl
in signal. As an example the cuts put on the Figure 5.13 are

”its?

40 '6—0 —1 >0 (0.6)

for electron channel and for muon channel it is:
p72 pjl
_1; + T

109

 

 

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10.9.20:—
“III-—

 

Figure 5.11: The di-jet mass distributions for signal (left hand side) and back-
ground (right hand side) Monte Carlo events for electron (first raw) and muon
(second raw) channels. To preserve the relative strengths of the distributions, they
are not normalized one.

110

 

 

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events. The one on the right Side 1S for the

18
There is an obvious skewness towards right in

Figure 5.12: The distributions for n
by using only the signal Monte Car

background Monte Carlo events.

the signal distribution, which is expected.

111

 

 

 

 

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40 so so 100 120 140 160”

20

 

 

  

 

6 6°

on v N
(A30) ZN

 

Figure 5~]—:3: The distributions for pfrl vs 133112. The left column is for electron
channel and the right column is for muon channel. The lines show a probable cut
on these twO variable together. It is obvious from the plots that background events
are mOStly below the line.

112

Before giving the values of these cuts, another different aspect of this anlysis
should be clarified. It is discovered that, instead of blindly applying all the cuts to
all the events, it is much wiser to select cuts event by event. Due to time restrictions
on the analysis, it is chosen to separate events into four different regions and apply

an average cut on the events in their regions. For this purpose AR between the
first two jets is used. The regions are shown in Table 5.1. In the following section

it will be explained why one separates the phase space into four regions.

Region I II III IV
AR < 1.8 2 1.8, < 2.3 2 2.3, < 2.9 > 2.9

 

 

 

 

 

 

 

 

 

Table 5- 1 : The division of regions with respect to the distance between the two
highCSt pT jets in the events.

The liInits of the regions are chosen so that on average the changes in the
bEhaViOUI‘ of the distribution would be captured. Although it is mentioned that in
different regions different cuts are applied, what is shown in the previous figures
are all of the events Without dividing them into four regions. So that the reader
has a general idea of what to expect. For the di-jet mass window cut please see

Table 5- 2

 

Region For all regions
Di—jet mass cut 6 channel 50 < M j j < 130 GeV
Di—jet mass cut u channel 50 < %L< 130 GeV

 

 

 

 

 

 

Table 5.2: The di—jet mass cut is kept constant over the regions.

The next tables, Tables 5.3 and 5.4, show the cuts put on the 77j‘77j and the

PT-PT variables respectively.

 

   

Region I II III IV
njetl * mm for electrons > —0.725 > —0.525 > ——0.425 > —0.425
> —0.825 > —0.725 > —0.925 > -0.525

 

 

 

 

 

 

 

77jet: 1 >1: 77jet2 for muons

 

T331233: 773-1951 *"jet2 cuts are shown in different regions of AR for both electrons
an Ils-

113

 

Region I II III IV
17%} .vs pi} for electrons (74,53) (73,42) (73,34) (49,46)
pg; vs 17%? for muons (201,39) (114,29) (84,24) (33,52)

 

 

 

 

 

 

 

 

 

Table 5.4: 17;} vs p371? cuts are shown in different regions of AR for both electrons

and muons. The numbers given here are the intersection points of a line with p79}

and pg]? plane.

If an event has a value for 77j‘77j greater than the one mentioned in the table, it
passes this cut. If an event falls in the region above defined by the line intersecting
with :1: — y (pg-1137i?) axes at points given in the Table 5.4, it passes this cut also.

The values of the cuts for the different channels are shown in the same tables.
They are calculated by finding the values for which the significance of the signal

13 highest. Its definition is given below:

N

 

 

a = signal ( 5_ 8)
\/ N signal + N background
Where N 32- gnal is the number of signal Monte Carlo events passing a certain

c
ut and Nba ck ground is the number of background Monte Carlo events passing
th
e same cut. The cut point for which this value is the maximum is chosen for the
mo
St Opt imum cut. For all of the three cuts mentioned above this formula is used.

The -
OI)tilrnized cuts are applied for the following optimization.

5.
5 ‘ 2 Likelihood Method

For
tllis analysis, a modified simple likelihood is chosen to separate signal from the

backgi‘ound.

111 the very early versions of the method, we were using only five variables and

l‘ Of them were 77j1 X 773-2 and Ale j2' They are taken out of the list of the
l 3

Q1iliood variables for the following reasons: The cut imposed on the former one

is powerful and removes dissimilarities between the signal events and background
events, we didn’t want to use it in the likelihood any further. The latter, on the
other hand is used to define different regions. The idea behind it is that not all
of the variables have the same discrimination strength in every phase space. For
that purpose we compared variables in different regions for their effectiveness and
separation power. When building the likelihood, we use only those variables that
are more powerful in that particular region where the event falls. The comparison
is done based on the histograms and the k-test. For that test the ‘R’ program 8 is
used. By the same token, one should doubt the validity of the implications such as
any Cut has the same significance in every point in phase space. That is why, after
the division of the phase space, we re—optimize the cuts specific to this analysis. It
turned out that, indeed, applying a cut blindly, with an assumption that in every
regjOn it has the same desired effect is wrong. One can only optimize a cut to
the aVerage this way. However, optimizing the cuts for different regions could buy
Some Significance for the analyzer.

In 01‘ der to build the likelihood among the many possible variables, the ones

th . .
at 88D arate Signal and background best 1n Monte Carlo events are chosen. They
are:

. T}1e reconstructed di-jet mass

. The transverse momentum of the leading jet

- The transverse momentum of the trailing jet
\

The rapidity of the Z boson in the W Z / ZZ frame

‘ The angle of OR

‘ The pT difference of the di-jet and Z

 

Q .
Please see http: //www.r-pr0ject.org

115

o The pT of the di-jct object
0 The pT of WZ/ZZ frame
0 The cosine of the angle between the two jets

O The cosine of the angle between the Z and jet

The definition of the likelihood is given below:

 

_ P3i9(r) r:
13(3) “ Psiga) + Pbkgm (0'9)
P3ig(‘r) : HPS'iQ(Ii) (5-10)
’t
Pbkg(l‘) = HPbkg(xi) (5.11)
’1.

Where a: is a vector of afore mentioned variables; Psigkfi) is the probability
of being a signal (WZ/ZZ) event; Pbkgmi) is the probability of being the total
baCkgrOIInd events (Z+ jets and top—antitop). These probabilities are obtained from
the Monte Carlo distributions of the variables entering the likelihood calculation.

Again, there are four different MC distributions for a variable corresponding to
four different regions of the phase space. After obtaining distributions of the
variables for different regions, these distributions are normalized to unity to get
C(‘n‘regbonding probability for that variable in that region. This means that the
fistribution of the variable is translated to a binned probability distribution for
[3:6.‘ gignal and background Monte Carlo events. Some work went into finding the
0 IE" binning for the histograms when calculating correspoding probability. If one
g:hgiders the limiting cases it will be apparent why one needs an optimum set of

111Ting. For instance, if all of the histograms had only one bin then the likelihood

Wes
1lld come out as 0.5. If, on the other hand histograms had too large binning then

116

we would see unphysical accumulation and spikes on the two extremes; many of the
events whould not have a valid likelihood value. Because very fine binning means
empty bins in the distribution’s tail for some of the variables, such as transverse
momentums. It is essential that without including nonphysical cases, the likelihood
distribution has discriminative power. Therefore it is required that the likelihood
distribution be a smooth one.

Ideally, one should use

Pass.) = PM.) (5.12)

for calculation of probabilities. That is to say if there are ‘n’ variables, one
ShOUId use an ‘n’ dimensional probability space for calculating p values entering
the likelihood. However, this requires infinite amount of signal and background
Monte Carlo events, especially for the case in the hand since we have ten variables.
For an ‘n’ dimensional likelihood to be effective, every cell in ‘n’ dimension should
have Sigllificant number of events in them. Instead, we chose not to include some
Of the Variables in some regions when calculating the likelihood.

Shown in the Figure 5.14 is the example of a distribution and its correspond-
ing prQ13ability distribution. It is required to remove the legends in some of the
diStri“Ollijons for their clarity. Thus, in this picture is explained the color codes
used tllroughout this section. The hatched histogTamS, always in red (signal MC)

an
(1 black (background MC), are for probability distributions. Other histogram is

for
the comparison of the data points with the signal + background distributions.
rI‘
11% reconstructed di—jet mass
III

t-h (Order to calculate the di-jet mass, an event should at least have two jets. Thus
fire is an implied cut on the number of jets in the events. If an event has more

‘11

{all two jets, then the recipe is to utilize only the ones that have the highest

- 117

 

r p . .. . — . _> . _ . I u .
.w <. w p‘. 0 r‘.
'0- . 1. ‘7- ‘1
I'll-v ’0' .--U uhadA-FI-Ilc

 

10.
:1: I
l“(

  

PROBABILITY
signal

 
    

NW9)
meme

number of events

 

     

I .I 1 '1 ll 1 ’1‘
MassJ 1J2 in region I (0.5 <= AR < 1.8)

MasleJZ

Figm‘e 5.14: An example distributions showing the color codes used in this thesis.

transverse momentum. There is an error associated with this choice, since a jet

p mdUCed with WZ or ZZ events is not guaranteed to have less pT than those jets
decaying from the bosons. More than 90% of the time the selection for the highest
pT is Cc>1‘1"ect, which means that it comes from the W or Z, however for the second
jet this efficiency goes down close to 85%. As mentioned earlier the di-jet mass
is the IIlost powerful discriminant, because coming from a high mass particle (W
or Z) ’ 13'11e di-jet has a definite peak in its mass distribution whereas background
(10031131; form due to the fact that there is almost no relation between the jets. See
FigureS 5.15, 5.16, 5.17 and 5.18. In these figures left column shows the data
MC e\b'ent comparison whereas in the right column the corresponding probability
dIStr ithitions are shown. Probabilities of the individual events are obtained from

the
SQ probability distributions for the likelihood discriminant.

1‘»

ahsverse momentum of the leading jet

111
the previous bullet it is mentioned that the selection of the first jet is usually cor-

r
Q
Qt. That’s why the average pT is higher in signal MC events than in background

118

 

9:~ .

IVIC events. Moreover the background MC events has a long tail, indicating that
they are not strongly coupled to other objects in the event. See Figures 5.19, 5.20,
5.21 and 5.22. The left column shows data MC event comparison and the right
column shows corresponding probability distributions. Probabilities of the indi-
vidual events are obtained from these probability distributions for the likelihood

discriminant.

’I‘ransverse momentum of the trailing jet

Trailing in this context means the second highest pT. Due to requiring a second jet

in the event, we are placing an implied lower cut on the number of jets, but there is

no Upper cut on the number of jets that may be found in the event. Again having
deCaYGd from a heavy particle, for signal MC events pT distribution has higher
Mean Values compared to background MC events. One can see a tail for background
events also. See Figures 5.23, 5.24, 5.25 and 5.26. The left-hand side column
Shows data MC comparison whereas right-hand side column shows corresponding
p r0bability distributions for signal and background MC events. Probabilities of
the individual events are obtained from these probability distributions for the

l' '
lkehho Qd discriminant.

Th
e 1‘alidity of the Z boson in the WZ/ZZ frame

In theer both of the bosons may be utilized equally, however, since Z bosons are
const’l‘l‘icted by leptons, and their measurements are more reliable due to the fact
that IIiost of the events have only two leptons, W bosons are not used for this
variable. As seen in the Figures 5.27, 5.28, 5.29 and 5.30 the background events

DC)
DIllates the y = 0 region. This is a result of the balancing of the dj-jet object in

-

81
Q Qua] (WZ/ZZ) events. Whereas in the background the di-jet object is not fully

1\‘l‘elated with the di-lepton object due to inclusion of an unrelated jets (first

119

or second highest pT jet). The rapidity of the leptonic boson is expected to be
central in background from the previous measurements of Z boson rapidity. The left
column in these figures are for data MC event comparison, whereas the right one is
for corresponding probability distributions. Probabilities of the individual events

are obtained from these probability distributions for the likelihood discriminant.

The angleR : a R

angleR is the angle between the reconstructed Z object in the W Z / ZZ frame and
the direction of the WZ/ZZ frame itself. From the Figures 5.31, 5.32, 5.33,
and 5.34, the distribution of this variable for signal events has a dip towards the
center (especially in second and third regions), whereas the background distribu-
tion is more or less constant. This variable is one of the last additions to the set
of variables. Data MC comparison is shown in the left column and probability
distributions used in likelihood discriminant are shown in the right column. Prob-
abilities of the individual events are obtained from these probability distributions

for the likelihood discriminant.

The transverse momentum difference : Apg’fl

The transverse momentum difference of Z boson and di—jet object could be used
as one of the discriminating distributions because of the correlation between di-jet
and di-lepton objects. In the signal case they should balance each other, whereas
in the background, we expect to see a slight skewness in the distribution. This

variable is defined as

p711] — p% (5.13)

See Figures 5.35, 5.36, 5.37 and 5.38. Data MC comparison is shown in the left
colurrm and probability distributions used in likelihood discriminant is shown in

the right column. Probabilities of the individual events are obtained from these

120

 

 

 

probability distributions for the likelihood discriminant.

The transverse momentum of di-jet : p?

The transverse momentum of the di— jet object. It is expected to behave differently
from the real W events since the jets cannot make a real W. The mean value
for this distribution is expected to be greater in signal than in background. See
Figures 5.39, 5.40, 5.41 and 5.42. Data MC comparison is shown in the left
column and probability distributions used in likelihood discriminant is shown in
the right column. Probabilities of the individual events are obtained from these

probability distributions for the likelihood discriminant.

The transverse momentum of center of mass : pgyz

The transverse momentum of the WZ/ZZ frame is in a way an opposite to the
transverse momentum difference. Any difference that is overlooked should emerge
in this variable. This distribution behaves differently in electron channel than in
muon channel. We suspect that since the only difference is the usage of muons
instead of electrons while reconstructiong the leptonic Z boson, the resolution ef-
fects of the muon detector plays an important role here. See Figures 5.43, 5.44,
5.45 and 5.46. Data MC comparison is shown in the left column and probability
distributions used in likelihood discriminant is shown in the right column. Prob-
abilities of the individual events are obtained from these probability distributions
for the likelihood discriminant.

The angle between to jets : cos an]?
The correlation between the two jets for signal (WZ/ZZ) events should manifest
itself as a difference in the distribution of the angles between the two jets making

the hadronic boson. For the cosine of the angle between the two jets having the

121

highest pT see Figures 5.47, 5.48, 5.49 and 5.50. As mentioned before there is
an uncertainty attached to the selection of the correct jets combination making up
the boson (correct for 85% of the time). Data MC comparison is shown in the left
column and probability distributions used in likelihood discriminant is shown in
the right column. Probabilities of the individual events are obtained from these
probability distributions for the likelihood discriminant.

The angle between the first jet and Z : cos an Z
There is another angle which should be different between signal (WZ/ZZ) and
background is the angle between the first jet and the reconstructed Z boson. Z bo-
son and the first jet combination is more reliable because the first jet assignment is
90% of the time correct, that’s why the angle between second jet and the leptonic
boson was not chosen. For the distributions please see the Figures 5.51, 5.52,
5.53 and 5.54. Data MC comparison is shown in the left column and probability
distributions used in likelihood discriminant is shown in the right column. Prob-
abilities of the individual events are obtained from these probability distributions 3
for the likelihood discriminant.

In the Tables 5.5 and 5.6, the variables and their respective regions are shown
for electron and muon channels respectively.

There are correlations between the variables. In order to properly take into ac—
count for these correlations, one should build the likelihood in multiple dimensions.
Although this is not impossible, yet it is quite impractical, since for building such
multiple dimensional likelihood one literally needs hundreds of millions of Monte
Carlo events and one can make some assumptions to ease the burden on the event

generation. The number of necessary events is so large because of the following

1‘ 6880118:

0 For this method to work, one has to bin the phase space in the same number

122

 

 

Region

 

 

 

II III IV
AR < 1.8 2 1.8, < 2.3 2 2.3, < 2.9 > 2.9
MJJ MJJ MJJ MJJ
P711 P141 PT”. PT”
197.12 P742 31.12 107.12
“R “R 05R
312 92 $12 92
EM Channel Variables cos aJ1,Z cosaJ1,Z cos aJ1,Z cosaJ1,Z
cosaJ1,J2 cosaJl, J2 cosaJ1,J2
P¥1J2’Z P1.{1J2,Z
AP%1J2’Z AP%1J2’Z
Pill]? PillJ2

 

 

 

 

 

Table 5.5: The names of the variables are given in their region

123

 

 

Region

 

 

 

 

 

 

II III IV
AR < 1.8 _>_ 1.8, < 2.3 2 2.3, < 2.9 > 2.9
MJJ MJJ MJJ MJJ
13%1 PT” PT”
P7J2 P112 P112 P112
0‘12 OR OR GR
312 y2 312 92
MUChannelVar'iables cos aJl, Z cos aJl, Z cos aJl, Z cos aJl, Z
cosaJl, J2 cos aJl, J2
P7J1J2, Z PJJ1J2, Z P1J1J2, Z P7J1J2,Z
APiZlJQ’Z APCIJIJ2, Z AP7J1J2,Z
P1J1J2 P1J1J2 P7J1J2

 

 

Table 5.6: The names of the variables are given in their region

124

 

of dimensions as the number of variables which results in very few to none

events in some bins. This causes unrealistic results,

0 One can increase the bin sizes, however after a point the goal of using this

techniques blurs away and the method doesn’t deliver any separation power.

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Figure 5.15: The distributions for di-jet mass for electron channel in first and

second regions for likelihood discriminant input.

125

   

 

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126

 

 

 

 

 

 

   

 

 

     

 

 

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Figure 5.17: The distributions for di—jet mass for muon channel in first and second

regions for likelihood discriminant input.

127

 

PROBABILITY

COMPARISON

 

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regions for likelihood discriminant input.

128

 

  

 

 

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second regions.

129

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fourth regions.

130

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131

 

 

   
   

   
    
 
  

 

 

 

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Figure 5.22: The distributions for leading jet pT for muon channel in third and

fourth regions.

132

 

 

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Figure 5.23: The distributions for second jet pT for electron channel in first and

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133

 

 

 

 

 
  

 

 

 

 

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Figure 5.24: The distributions for second jet pT for electron channel in third and

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134

 

 

  
     

 

 

 

 

 

 

 

 

 

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Figure 5.25: The distributions for second jet pT for muon channel in first and

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135

 

 

     
  
    

   

         

     
  

 

 

 

 

 

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136

 

 

 

 

     
  

   
    
 

 

 

 

 

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Figure 5.27: The distributions for Z rapidity in the center of mass frame of W/ Z

(di-jet) and Z (di-lepton) frame for electron channel in first and second regions.

137

 

 

 
   

 

 

 

 

 

 

   

 

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138

 
 

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Figure 5.30: The distributions for Z rapidity in the center of mass frame of W/ Z

(di-jet) and Z (di-lepton) frame for muon channel in third and fourth regions.

140

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Figure 5.33: The distributions of the angle between reconstructed Z object and the

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in the first and second regions. '

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Figure 5.34: The distributions of the angle between reconstructed Z object and the
Center of mass frame of W/ Z (di—jet) and Z (di—lepton) objects for muon channel

in the third and fourth regions.

144

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Figure 5.35: The distributions for pr difference of W/ Z (di-jet) and Z (di-lepton)

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145

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Figure 5.36: The distributions for PT difference of W/ Z (di-jet) and Z (di—lepton)

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146

 

 

 

 

 

 

 

 

 

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147

 

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148

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Figure 5.39: The distributions for di-jet pT for electron channel in first and second

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149

 

 

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Figure 5.40: The distributions for di-jet pT for electron channel in third and fourth

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150

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Figure 5.41: The distributions for di—jet PT for muon channel in first and second

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151

 

 

   
  
 
 
    

 

 

 

 

 

   

 

 

 

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152

 

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Figure 5.44: The distributions for the pT of the center of mass system for di-jet

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154

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155

 

 

  
  

  
    

 

 

 

 

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157

 

 

 
 
    
   
   

        
  

  

 

 

 

 

 

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Figure 5.48: The distributions for the cosine of the angle between highest pT jet

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158

 

 

  

 

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Figure 5.49: The distributions for the cosine of the angle between highest PT jet

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159

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Figure 5.50: The distributions for the cosine of the angle between highest pT jet

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160

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-| v-I F" _0
uuaAa ’0 19(1an SJIIOAO JO .laqulnu

   

 

...1...1...z..ni.'..
so 0 v N

 

EPiqgure 5.53: The distributions for the cosine of the angle between the highest PT

J $1 and the Z (di—lepton) object for muon in first and second regions.

163

 

 

        
   

l

 

\\\\\\\\\\\\\\\\‘\F: ""
k "
\\ \‘\\\V

0.5
PROBABILITY

PROBABILITY

.5 0
Colel in region [11 (2.3 <= AR < 2.9 )

-1

 

 

 

 

 

OOMDAHKON
COM PARISON

ColeZ

    

 

   

 

lllll|llllllllll
O N 6
fl _ _ fl
swam JO Joqmnn

llllllllllllllll
on 5O Q N O

   

F igure 5.54: The distributions for the cosine of the angle between the highest pT

5 Qt and the Z (di—lepton) object for muon in third and fourth regions.

164

 

 

Chapter 6

Results

Yag’zz At

“iwrct beklz'yorum, yag’zz atzm eg‘erlz';
Yananm sorarlarsa ‘ne getz'rdz'n defierli?’ "’
Necz'p Fazzl Kzsakiirek 1

This chapter mentions the result of the measurement explained in the previous

chapter.

6. 1 Likelihood Results

For the calculation of the cross section measurement we have used a modified
likelihood method which enabled us to pick differences between the signal and
background events. At this point it is necessary to re—mention the definition of our

likelihood:

 

L(:B) _—__ P3ig(x)

.. 6.1
P3739(33) + Pbkgtr‘) ( )

 

lSwart Stallion
Waiting for a sign, my swart stallion saddled;
Damned if they ask ‘what did you bring esteemed?’

165

I1!

where Psig is the probability for an event to be signal and Pbkg is the proba—
bility for an event to be background. The value of the likelihood for a signal event
is 1 and 0 for a background event. 4

By simply dividing the phase space into four regions and using different compo-
nents for the vector 23', we were able to build a likelihood powerful discriminant. The
discriminant histograms obtained by above method can be seen in Figures 6.1, 6.2.
In these figures the number of events in both signal and background Monte Carlo
events are normalized to one so that the discriminant for the background events

doesn’t overwhelm.

MC Likelihood

normalized to 1

 

 

 

 

 

8

6

4

2

:- filllllllllllgllllllfi

"0 0.2 0.4 0.6 0.8 I
likelihood

Figure 6.1: The distributions of likelihood discriminant for em channel. The left
hand side shows signal and background Monte Carlo events discriminant distribu-
tion. These distributions are normalized to 1, so that their shape could be seen
easily. The right hand side shows the discriminant for RunIIa events passing all
the cuts previously mentioned. Total number of RunIIa data shown in this figure

(right hand side) is 475 events.

166

MC Likelihood
signal
bac r

   
    

Data Likelihood
+ data

    

G

normallzedtol

number of events
N N b) b) &
9 UI Ul

ITIIVIIIIIIIIIIIIIIIIIIIIII

 

 

 

€“tr fi ts‘tg i 60 a2 a .
likelihood likelihood
Figure 6.2: The distributions of likelihood discriminant for muon channel.The left
hand side shows signal and background Monte Carlo events discriminant distribu—
tion. These distributions are normalized to 1, so that their shape could be seen
easily. The right hand side shows the discriminant for RunIIa events passing all
the cuts previously mentioned. Total number of RunIIa data shown in this figure

(left hand side) is 381 events.

The total number of RunIIa data surviving all the cuts mentioned until here;
namely object selection 'cuts for leptons (electron and muon), and jets, dilepton
mass, MET, dijet mass, eta-eta and ptjetl-ptjet2 cuts, are 475 events for the
electron channel and 381 events for the muon channel.

The calculation of the cross section is done by the following method. To de-
termine the cross section, we need to separate signal and background events in th
data. We assume that the data is a linear combination of signal events (F) and
background events (F) Then the total number of data events and their likelihood

distribution is given by

D=FXS+F’XB (6-2)

167

where D is the absolute likelihood distribution for data and S and B are the
normalized likelihood distributions for signal and background. We perform a fit

using 6.2 in order to determine signal and background in the data.

electron channel likelihood

 

 

 

Figure 6.3: Likelihood discriminants and their fits to data for electron channel.
The points are for RunIIa data, the fit result is overlayed on them represents data

as signal (red) and background (blue) contributions.

168

 

Channel Signal Background
electron 39.1 :1: 10.4 436.1 :I: 43.1
muon 32.7 i 8.7 346.4 :l: 35.5

 

 

 

 

 

 

 

Table 6.1: Number of estimated events in the RunIIa. data using the MC discrim-
inant distributions as templates.

muon channel likelihood

 

rrTTTTrII‘I'ITrr'TIrrl‘I

 

   

 

Figure 6.4: Likelihood discriminants and-their fits to data for muon channel.The
points are for RunIIa data, the fit result is overlayed on them represents data as

signal (red) and background (blue) contributions.

To obtain these histograms, the equation 6.2 is solved for F and F’ by fitting
the unit normalized signal and background likelihood distributions to the data plot.
By scaling up these distributions by their relative ratios (F, F’) and overlaying the
monte carlo distributions on data we got Figures 6.3 and 6.4. From this we obtain
the number of signal and background events as shown in the Table 6.1

For the cross section measurement we used

 

(6.3)

where N is the number of events seen (or more truely expected from the fit, 6 is the

169

 

Channel RunIIa Luminosity
electron 1044 i 72 pl)“1
muon 948 d: 66 ply—1

 

 

 

 

 

 

Table 6.2: Table of luminosity values for RunIIa run period.

 

Channel Combined Efficiency
electron 0.014 2}: 0.003
muon 0.010 :l: 0.004

 

 

 

 

 

 

Table 6.3: Table of overall efficiencies for WZ/ZZ event selection.

combination of all of the efficiencies andiacceptances (which includes geometric and
physics acceptances as well as object identification and reconstruction efficiencies)
and L is the luminosity. Please refer to the Table 6.2 for luminosity values for
RunIIa data taking period. The source of the errors in themeasurement of the
luminosity come from the uncertainties in the measurement of the total proton-
antiproton cross section. The Table 6.3 shows the combined efficiencies for the
two processes. In this table what is referred as combined efficiencies includes the

following:

o The branching ratio’s of the final products ( two charged leptons and two
jets). The Monte Carlo generated files include all the decay channels. For

W'Z / ZZ process to decay to eejj or npjj, the branching fraction is 2.3%
e The object reconstruction efficiencies

e The inefficiencies related with the structure of the detector like uninstru-

mented regions of the detector etc

Essentially, the probability of observing an WZ/ZZ event (including all the possible
final states) in the DQdetector is given by this efficiency. for

At this point we are ready to calculate cross section of the processes by using
the quantities given in the tables above. For the values of the cross sections of the

processes please see the Table 6.4.

170

 

Process Channel Cross Section

 

 

 

 

 

 

 

Table 6.4: Table of measured cross sections for electron and muon channels for both
WZ and ZZ processes. The measurement uses almost 1 f m“1 of data collected by
DQdetector in both channels.

 

Luminosity 6.1%

Jet Energy Scale 6.0%
JSSR 4.2%

Jet ID 2.1%
Electron ID 5.9%
Muon ID 4.0%
Triggers 6.3%

Jet 77 and AR r.w. 1.6%
Z + jets cross section 20%

 

 

 

 

Table 6.5: Table showing the systematic uncertainties of the different sources.

Before continuing on to the next section we should point out that the errors
on the cross sections are calculated by propagating the errors in the cross section
formula; namely statistical error on the number of events, error on the efficiency
and error on the luminosity. In the electron channel the biggest contribution comes
from the error in the number of events from the fit. Whereas in the muon channel
the biggest contribution comes from the uncertainty in the total efficiencies.

As is evident from the Table 6.1 the uncertainty in the number of background
events is on the order of the number of observed signal events. So there is room

for improvement in this analysis in the future.

6.1.1 Systematic Errors ‘

This analysis suffers from many sources of uncertainties which are listed in the

Table 6.5.
As can be seen from the table the most important uncertainty comes from

the Z + jets cross section measurement. Uncertainties on triggers and luminosity

171

measurements follow it.

The luminosity uncertainty is provided by the luminosity group to the whole
experiment. It comes from the discripancies in the measurement of the luminosity
by DQand accelarator division. The uncertainties on the object identifications are
provided by the respective object identification group. They reflect systematic and
statistical uncertainties on the measurement of object identification measurements.
The error on efficiencies used in the cross section measurement includes errors
on JES, JSSR, jet-id, lepton-id, trigger and jet-eta errors. Z + jets uncertainty
. results from the lack of our knowledge of expressing this process in our monte
carlo programs. Except the last of these errors, all of the others are included in
the calculation of the uncertainty of cross sections.

For the calculation of these uncertainties, one changes object identification
efficiencies by their uncertainties redo the ‘whole analysis and calculates the dif-
ferences. Instead of following these steps, we used uncertainty numbers from a
very similar, having the same object definitions, analysis (WZ / WW cross section
measurement).

The trigger group at DQprovided uncertainty on “Super-OR” ed triggers which
means that all the single lepton triggers are combined with lepton + jets triggers
in order to increase acceptance for the process.

Then for WZ /Z Z process the total systematic error for the electron channel is

1.29 pb and for the muon channel it is 2.31 pb.

6.2 Conclusion

Being a very challenging-physics analysis, it was possible to measure the combined

cross section of WZ/ZZ processes.

172

, and

aWZ/ZZ = 3.45 :l: 0.92 (stat) :l: 2.31 (syst) pb

The theoretical values for the WZ and ZZ processes are given below:

Ul/VZ = 3.68 pb
and
UZZ = 1.46 pb

. Therefore for the WZ/ZZ process the theoretical cross section is 5.14 pb. Al-
though the theoretical values for the cross section lies within the uncertainty of

the measurement, it is obvious that we have still many improvements to make.

173

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