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THESIS

. 9339 llllllllllllllllllllllllllllllllllllllllllllllllllll ll

31293 01810 4301

This is to certify that the
dissertation entitled
Implementation and Calibration of a KI‘ Jet Finding
Algorithm for Use in p13 Collisions at Square Root (8) = 1.8 TeV
presented by

Katherine Chiyoko Frame

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Physics

 

 

VLK weak

 

Major professor

Date May 26, 1999

 

MS U is an Affirmative Action /Equal Opportunity Institution 0-12771

 

LIBRARY
Michigan State
University

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINE return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1M WWW-p.14

 

IMPLEMENTATION AND CALIBRATION OF A kl JET FINDING
ALGORITHM FOR USE IN p15 COLLISIONS AT \/5 = 1.8 TEV

By

Katherine Chiyoko Frame

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1999

 

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ABSTRACT

Implementation and Calibration of a It; Jet Finding Algorithm For Use in

p13 Collisions at \/E = 1.8 TeV

By

Katherine Chiyoko Frame

Jets are widely used as probes of the fundamental parton collisions in Quantum
Chromodynamics. Jets, which are believed to represent the energies and directions
of the emerging partons, are viewed by the experimenter as collimated distributions
of hadrons. The momenta and angles of these hadrons must be combined to form
the parent jet. Because of measurement resolutions and the unavoidable presence of
backgrounds, a jet is thus dependent on the precise nature of the combination algo-
rithm. This thesis studies a new type of jet algorithm and, in particular, investigates

its dependence on the energy and pseudorapidity scales of the DO detector.

For my parents, Eleanor 0. Frame and William V. Frame.

iii

 

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and

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Rick
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have

ACKNOWLEDGEMENTS

It is with great pleasure that I take this opportunity to acknowledge some of the
people who have contributed to this work. I owe most of my understanding of the
current theory to C.-P. Yuan. His patience in explaining very complex ideas to me
has been exemplary. I have also learned a great deal in conversations with Mike Sey-
mour, Walter Giele and James Stirling. I would also like to thank all the individuals
and institutions involved in the building and running of the DO experiment. The
QCD and k; groups at DO have provided much feedback and constructive criticism.
In particular, I thank Rob Snihur and Daniel Elvira. A special thanks is needed for
Rich Astur and Bernard Pope. Rich took me under his wing in my early days at
DC and Bernard has been like a second advisor to me. I am extremely fortunate to

have had the benefit of their guidance and support.

I would like to take a moment to acknowledge those who have influenced me
outside of the academic arena. First and foremost, I thank my family for their
love and support throughout my life. Joanna Guttmann, Linda Tartof and Shojiro
Sugiyama taught me the virtues of commitment and discipline. My friendships
with Todd Cruz, Lenny Apanasevich, Ken Johns and Sal Fahey have brought me
much laughter and joy, and I have learned much of human virtue by their examples.
Elizabeth Gallas provided an infinite wealth of wisdom and advice for which I am

extremely grateful. I have also had the good fortune to have befriended Steve J erger,

iv

 

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paiiv

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possi

Tom Rockwell, Joelle Murray, Mike Wiest, Gian Diloreto, Tina Hebert, Florencia
Cannelli and Lisa Oravecs. I would also like to thank the guys at the Fermilab
gym who taught me how to play basketball at the Fermilab gym: Rick Jesik, Ryan

Hagler, Noah Wallace, Carl Penson, Walsh Brown, and Wayne Waldon.

Most Importantly, I must thank my advisor, Harry Weerts. His strong sense
of honor and duty is inspirational. He has been an unending source of guidance,
patience and wisdom throughout the years. None of this work would have been

possible without his hand. Thank you, Harry.

C(.

1111

 

 

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Contents

1 Introduction

1.1 Fundamental Constituents of Matter ..................

1.2 The Thesis .................................

2 The Standard Model
2.1 Electroweak Interactions .........................
2.2 Quantum Chromodynamics .......................
2.3 The Running of the Couplings ......................
2.4 Cross Sections ...............................

2.5 Renormalization and the Strong Coupling, a, .............

3 Jet Production in p13 Collisions
3.1 mi Collisions ................................
3.2 pg? Event Variables ............................

3.3 Monte Carlo Event Generators ......................

vi

11

15

16

18

21

25

26

29

30

3.4 Jets ....................................

3.5 R32 .....................................

4 The Tevatron and The DO Detector
4.1 The Fermilab Tevatron Collider .....................
4.2 The DC Detector .............................
4.2.1 The Level Zero Detector .....................
4.2.2 The Tracking System .......................
4.2.3 The Calorimeter .........................
4.2.4 The Muon Spectrometer .....................
4.2.5 The DC Trigger System .....................

4.2.6 Offline Reconstruction ......................

5 The kl and Cone Jet Algorithms
5.1 The Fixed Cone Jet Algorithm .....................
5.2 Clustering Algorithms for e+e’Collisions ................
5.3 Adaptation of the kl Algorithm for p13 Collisions ............
5.4 kl Jets at DC ...............................

5.4.1 Monte Carlo Event Jet Rates ..................

6 Introduction to kl Jet Momentum Calibration

vii

34

37

37

40

41

43

44

48

49

50

52

54

58

60

62

66

69

6.1 General Overview of kl Jet Momentum Calibration .......... 70

kl Jet Offset Correction 72
7.1 Monte Carlo Data With Overlay ..................... 74
7.2 The Method ................................ 75
7.3 Verification of the Overlay Method ................... 79
7.4 Offsets for the kl Algorithm ....................... 83
7.4.1 Offset Due to Noise, Pile—Up and Multiple Interactions . . . . 83
7.4.2 Offset Due to Physics Underlying Event ............ 89
kl Jet Response Correction 96
8.1 The Missing ET Projection Fraction Method ............. 97
8.1.1 The Energy Estimator, E’ .................... 99
8.2 'y-Jet Data ................................. 100
8.2.1 Photon Event Requirements ................... 100
8.2.2 Cone Jet Requirements ...................... 102
8.2.3 Additional considerations for kl Jets .............. 103
8.3 Cryostat Factor Correction ........................ 104
8.4 E’ —->Pkt Mapping ............................. 105
8.5 Response vs. Pk, ............................. 107
8.6 ICR Correction .............................. 110

9A

 

10;

 

8.7 Jet-Jet Data ................................ 110

8.7.1 Measurement of Fn ........................ 113

8.8 The Low ET Bias ............................. 120
8.9 Low PM Jet Response ........................... 121
8.10 The Jet Response Errors ......................... 126
8.10.1 Errors and Correlations of the RM Fit ............. 126

8.10.2 Low Momentum Errors ...................... 127

8.10.3 17 Dependent Correction Errors ................. 129

9 K i Jet MPF Closure 133
9.1 The Data ................................. 134
9.2 Monte Carlo Jet Corrections ....................... 134
9.2.1 Monte Carlo Underlying Event Offset .............. 134

9.3 Monte Carlo Jet Response ........................ 135
9.3.1 Monte Carlo Cryostat Factor .................. 135

9.3.2 Jet Response vs. kl Jet Momentum ............... 137

9.4 Monte Carlo Closure ........................... 137

10 kl Momentum Calibration Summary 144
10.1 Summary Plots of Corrections and Errors ................ 146

ix

 

 

 

11

(I)

11 R32 Preliminary Results

A Photon and Jet Triggers
A.1 Photon TTiggers ..............................

A.2 Jet Triggers ................................

B Cone Jet Offset Comparison
8.] Smeared Versus Unsmeared Quantities .................

B.2 Dependence of the Offset on ET .....................

B.3 Dependence of the Offset on Luminosity ................

C Showering Effects on the Jet Response

152

154

154

156

159

160

165

171

172

 

 

 

 

 

 

8.2
8.3
8.4

8.5

8.5 l

List of Tables

2.1

2.2

2.3

2.4

2.5

7.1

8.1

8.2

8.3

8.4

8.5

8.6

The Standard Model Quarks. ...................... 9
The Standard Model Leptons. ...................... 10
The Standard Model Vector Bosons and their respective forces. . . . . 10
The Scalar Higgs Boson. ......................... 10
Summary of 0, measurements [15]. ................... 23
Availability of ET , luminosity and 17 for overlayed Monte Carlo data. 75

Cryostat corrections applied to the energy in the calorimeter cryostats

introduced for the DOFIX environment. ................ 104
Fit parameters for E’ to PM mapping ................... 107
Fit parameters for hadronic response correction ............. 110
Triggers and thresholds .......................... 112

Correlation matrix for error band in hadronic jet response correction

for It; jets .................................. 129

Residuals ................................. 130

xi

9.1 Herwig v5.9 underlying event energy density ............... 135

9.2 Fit parameters for Rjet vs. PM in Monte Carlo data ........... 137
A.1 Triggers used in the photon event selection. .............. 155
A2 Triggers used in jet event selection. ................... 157

xii

 

LI

 

 

3.5

4.1

4.2

«(U

List of Figures

2.1

2.2

2.3

2.4

2.5

3.1

3.2

3.3

3.4

3.5

4.1

4.2

4.3

Feynman diagram for e‘u —> Ved by W exchange ........... 14
Feynman loop diagrams ......................... 17
Factorization of the 125 matrix element. ................. 20
Feynman diagrams for qg—9qg via gluon exchange ........... 21
Summary of 0, measurements ....................... 24
Feynman diagram for qg —> qg by gluon exchange ............ 27
qg —> qg (before). ............................. 27
qg —-) qg (after) ............................... 28
An event as seen by the DO detector ................... 29
An example of 0(a3) Feynman diagram contributions ......... 32
Overview of the Fermilab Tevatron. ................... 38
Cutaway view of the DO detector ..................... 42
The four detectors which comprise the tracking system ......... 43

xiii

 

5.3

5.4

5.5

‘1
‘1

Fl};

 

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Dis

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Riff;

Me;

4.4

4.5

4.6

4.7

5.1

5.2

5.3

5.4

5.5

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

Cutaway view of the DO calorimeter detector. .............
Schematic view of a liquid argon readout cell. .............
One quadrant of the DO calorimeter. ..................

Block diagram of the DO trigger system. ................

Lego plot of a 2 jet event .........................
Fixed cone jet. ..............................
lei jet clustering. .............................
Jet Clustering in e+e‘Collisions .....................

k‘L Jet Rates as a function of font in Herwig v5.8 Monte Carlo Data. .

Separation of overlayed and non-overlayed kl jets ............

ET differences between noise overlayed and non-overlayed kl jets. . .

Ranking of overlayed kl jets compared matched to non-overlayed jets.

Distribution of reconstructed ET for ki jets without noise overlay. . .
0.7 cone jet occupancy vs. jet 1) for jets found in minimum bias data.

0.7 cone jet occupancy vs. jet 1] for jets found in Monte Carlo with

minimum bias overlay data. .......................
Measured Ozb vs. kj jet ET at £20.1x1030cm‘2sec‘1. ........
Measured 02,, vs. kl jet ET at £=5x103°cm’2sec"1. .........

Measured Ozb vs. kl jet 77 at various luminosities. ...........

xiv

45

47

49

53

59

68

77

77

78

79

80

86

T.13 (*

7.14 .\I

7.15 .\I

7.16 O.

8.1

8.3

8.4

8.5

8.6

8.8

8.9

 

 

Rf

 

 

 

an

jot:

Res.

Res

C01

Reg

7.10 Measured 0,”, vs. kl jet 77 at £=5 and 30<ET <50 GeV. ....... 87
7.11 Parametrization of 02,, vs. kl jet 77 for jets with 30<ET <50 GeV, for

various luminosities. ........................... 88
7.12 0M, correction vs. kl jet ET . ...................... 90
7.13 OM, correction vs. k_L jet 77 ........................ 91
7.14 Measured One vs kl jet ET . ....................... 92
7.15 Measured 0,“. vs kj jet 77 ......................... 94
7.16 0,“, correction vs kl jet 17. ........................ 95
8.1 Response versus E’. Open symbols are from the full *y-jet data sample

and solid symbols are from the smaller sample reconstructed with k_1_

jets. The additional DOFIX cryostat corrections were removed from

kl jets .................................... 106

8.2 It; jet P versus E’. Straight lines were fit to the CC and EC separately.108

8.3 Response versus PM ............................ 109
8.4 Response fit versus jet PM. Rjet(Pkt) = a + b - ln(PM) + c - ln (P)2. . . 111
8.5 Response versus 17 >00 for jet-jet data .................. 114
8.6 Response versus 17 <0.0 for jet-jet data .................. 115
8.7 Correction factor F" ........................... 116
8.8 Correction factor F" ........................... 117
8.9 Response versus 17 after 1] dependent corrections ............. 118

XV

8.1-3 Th

 

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8.10

8.11

8.12

8.13

8.14

8.15

8.16

9.1

9.2

9.3

9.4

9.5

9.6

10.1

10.2

10.3

Response fit versus jet E with and without the ICR correction. Rjet(E) =

a + b - ln(E) + c - ln (E)2. The two curves are virtually identical. . . . 119
A¢7 jet distribution ............................ 122
Et distribution of first 4 objects ..................... 123
Low momentum jet response ....................... 125
Error correlations for kl jet response fit. ................ 128
The fractional difference between Rm...” and lec for partially cor-
rected jets. AR = (Rmeas — R6010) / R6016. ............... 131
The distributions of fractional differences between Rmm and lec. . 132

Monte Carlo Cryostat Factor ....................... 136
Rjet vs. Pktin Monte Carlo data ...................... 138
Monte Carlo Closure in CC ....................... 140
Monte Carlo Closure in EC ....................... 141
Monte Carlo Closure in EC ....................... 142
kJ_ algorithm dependent correction, Rm. Errors are shown as dotted

lines ..................................... 143
Corrections and Errors for 77;“th =0.0, R =0.7. ............ 147
Corrections and Errors for 7);“th =1.2. ................. 148
Corrections and Errors for 7);“th 22.0. ................. 149

xvi

 

 

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10.4 Corrections and Errors versus 77mm, Jet PT = 20 GeV. ........ 150

10.5 Corrections and Errors versus may-ct, Jet PT = 100 GeV, Ram = 0.7.

151

11.1 R32, VS. HT3 ................................ 153

3.1

8.2

8.3

BA

85

8.6

The 0.7 cone jet offset density, Dzb, as obtained by selecting the lead-

ing jets either in the 25 (full boxes) or in the 1:2: sample (full circles).

The open circles are from CAFIX 5.1 ...................

Unsmeared Dzb offset vs. ET in five 17 ranges for 0.7 cone jets. The
cut in ET is applied either to the raw 1m: jets (stars), or to 25 jets
(full circles) weighed to a flat distribution in ET . The result from

CAFIX5.1 (open box) is shown for comparison on the left, but no ET

is associated with it. ...........................

The smeared (open circles) and unsmeared (full circles) Dzb offset for
0.7 cone jets. Both sets of points differ only by the weight assigned to

the generated jets. The open box shows for reference the result from

the J ES DON ote. .............................

Dependence of Du,3 on ET for cone jets. The result from CAFIX5.1 is

shown for reference ............................

Jet energy dependence of occupancy for zero bias luminosity 5 and

R = 0.7 cone jets ..............................

Dependence of mO-xa: on ET for cone jets ...............

xvii

161

166

167

169

8.8

CI .

B.7 Dependence of zb-xx on ET for cone jets. The dependence is the same

8.8

CI

as in the previous figure, and cancels when getting Due by taking the

difference ................................. 170

The unsmeared offset Dzb (stars) at different luminosities for 30<ET < 50
Gev jets (our result depends on jet energy). Full circles are from

CAFIX5. 1, for comparison. ........................ 171

Showering effects in the MPF method. (a) A photon is balanced by
three particles, 1, 2, and 3, in the transverse plane. E1 > E2, E3 and
R1 > R2, R3. (b) The 2nd and 3rd particles are deflected away from

the jet axis in the calorimeter ....................... 173

xviii

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“When the objects of an inquiry, in any department, have principles, conditions,
or elements, it is through acquaintance with these that knowledge, that is to say
scientific knowledge, is attained. For we do not think that we know a thing until we
are acquainted with its primary conditions or first principles, and have carried our
analysis as far as its simplest elements. Plainly therefore in the science of Nature, as
in other branches of study, our first task will be to try to determine what relates to its

principles.”

Aristotle’s Physics

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Chapter 1

Introduction

Throughout our history and in our individual lives, humans have endeavored to attain
some understanding of the human condition. Academic institutions are divided into
disciplines which focus on various aspects of this. Since we inhabit a physical universe
and are physical beings ourselves, it follows that we have the various branches of
physical science. In particular, Elementary Particle Physics is the study of the

fundamental building blocks of matter and the forces which govern their behavior.

At present, four forces are believed to dictate all physical interactions: gravity,
electromagnetism, the weak force and the strong force. The current Standard Model

theory encompasses all but gravity.

1.1 Fundamental Constituents of Matter

In Aristotle’s day, all matter was believed to be made up of four elements: earth,

wind, fire and water. In Medieval times, a few of the Chemical elements were recog-

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nized. By the 19th century, about 30 chemical elements were identified and it was
discovered that the combinations of these elements could account for the profuse
number of chemical compounds found in nature. In the early 1800’s, John Dalton
proposed that the chemical elements are composed of units (atoms) of matter which

could be characterized by their weight.

Throughout most of the 1800’s, the atom was considered to be the fundamental
unit of matter. By the turn of the century, the electron had been discovered and
believed to be an essential part of atomic structure, but classical theories proved
inadequate to describe this structure. In 1900, Max Planck introduced the idea of

quantized radiation and quantum theory was born [1, 2].

The years that followed saw huge advances in both theoretical and experimental
physics. In 1905, Albert Einstein put forth his theory of special relativity and pro-
posed a quantum of light behaving like a particle [4] (later to be named photon). This
was received with much skepticism, but in 1916, Millikan published his results on
the photoelectric effect confirming Einstein’s photon theory [5]. Doubt still lingered,
but in 1923, Compton observed shifts in wavelengths in light scattering experiments
which could only be explained using a photon theory of light. In the same spirit,
de Broglie considered the possibility that if something previously thought to have
only wave attributes could also behave as a particle, than perhaps particles could
behave like waves. Shortly after Compton’s experiments, de Broglie proposed the
wave property of matter and a couple of years later Schroedinger developed wave

mechanics for describing quantum systems for bosons.

Meanwhile, physicists were also making progress in their understanding of atomic

structure
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structure. Hans Geiger and Ernest Marsden (under the supervision of Ernest Ruther-
ford), performed experiments in 1909 scattering alpha particles off a gold foil. The
large scattering angles they observed suggested a small, dense, positively charged
nucleus in atoms. It wasn’t until a decade later that Rutherford was able to find
the first evidence of the existence of the proton. In 1913, Niels Bohr constructed
a quantum theory of atomic structure, and then, several years later, in 1925, Pauli

formulated the exclusion principle for electrons in atoms.

In 1930, there were believed to be three elementary particles: photons, electrons
and protons. However, theoretical and experimental developments implied otherwise,
and the next few decades proved to be one of the most exciting periods in particle
physics history. A plethora of new particles were predicted and/or experimentally
observed and some of the most fundamental building blocks of the current Standard
Model theory were established, namely, the Dirac equation and the theories of weak

and strong interactions.

In 1928, Dirac was able to describe electrons combining quantum mechanics
and special relativity. After a few years, he realized that his equation implied the
existence of a new particle that is identical to the electron except that it is positively
charged. He called it a positron. No one had ever conceived of an antiparticle
before and this turned out to be an important discovery. The positron was later

experimentally observed in cosmic ray experiments in 1932.

The continuous energy spectrum seen in beta decay experiments in the late 1920’s
led Pauli to suggest that an additional particle, a neutrino, carried away the missing

energy. Following that, Fermi introduced the weak interaction to describe beta decay

quark

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using Pauli’s neutrinos. This was another notable moment in our history because
this was the first theory to imply particle flavor changes (e.g. neutron changing to a

proton plus electron plus neutrino).

The road to our current understanding of strong interactions was not so smooth.
In 1931, Chadwick discovered the neutron, but as more was learned about nuclear
structure, the mechanisms of nuclear binding became more obscure. Around 1934,
Yukawa put forth a theory combining relativity and quantum theory to describe the
strong interactions in the nucleus. He introduced a mediator particle called the pion
and estimated its mass to be about 200 times that of the electron. In 1937, a particle
with approximately this mass was discovered in cosmic ray experiments. Of course,
it was thought to be the pion, but it was much later (1946) that it was actually
discovered to be a muon. The muon was quite unexpected as it is the first time
a second generation of matter was observed, and the famous phrase was uttered,
“Who ordered that?” (by I. I. Rabi). Soon after the muon was revealed, however,

the pion was also observed in cosmic rays.

In the following decade, a proliferation of particles was observed, and in electron-
nuclei scattering experiments in the mid 1950’s, a charge density distribution was
seen in protons and neutrons suggesting an internal structure to nucleons. In 1964,
Cell-Mann and Zweig theorized the existence of three elementary particles called
quarks [6, 7]. The up, d0wn and strange quarks are fermions with charges of +§,
-§ and -% respectively. Many new particles could be described as combinations of
these quarks. For example, the proton is composed of two up quarks and one down

quark and the neutron is composed of two down quarks and one up quark. The third

quark. $1

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quark, strange, was used to build some of the more exotic particles.

In experiments at the Stanford Linear Accelerator Center (SLAC) in the late
1960’s, electrons scattered off protons appeared to be bouncing off of hard cores
inside protons. Bjorken and Feynman used a constituent particle model to interpret
the data [3]. Although they did not refer to the constituent particles as quarks (but
as partons), this provided supporting evidence that the proton is a composite particle

and supported the quark theory.

Meanwhile, Schwinger, Bludman and Glashow independently came up with the
idea that the weak interactions are mediated by charged heavy particles (later named
the W+ and W"), and in 1967, Weinberg and Salam (again independently) developed
a theory that unified the electromagnetic and weak interactions. They suggested the
existence of a neutrally charged vector boson, Z”, which (in addition to the W+,
W‘) acts as a mediator of weak interactions. In an effort to explain the masses of
the vector bosons, they also introduced a massive scalar boson called the Higgs, H.
The W+, W", and 2° bosons were all observed in 1983, but the Higgs has yet to be

observed and remains a major missing piece of the current theory.

At this point, the current electroweak theory was pretty well developed, but the
theory describing strong interactions needed some modification. Because the leptons
appeared in pairs, e and V3 and p and u”, it was theorized that the quarks would
behave in a similar manner and the charm quark (+§ charge) was introduced to
be paired with the strange (the other pair being the up and down). Fritzsch and
Cell-Mann put forth the theory of quantum chromodynamics (QCD). This theory

is similar to electroweak theory. Where electroweak has the photon, Wi and Z0

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Standard }
for the 9x1

elusive,

F0? tilt
ably Stab?
them)" is
does not .
Utttrjeldy‘

9211101] 0[

A, n

as its mediators, QCD has the gluons. Evidence for gluons was first experimentally

observed in 1979 in electron positron collisions.

In 1974, the J/\II was discovered at Brookhaven/SLAC by Ting/Richter [8, 9].
The J/‘Il is composed of a charm and an anti-charm. The addition of the charm
quark implied the existence of a group of new particles which were subsequently

observed. The charm quark, itself, was observed in 1976.

With the success of the 2 generation theory, the possibilities of there existing
3 third generation of quarks and leptons was theorized, and, sure enough, the Tau
lepton was discovered in 1976 at SLAC and the bottom and top quarks were observed

at Fermilab in 1977 and in 1995 respectively [10].

Today, the tan neutrino, VT, and the Higgs boson, H, are the only particles of the
Standard Model theory that have not been experimentally observed. Strong evidence
for the existence of the Tau neutrino exists while the Higgs remains somewhat more

elusive.

For the past 20 years the Standard Model theory has proven itself to be remark-
ably stable. No experimental measurement to date contradicts it. However, the
theory is not complete for it cannot account for the masses of the fermions and it
does not accommodate gravity. It is defined by 18 parameters making it somewhat
unwieldy, and only the electromagnetic and weak interactions are unified. Several
theoretical models are being developed with a view toward completeness and unifi-

cation of the 4 forces, electromagnetic, weak, strong and gravitational.

As mentioned above, the parameters of the Standard Model theory are not com-

pletely t
able ext

inconsis'

1.2

 

 

hlost of t
(’Xperirrtt
energies

the inter

This
collided
COnstitt
Pair Co]
are 2 0
The Ori
with 3
of the
Hutch

Tr
taut-J]
the i

LS Dr

pletely nailed down. Perhaps, as our measurements become more precise and we are
able explore regions of phase space previously unavailable, we will see phenomena

inconsistent with the current theory and this will guide us in a new direction.

1.2 The Thesis

Most of today’s particle physics experiments are similar in principle to Rutherford’s
experiment scattering alpha particles off of a gold foil. Particles are collided at high
energies (either using two colliding beams or a beam focused on a fixed target) and

the interactions are studied by examining the outcome.

This thesis involves data from an experiment in which protons and antiprotons are
collided at extremely high energies. The high energy is needed in order to study the
constituent quarks and gluons that make up the proton and antiproton. When the
pair collide, typically, 2 or 3 jets of particles emerge and are detected. Whether there
are 2 or 3 jets detected is closely related to the strength of the strong interaction.
The original intent of this thesis was to perform a measurement of the ratio of events
with 3 jets to 2 jets, R32. This would give us a better understanding of the nature
of the strong force. We are able to look at interactions with center of mass energies

much higher than what has previously been looked at.

To make an experimental measurement of R32, a tool had to be developed and
calibrated. This task, while meritorious in itself, has diverted much effort away from
the intended measurement and, therefore, that analysis is left outstanding. What

is presented here is the work done developing and calibrating the kl jet algorithm

7

along tr:

The '
|
bllPl OW
durtion 1
a deserh
finding a
erahle lip
its derive.

measurer:

 

 

 

along with some very preliminary results for our measurement of R32.

The thesis is organized in the following way. In the following chapter, we give a
brief overview of the Standard Model theory. Following that, we describe jet pro-
duction in pp , physics and motivate the measurement of R32. Chapter 4 contains
a description of the experimental apparatus, and in Chapter 5, we will discuss jet
finding algorithms. The momentum calibration of jets in the detector is a consid-
erable task requiring much attention, and, therefore, five Chapters are devoted to
its derivation, testing, and summary. Finally, we will present a very preliminary

measurement of R32.

 

Ch

The

 

The partir
[Table 2.1
[Table 2,4
37005. th
masses. _\

quarks all

'lS Sta

Chapter 2

The Standard Model

The particles of the Standard Model theory can be categorized into 4 groups: quarks
(Table 2.1), leptons (Table 2.2), vector bosons (Table 2.3) and the Higgs scalar boson
(Table 2.4). Quarks and leptons are fermions (spin 1/2 particles) and, within these
groups, there are 3 generations. The three generations are identical except for their
masses. Most matter is comprised of the first (lightest) generations (up and down

quarks and electrons).

As stated previously, all matter interacts via four forces (gravity, electromag-

Table 2.1: The Standard Model Quarks.

 

 

 

 

 

[[ FCharge [Mass (M eV/cTfl]
up 3 1.5 - 5
down —§- 3 - 9
charm Z 1,100—1,400
strange —§ 60-170
t0p 3 174,300 :1: 5,100
bottom —2 4,100-4,400

 

 

 

 

 

 

 

 

 

Tabh

 

Table 2.2: The Standard Model Leptons.

 

 

 

 

 

 

 

 

 

[ Charge Mass (MeV/CQ) [
e" -1 0.511
V8 0 < 5.1 x 10‘6
,u‘ -1 106
up 0 < 0.27
T -1 1,777
11.,- 0 < 31

 

 

 

Table 2.3: The Standard Model Vector Bosons and their respective forces.

 

 

 

 

 

 

Force J Charge Mass (M eV/ CT)
'7 Electromagnetic 0 0
gluon Strong 0 0
W3: Weak :l:1 80000
Z 0 Weak 0 91000

 

 

 

 

 

 

 

 

Table 2.4: The Scalar Higgs Boson.

 

Charge

Mass (MeV/cz) []

 

 

[[H 0

 

> 58400 [15]

ll

 

10

netisrri.

eneompu
in the fr;
weak fort
is deserii
boStjirts r-t
scalar Hi
confirmet

bosons in

What
PDT 3 mm

 

2.1

The eleclft‘

CG

1, and Um}

bszf

 

act's (JHlV u.

netism, the weak force and the strong force). The current Standard Model theory
encompasses all but gravity. In the Standard Model theory, interactions are described
in the framework of the U(1) xSU(2) L xSU(3) gauge group. The electromagnetic and
weak forces are unified in the electroweak gauge, U(1) xSU(2)L, and the strong force
is described under SU(3). The forces are mediated by the exchange of the vector
bosons corresponding to the symmetries of the group as shown in Table 2.3. One
scalar Higgs boson, H, is predicted (shown in Table 2.4). Its existence is not yet
confirmed, but it is necessary to account for the masses of the Wi and Z0 vector

bosons in the present theory.

What is presented here is a very minimal view of the Standard Model theory.

For a more rigorous description the reader is directed to the references, [16, 17, 18,

19,20,21]

2.1 Electroweak Interactions

The electromagnetic and weak interactions are unified in the Standard Model under
the gauge group, U(1) xSU(2)L. U( 1) symmetry implies conservation of hypercharge,
Y, and under SU(2)L, isospin, T, is conserved. Electric charge, Q, is related to these
by Q = T 3 + g where T3 is the third component of isospin. Therefore, Q is also
conserved in the electroweak gauge. The subscript, L, denotes that the SU(2) group
acts only upon the left handed component of the field. No right handed neutrinos

have been observed. The group acts on left handed doublets and right handed

11

sngen

h
The (pin?

The hot ._
in Table '

‘15ng the

This gim-
qualk can
COUphngS

diagftnal C

 

In the

$61th [3080

done throuJ

singlets. The lepton doublets and singlets are written as

Ve V“ VT
a a a 633 ”Ra TR -

8 7'
L [1' L L

The quark doublets and singlets are

u c t
a a 7 UR: CR, tRa dRa 8R) bR '
d’ s’ b’

L L L

The bottom components of the quark doublets are different from the mass eigenstates
in Table 2.1. They can be written as linear combinations of the mass eigenstates

using the CKM matrix (named after Cabibbo, Kobayashi, and Maskawa):

d’ Vud Vchtd d
8’ = Vus V68 ‘48 s
5' Vuchthb b

This gives us some mixing between the different quark generations (e.g. the up
quark can couple to the strange and bottom quarks as well as the down quark). The
couplings between the different quark generations are rare and, therefore, the off

diagonal CKM matrix elements are << 1.

In the vacuum (ground state), the U(1)xSU(2)L Lagrangian requires the four
gauge bosons to be massless. The symmetry of the ground state must be sponta-
neously broken to account for the masses of the W+, W’ and Z0 bosons. This is
done through the Higgs mechanism. The result is the scalar Higgs boson and in

addition to mass, the W and Z bosons gain a longitudinal polarization component.

12

The
by 3 fur;
g'. and t

are give:

 

and

 

 

and

511’ .

The masses of the mediators and the strength of the interactions are determined
by 3 fundamental parameters: the weak isospin coupling, gw, hypercharge coupling,
9’, and the vacuum expectation value for spontaneous symmetry breaking, 12. They

are given by the following relations:

 

 

 

e
w : . y 2.1
9 sm 9w ( )
, e
= 2.2
and
1/ = 224W , (2.3)

where e is the magnitude of the charge of the electron, MW is the mass of the Wi
and 9w is the weak mixing angle. It is often convenient to express these in terms
of 3 other variables: the fine structure constant, am, the Fermi constant, G p, and

sin2 0w. am and G p are related to 9“,, g’, and u by

2 1 1
Gem = 3:“ = :1— (T—T) , (2-4)
7? 77 E + 313
and
1 2
Gp = -—— 9‘" (2.5)

«axe-1m-

sin2 6w is given by the masses of the W, MW, and 2", M z, by

M2
sin20w = 1 — J . (2.6)
Mg

13

Current

.11

 

 

 

Ari e
Figure 2
all Gleetr
With 501‘
by 8 50:
901111111]
for W (

line an.

Current experimentally measured values for am, G p, MW and M z are

1
em 3 : _— , 2.
a (m ) 137.0359895 ( 7’
GF = 1.16639 x 10-5GeV-2 , (2.8)
MW = 80.410 :1: 0.044 GeV/c2 and Mg = 91.187 i 0.007 GeV/c2 . (2.9)

An example of a weak interaction is illustrated using a Feynman diagram in
Figure 2.1a in which an electron and an up quark exchange a W boson resulting in
an electron neutrino and a down quark. In Feynman diagrams, time runs horizontally
with some space coordinate on the vertical axis. By convention, fermions are depicted
by a solid line with an arrow pointing in the forward direction of time. An arrow
pointing in the reverse direction indicates an antiparticle. A dashed line is drawn
for W (and Z) bosons. In succeeding diagrams, photons are represented by a wavy

line and gluons by a helix as shown in 2.1(b).

 

 

(b) ——>-— W ————— W
fermion photon W, Z gluon

Figure 2.1: (a) Feynman diagram for e‘u —+ ued by W exchange. Time flows from
left to right. (b) Fermions are depicted by a solid line with an arrow pointing in the
forward direction of time (an arrow in the reverse direction denotes an antiparticle).
Photons are represented by a wavy line, W and Z bosons by a dashed line, and
gluons by a helix.

14

The
betweer.

the fern,

2.2

Quattturt
Under 8:

color lll(i

 

 

charge_

can be es

where r:

In “an

made of qt

The Z 0 and W33 are self coupling, and in addition, there are mixed couplings
between the photon, W:t and Z0. The Higgs couples only to the W:t and Z0 and

the fermions.

2.2 Quantum Chromodynamics

Quantum chromodynamics in the Standard Model is based on the SU(3) gauge group.
Under SU(3) symmetry, color charge is conserved. Each quark carries one of three
color indices, 7”, g, b = red, green, blue), and an octet of gluons carry color anti-color
charge. The group acts on color triplets for each of the six quarks. The gluon octet

can be expressed in the following color states:

II) = (75 + MW? I5) = —z’(79 + gfl/x/i
[2) = —z‘(rB + hem/2 |6) = (bg + gB)/\/§
13> = or + bB)/\/§ I7) = —z'(bo + gem/2’

(4) = (rg + gF)/\/2 IS) = (W + or; + 2g§)/\/6 (2.10)

where r=red, b=blue, and g=green. The quark triplets are

ur 6,- tr dr Sr br
17;, 7 65 7 tb 7 db 7 Sb , 05
“9 Ca to do 59 by

In nature, only color singlet (i.e. colorless) quark combinations exist. Mesons are

made of quark anti-quark pairs with color anti-color respectively, qarfa, and baryons

15

consi

tense

do n
Strut
deset

if’l;

2.3

'The
theh
defir

Stro

lick
fins
ilst
hag
anti

.DOTQ

consist of 3 quarks with 3 different colors, cabcqaqch where 6““ is the antisymmetric

tensor.

Leptons (and their respective neutrinos) do not carry color and, therefore, they
do not participate in strong interactions. Only quarks and gluons interact via the
strong force. The gluons are massless and one parameter, the strong coupling, 9,,
describes the interactions. In a similar manner to the weak couplings of the W:t and

Z0 bosons, the gluons are self coupling.

2.3 The Running of the Couplings

The strengths of electromagnetic, weak and strong interactions are quantified by
their respective coupling constants. The strength of the electromagnetic force is
defined by the Fine Structure Constant, am (Equation 2.4), and the weak and

strong coupling constants, aw and 07,, are given by

aw = 3% and as = 219% . (2.11)

The strengths of the forces depend on the distance between the interacting par-
ticles and, therefore, these so called constants vary. For the electromagnetic force,
this can be understood if we imagine that the vacuum acts like a dielectric medium.
As the separation between two charged fermions increases, fermion antifermion pairs
(e.g. e+e") begin to pop up in the vacuum. These pairs screen the bare charges

and give an effective charge that is somewhat reduced. This is referred to as vacuum

polarization. In Figure 2.2(a), this is depicted in a Feynman diagram. The fermion

16

andlerx

agator.

figure L

(bl ll'a

 

antifermion pairs are represented by a fermion loop (or bubble) in the photon prop-

agator.

- (“\
(b) >-(‘)--*/--<

Figure 2.2: Feynman loop diagrams. (a) Fermion loops in the photon propagator.
(b) W and Z loops in the Z propagator. (c) gluon loops in the gluon propagator.

At distances greater than 2.43 x 10‘10cm (the Compton wavelength of the elec-

1

E' If we increase our

tron), the electronic charge is fully shielded and 078m z
energy (decrease deBroglie wavelength) to 80 GeV (chz), the coupling increases
to am z 1%.

In the cases of the weak and strong forces, matters are complicated by the self
coupling of the force mediators. In addition to fermion loops, we have W*, Z 0, and

gluon loops (see Figure 2.2(b) and 2.2(c). These compete with the fermion loops so

that the forces actually decrease as energy increases (wavelength decreases).

This was a very important discovery in QCD physics because the quarks, while
inseparable at low energy (known as confinement), behave as free particles at very

high energies. This is referred to as asymptotic freedom.

17

234

ill Clib‘
over 11":
for an

interes' ‘
have [it
1119 par
Ohhtts
and str

study (l

Where I.
bl" 23,
alder
andom

 

Coupling:

Etc. ].

1“ 1h

2.4 Cross Sections

In classical physics, the cross section for a given interaction is defined as the area
over which the desired interaction can take place. For example, the cross section
for an arrow hitting a target is the area of the target. The interactions we are
interested in, however, are not simply “hit or miss” interactions. Particles do not
have to “touch” to interact. In these interactions, it may be more useful to imagine
the particles as fields (electroweak and / or strong fields) rather than hard point like
objects. Since the forces span to infinity, the absolute cross sections for electroweak
and strong interactions are infinite. To make some quantitative sense out of this, we

study differential cross sections, do, for various kinematical cuts. This is defined as
Zn 2
do = thl x (phase space) , (2.12)

where h is the reduced Planck’s constant, h/27r = 6.5822 x 10‘22MeVsec, divided
by 27r, M is the amplitude (or matrix element). The phase space term contains
all the kinematic constraints (e.g. masses, energies and momenta of the incoming
and outgoing particles). This is handled by integrating over the 4 momenta of the
outgoing particles (in the kinematic region of interest) with a delta function included
to ensure conservation of 4 momentum. The matrix element contains the meat of the
calculation. This contains all the dynamical information about the interactions (e.g.
coupling strengths, vacuum polarization, 4 momenta of the internal propagators,

etc.).

In the case of pp collisions, the matrix element is complicated by the fact that

18

protor.
for on
betwet
in ‘2 or
mmflt
cont irxl
where }
parton-
for thi~
defines
i and T

elt’mert'

Where (
$fl9w]

pTOCESS

 

functio
(aflliprc

th
men’s? 1
hard Se;

Th9 5(7);

protons and antiprotons are composite particles made of partons (a generic term
for quarks and gluons). We are interested in pp collisions in which an interaction
between one parton in the proton and one parton in the antiproton interact resulting
in 2 or more hard (i.e. energetic) partons emerging at large angles with respect to the
collision axis. The remnant partons which did not take place in the hard interaction
continue along the collision axis. An example of this is illustrated in Figure 2.3
where partons i and j (in the proton and antiproton respectively) interact producing
partons j and k (plus the proton and antiproton remnants). The matrix element
for this interaction can be factorized into two parts: the scattering amplitude which
defines the hard process, 6(2', j —> k,l), and the probability that we find partons
i and j in the proton and antiproton respectively, f,- (fj). With this, the matrix

element can be expressed as

Mi,j—>k,l = fi($i,Q2,MF)fj($j,Q2,l1F)&(iij —> kit) , (2-13)

where Q2 is the momentum transfer in the hard process, and up is the factorization
scale which defines the separation between interactions calculated as part of the hard
process and what gets absorbed into f, and fj. f, (f,) are called parton distribution
functions (PDFs) which tell us the probability that parton i (j) carrying proton

(antiproton) momentum fraction, at,- (5'37), will participate in the interaction.

Richard Feynman developed a method to calculate the scattering matrix ele-
ments, 6. Using his diagrams, be devised a set of rules with which to calculate the
hard scattering amplitude, 6. A full explanation of the Feynman calculus is beyond

the scope of this thesis. So we will point out just a few notable features and direct

19

 

 

 

the tea

o .1

0:1

0R

ar

‘ Ar

fer

 

 

——>
remnants

Figure 2.3: Factorization of the pp matrix element.

the reader to any one of the references, [18, 16, 17, 19, 20], for further enlightenment.

0 At each vertex, 4 momentum must be conserved. In Figure 2.4a,

pl’ = P‘a’ + q" and 195 = p: - 0" - (2-14)

0 At each vertex, a term proportional to g is included (9; DC a, for all vertices in

Figure 2.4).

o For each internal line, a term proportional to 1/(q2 — m2) is included, where q
is the 4 momentum of the propagator and m is its mass. The internal particles
are virtual particles and, therefore, q2 75 m2. Since the gluon is massless, the

propagator in Figure 2.4a is just 1/q2.

0 An integration over all undetermined internal momenta is performed (the

fermion loop momenta in Figure 2.4b).

20

figure

(01a?

5

2.5

 

In (‘altt‘
0\‘er lot

addillot
TOWS us

some lit
abSOtbit
”1100717.
01 energ,
Same 01).
ll] (30ml);

diSCuSSl-U

The

“here Q

 

 

V
1

\q

(a) q 0» as 3/5 :29
l \ /
p2 P4 792 194

013 as

Figure 2.4: Feynman diagrams for qg-—>qg via gluon exchange. (a) Lowest order
(0(af)) diagram. (b) 1 Loop (O(a§)) diagram

2.5 Renormalization and the Strong Coupling, as

In calculating the contributions from internal loops in Feynman diagrams, integrals
over loop momenta lead to divergences at very small momenta. To eliminate these,
additional parameters are introduced through a regularization procedure. This al-
lows us to write the divergent terms in some well-defined way (they still diverge in
some limit of the regularization parameters). The divergences are then removed by
absorbing them into the definitions of the physical quantites. Thereby, the theory is
renormalized. This has the side effect of introducing a new parameter, MR, with units
of energy. The exact renormalization procedure is arbitrary, but all must lead to the
same observables. Therefore, the renormalization scale, [13, plays an important role
in comparisons between theory and experiment. In this thesis, we will confine the

discussion to predictions using the modified minimum subtraction scheme [22], M S .

The running of the strong coupling constant, as, is determined by the renormal-

ization group equation,
6a,

2
Q 8622

 

= Mas) - (2.15)

where Q is the energy scale of the hard interaction. The 6 function expansion in

21

pow;

Win

(‘0

It

powers of a, is given by [20],
ma.) = 4263 (1 + b’a, + 0(a§)) , (2.16)

where b and b’ are defined as

 

33 — 2n;
b — T ,and
153 — 197i
b’ — f . 2.17
27r(33 — 2m) ( )

n; is equal to the number of quark flavors available at a given Q2.

Using only the leading order term in Equation 2.17, the dependence of the strong
coupling constant, a,, on the renormalization scale, ,u = #3, at a given 622 can be
written as

_ 030‘?) _ Q2
03(Q2) — W , t— 111-’72- . (2.18)

Including the next-to—leading order term, it is written as an implicit function,

1 1 7 03(Q2) I 03012) _
3.472) + 3.0.2) “T b T" 1 + vase?) ‘ b 1“ W ‘ b" “'19)

 

 

Equations 2.18 and 2.19 tell us how a, varies with a}; for a given Q2, but they
don’t tell us the absolute value. This must be measured by experiment. Once a, has
been measured at one value of Q2, it is determined for all Q2 values. Experimentally,
a, has been measured for Q2 values ranging from 1.5 GeV to 130 GeV. These different

values are compared by scaling each value to the mass of the Z 0. The current world

22

average

A sunn

measure

AHO‘

periljrh

EXPIQSS‘

 

 

Process Q (GeV) a,(Q2)

7' Decay 1.777 0.35 :l: 0.03
pp $731,ng MW 0.123 :1: 0.025
Quarkonium Decay 9.45 0.163 :t 0.014
e+e'—+ Hadrons 35 0.146 :L- 0.03
e+e‘Event Shapes 58 0.125 :1: 0.009

34 0.14 :l: 0.02
29 0.160 :1: 0.012
130 0.114 :1: 0.008
e+e‘Fragmentation 91.2 0.125 :1: 0.009
e‘p —> e‘+Jets 91.2 0.118 :1: 0.008
Lattice QCD 91.2 0.117 :1: 0.003

 

 

 

 

 

 

Table 2.5: Summary of a, measurements [15].

average is [15]

a,(Mz) = 0.119 :1: 0.002 . (2.20)
A summary of these measurements is shown in Table 2.5 and Figure 2.5. Our
measurement (if completed) would span values of Q2 from 100 to 900 GeV.

Another way of looking at this is to introduce a parameter, A, which represents
the energy scale at which the coupling diverges. This defines the boundary of the

perturbative domain and is defined by

Q_’__ °° £1
1" 12 “ (.1663th (2'21)

Expressed in terms of A, the leading order and next-to—leading order a, are

L0 013(6)?) = b—IL-
2 _ _1_ -5115
NLO a,(Q) _ bL (1 b L ), (2.22)

Figu
Sport
legit)

Wher

Caleu

flal'Ol

 

 

 

. 04
d _
0.35; 3 Region accessible i
: 5 using jet roles
C ot DO
O.3-
L
r
0.25L
p
I
0.2—
p
015*-
0.1—
005*—
L
0" L L 1444111 1 A 1 111111 A L 1 :LLALI

 

 

 

2 103
02 (GeV)

Figure 2.5: Graphical representation of the data from Table 2.5. The curve corre-
sponds to the next—to—leading order running of a,(Q2) setting a,(Mz) = 0.119. The
region accessible using jet rates at D0 is also shown.

where L = ln(Qz/Az). The value for a,(Mz) quoted above gives a value of [15]

N5) = 237i§gMeV , (2.23)

calculated at next-to—leading order ((5) denotes a theoretical calculation including 5

flavors of quarks).

24

Jt

Xex
We 1
U191
the

6Vet:

Chapter 3

Jet Production in pp Collisions

At the Fermilab Tevatron, protons collide with antiprotons at a center-of-mass en-
ergy, \/s = 1.8 TeV. Most often, these collisions result in sprays of highly energetic
particles (called jets). In this chapter, we will discuss the physics specific to jet

production in pp collisions.

We begin with a quick view of a typical event in pp collisions which produces jets.
Next, we define the variables used to define the kinematics of such events. Then,
we give a brief description of the Monte Carlo event generators we use to test our
methods and compare our results to theoretical predictions. Finally, we will discuss
the motivation behind the measurement of the ratio of events with 3 or more jets to

events with 2 or more jets, R32.

25

par
ant
pai‘.
intt

par

3H1}
ETPE

and

m PC

pTUr

3.1 pp Collisions

So far, we have considered only simple 2 -—> 2 particle reactions. What we actually
observe in proton antiproton collisions is much more complex. When a proton and
an antiproton collide at very high energies, their composite particles behave almost
independently of one another such that only two partons (one from the proton and
one from the antiproton) will most likely take part in the interaction. Two or more
partons emerge from the interaction along with the remnants of the proton and
antiproton. Immediately, these outgoing partons radiate gluons and/or produce
pairs of quarks and antiquarks in a shower of partons. Then, the partons recombine
into colorless composite particles (hadrons). The results of the collision are jets of

particles.

Let us consider an interaction where a quark from a proton interacts with a gluon
from an antiproton. The Feynman diagram for the interaction is shown in Figure 3.1.
Figures 3.2 and 3.3 depict the interaction at 3 different levels before and after the
collision respectively. Before the collision, we have a proton and antiproton at the
hadronic level (Figure 3.2a). If we look a little closer, we see that the proton and
antiproton are made up of a sea of quarks and gluons (Figure 3.2b). At the most
elemental level, two partons, a quark and a gluon, take part in the hard interaction

and the others do not participate (Figure 3.2c).

After the collision, two partons emerge from the hard process (Figure 3.3a). Im-
mediately, the quark and gluon begin to radiate gluons and quark-antiquark pairs

producing a shower of partons (Figure 3.3b). These partons fragment further, re-

26

 

Figure 3.1: Feynman diagram for qg —-) qg by gluon exchange.

a).

 

 

“d
V
11

"6|

 

 

b). -
’U. ‘ v17 ‘ a
d ~ ~ fi///% 1 gt
c).
u. = g

 

Figure 3.2: A quark from a proton interacts with a gluon from an antiproton (before).
(a) At the hadron level, a proton collides with an antiproton. (b) At the parton
shower level, a sea of quarks and gluons interact. (c) At the 2 —+ 2 parton level, a
quark interacts with a gluon.

27

combine and form jets of colorless hadrons (Figure 3.3c).

a). b). %

 

 

//

 

 

A
V

Figure 3.3: A quark from a proton interacts with a gluon from an antiproton (after).
(a) At the 2 -> 2 parton level, a quark and a gluon emerge. (b) At the parton
shower level, jets of quarks and gluons emerge. (c) At the hadron level, jets of
hadrons emerge.

Finally, these jets of hadrons deposit their energy in the detector. Shown in
Figure 3.4 is an event as seen by the DO detector. This is a side view of the detector
(the z axis is the horizontal axis) where the transverse components (perpendicular

to the z axis) are projected onto the vertical axis. The shaded regions depict energy

28

Fit
the

The
eDer
into,
drau

1.1005

deposition in the detector and we see two large clusters of energy emerging from an

interaction vertex. The DO detector will be described in the following chapter.

 

D0 Side View 11—JAN—1993 10:15 Run 57023 Event 2519] S—DEC—1992 03:16

 

Max ET 2 137.2
I1.<E< 2.
X K E] Mk 3.
I 3.<E< 4.
x . 4.<E< 5. x
x xx v I 5.<E
X

 

 

 

 

 

 

 

 

 

Figure 3.4: An event as seen by the DO detector. The 2 axis defines left to right;
the information has been averaged in (D.

3.2 pp Event Variables

The partons participating in the hard interaction do not have a fixed energy. Their
energy is some fraction of the proton or antiproton energy. This allows us to study
interactions which take place over a wide range of center of mass energies, x/E. One
drawback to this is that the center-of-mass (c.m.) frame is likely to be Lorentz

boosted with respect to the lab frame. We desire, therefore, to define the kinematics

29

in

W

t(

It

TE
a;

ti

11

H.

in terms that are invariant under longitudinal Lorentz boosts.

We define the z-axis to lie along the proton-antiproton beams (the axis of the
Lorentz boost). Under these conditions, for a given momentum vector, the azimuthal
angle, 05, and the component of momentum in the x-y plane, PT = W, are
both boost invariant. In addition, we define a rapidity, y, which is also boost invariant

(except for an additive factor):

 

Wt)

where E is the energy and Pz is the longitudinal component of the vector momentum.
For massless 4 vectors, this reduces to the so called pseudorapidity, 77, which is related
to polar angle, 0, by

n = — In (tan g) . (3,2)

In pp collisions, the jets of particles are produced at high energies (P >> M) and,
therefore, the pseudorapidity is approximately equal to real rapidity, 77 z y. Because
77 is defined by the polar angle, 0, it is much more easily measured than the real
rapidity, y. Hence, the kinematic variables used are transverse momentum, PT, the
azimuthal angle, (,0, and pseudorapidity, 7]. For historical reasons, we often refer to

the transverse momentum, PT as “ET ”.

3.3 Monte Carlo Event Generators

We will describe two types of Monte Carlo event generators. The Jetrad [23] and

Herwig [24, 25] event generators provide good examples of both types and are the

30

[E

h

most frequently used in jet physics at D0.

As the parton shower develops, the available energy gets dispersed among the
partons. This causes the strong coupling to strengthen ((1, increases) and the radia-
tion becomes soft and/ or collinear. Perturbation theory requires the coupling to be
small and, therefore, at a certain point, the shower development cannot be calculated

analytically.

At present, the matrix element for p13 collisions can be calculated exactly to
C(03). The J etrad [23] Monte Carlo is one such event generator. It includes tree level
Feynman diagrams with 2 and 3 final state partons (no loops) and the interference
terms between the 2 parton final state diagrams with and without an internal loop.
An example of contributing Feynman diagrams is shown in Figure 3.5. The Jetrad

event generator includes at most 3 final state partons (evolution to hadrons is not

modeled) .

It is also possible to rearrange the terms in the calculation so that soft/collinear
radiation terms are resummed and included in the matrix element. This calculation,
however, breaks down when the radiation is hard and produced at large angles.
Thus, it is not possible to combine the two techniques into one calculation that
would cover the full range of hard and soft parton splitting. The Herwig Monte
Carlo event generator uses a resummation calculation evolved from a 2 ——) 2 matrix

element to predict the parton shower.

In addition to this, the process where partons recombine to form colorless hadrons
(called hadronization) is not well understood. It is approximated using a fragmen-

tation function which gives the probability of finding a given hadron with some

31

FiSure
MOrlte
Slate pa
diaglam
is negle<

 

I>r~v<vli M +>m
. |>w<+ (a2)
. 2n. >~m2<| l>m<l (a2)

+ (a3)

+ Not Included (a?)

 

 

Figure 3.5: An example of 0(a3) Feynman diagram contributions in the Jetrad
Monte Carlo event generator. 'Iree level Feynman diagrams with 2 and 3 final
state partons are included. The interference term between the 2 parton final state
diagrams with and without an internal loop is included too. The last term (C(03))
is neglected.

32

frarth
experi

the de

 

3.4

Given
0f the
1935 th
part0;
thrOug
Dang,
There
Splitti
felted
SF’litti
and, t

fraction of the overall momentum. Various models are used which are tuned using
experimental data and then, incorporated into Monte Carlo event generators. For

the details regarding the Herwig event generator, the reader is directed to [24, 25].

3.4 Jets

Given that energy and momentum must be conserved, we can infer the kinematics
of the partonic interaction by measuring jet properties. Defining jets, however, is
less than straightforward. At the simple 2 —> 2 parton level, there are two energetic
partons well separated in d), and there is little ambiguity even as the jet evolves
through parton showering and hadronization. At 0(a3), there can be 3 final state
partons. Recall that the calculation breaks down for soft and /or collinear radiation.
Therefore, jets must be defined in such a way so that they will be insensitive to these
splittings. Quantities which are insensitive to soft/collinear radiation are often re-
ferred to as infrared safe quantities. An ideal jet algorithm recombines soft /collinear
splittings. The specific jet definition determines which splittings are recombined,
and, therefore, the theoretical calculation for a given cross section depends on the
choice of jet definition. In Chapter 5, we will discuss two jet algorithms employed at

DQ: the fixed cone and kl algorithms.

33

l
I!

Wht'
Chal

pr Ol

At ]

PTO}

of E
for ,
0f ti
89m

isr.

3.5 R32

At lowest order, the hard scattering cross section for events with 3 final state partons

(jets), 020, is proportional to of,

020(Q2,u, J) = 03(Q2,#)C3(Q2, J) , (3-3)

where a, is given by Equation 2.18 and C3 is constant for a given momentum ex-
change, Q2, and jet definition, J. Likewise, the lowest order 2 jet cross section is

proportional to of,

0io(Q2,#, J) = 03(Q2,M)Bz(Q2, J) ~ (3-4)

At lowest order, therefore, the ratio of cross sections for 3 and 2 jet events, R32 is
proportional to as,
0'20 __ 03(Q2: J)

0 _
R342 — 0&0 " 82(Q2,J)a3(Q2’u) ' (35)

This makes it possible to extract a value of a, from an experimental measurement
of R32 given the constant terms, C3 and .82. At this time, the theoretical calculation
for R32 is not available at anything other than leading order. It is only a matter
of time before theorists will be able to calculate next-to—leading order 3 jet cross
section, and we can begin to speculate as to the method of extraction based on what

is available for the next-to—leading order 2 jet cross section calculation.

At next to lowest order, we can define an inclusive cross section for 2 jets (events

34

 

Cl

\l'
[(1]

UN

where there are 2 or more final state partons). The matrix element is given by

ofiio(Q2, u) = ai<Q2, u)Bz(Q2, J) + am 1084622, M, J) (3.6)

where the coefficient for the a? term, B3, has a dependency on u given by

2

Baez, u) = B2(Q2, J) In (7) + 83(622, J) . (3.7)

In the next to lowest order case, a, is given by Equation 2.19. The 3 jet inclusive
cross section calculation is not available at this time to next to lowest order. However,

we expect it to take a similar form,

aiiowz, u) = aw, mower, J) + 03(622, u)C4(Q2, Li, J) (3.8)

where 0.; is given by

C4(Q2,u) = 03(Q2, J) 111 (ii-2') + 02(Q2, J) ~ (3-9)

Here, the ratio of 3 to 2 jet events will be given by

Részo _ 613(sz J) + 03(Q2, H)C4(Q2,l1, J)

 

‘ 82(02, J) + aa(Q2,u)Ba(Q2,u, J) ‘1’“) ”0 ' (3‘10)

When the next-to—leading order calculation becomes available for 3 final state par-
tons (i.e. C4 is calculated), we will be able to extract a,I from the experimental

measurement of R32 using the above equation.

The extraction of a, is extremely sensitive to the choice of renormalization scale,

35

 

HR-
fixit;

prod.

order
and I
domi:

“R? a:

50 lbs

The (
Spa“)
Stand.

the th)

 

#R- As the calculations become available to higher and higher orders, the sensi-
tivity to the renormalization scale lessens and it is possible to get a more accurate

prediction.

The measurements of as shown in Table 2 .5 are extracted using varieties of leading
order (LO), next-to—leading order (NLO), next-to—next—to-leading order (NNLO),
and resummation calculations. Almost all of the errors quoted there are totally
dominated by theoretical uncertainties due to the choice of renormalization scale,
#3, and we expect the same will be true for a measurement using jet rates at D0.
So the necessity and / or usefulness of such a measurement may come into question.
The extraction of a, from a measurement of R32 at D0 probes regions of phase
space previously unavailable. And because a, is a fundamental parameter of the
Standard Model theory, such a measurement will become useful in the future when

the theoretical uncertainties are better understood.

36

Chapter 4

The Tevatron and The DQ

Detector

The DQ collider experiment is located at the Fermi National Accelerator Laboratory.
Protons and antiprotons collide at a center of mass energy of 1.8 TeV. At this time,
the Fermilab Tevatron produces the highest energy particles in the world (excluding
cosmic rays). We present here a description of the Fermilab Tevatron Collider and

the various components of the DE detector.

4.1 The Fermilab Tevatron Collider

Protons are accelerated to 900 GeV in 5 stages:

1. Hydrogen (H ‘) ions are created with 750 KeV.
2. The H ’ ions are accelerated to 400 MeV and the electrons are stripped off.

3. The protons are accelerated in the Booster ring to 8 GeV.

37

 

The '1

 

 

111

KEY (

an 91.91

Ne
made

SO Illa

4. The protons are accelerated in the Main ring to 150 GeV.

5. Finally, the protons accelerate in the Tevatron to 900 GeV.

The components involved in these 5 stages are shown in Figure 4.1

 

   

   

PBar Linac
Debuncher Pr eA cc
Boo to
Bar ‘ s r
Accurn Tevatron Extraction
for Fixed Target Experiments
1 A
\V ' fir
PBar Injection 7 MR 9 I 'ecti
:0 °" Tevatron
PBnr
Target A
T vat.
”RF" CDF
F0

Main RingRF

DO detector

Figure 4.1: Overview of the Fermilab Tevatron.

In the first stage, electrons are added to hydrogen atoms with an energy of 750
KeV (30 times the energy of electrons in a television picture tube). This is done in

an electrostatic generator called a Cockcroft- Walton.

Next, these negatively charged ions are introduced into a linear accelerator (LIN AC)
made up of drift tubes with an oscillating electric field. The oscillations are timed

so that the ions are accelerated in bunches by a positive potential. The negative po-

38

mm
the r
the i

Ollil

are a(
The l

an en

N6.

 

feet
COHSls
ll]? p}

1.30 c

D1
3 targ

in the.

tential occurs after the ions are free of the cavity. As the ions traverse the LINAC,
the tubes become progressively longer to accommodate the increase in the speed of
the ions. As they exit the LINAC, the ions pass through a carbon foil which strips

off their electrons resulting in a beam of protons.

The protons enter an accelerator ring called the Booster. The Booster is a 500
foot diameter synchrotron which consists of resonant frequency (RF) cavities and
magnets which bend the path of the bunches of protons into a circle. As the protons
are accelerated, the electromagnetic field increases to match the speed of the bunches.
The protons cycle around the Booster roughly 20,000 times before they leave with

an energy of 8 GeV.

Next, they enter what is known as the Main ring. The Main ring is buried 20
feet below ground surface in a 10 foot wide tunnel. It is 2 km in diameter and
consists of 1000 quadropole and dipole copper coiled magnets which focus and bend
the protons in the main ring. Here, the protons are accelerated up to an energy of

150 GeV before they are dropped down into the Tevatron for the final stage.

During the Main ring stage, some of the protons are syphoned off and focused onto
a target (typically nickel). Antiprotons (among many other particles) are produced
in these collisions. The antiprotons are selected and directed to a Debuncher ring.
The Debuncher ring is positioned in a separate tunnel and is shaped in a triangular
ring of 500 feet per side. In the Debuncher ring, bunches of antiprotons are collected
and “cooled” to within a small range of momenta and then they are stored in the
accumulator ring directly below the Debuncher ring in the same tunnel. Once a

reasonable store has been accumulated, the antiprotons are released into the Main

39

ring

they

is in
GeV
Cireul
magi:
Duriz.
Opera
intem

intera

4.2

 

The D
interac
detectC
0f Obsg

delf‘th

.ll

‘tl

.ll

ring where they will be accelerated in opposite direction to the protons. Finally,

they too are diverted down to the Tevatron for the final stage of acceleration.

The Tevatron synchrotron is positioned in the same tunnel as the Main ring. It
is in this stage that the protons and antiprotons reach their maximum energy of 900
GeV. In order to produce a magnetic field large enough to bend the beams into a
circular path at this energy, superconducting magnets are used. The superconducting
magnets are kept cooled to a temperature of -450 degrees Fahrenheit by liquid helium.
During the data taking run (1b) on which this thesis is based, the collider was
Operated with 6 bunches of protons and antiprotons (each) in the Tevatron. At two
interaction points, BQ and D0, the proton and antiproton beams collide. At either

interaction point, the time between bunch crossings was 3.5psec.

4.2 The D0 Detector

The DQ experiment is so named because the detector is positioned around the D0
interaction point in the Tevatron ring. The DQ detector is a multipurpose collider
detector. It is a multifaceted piece of apparatus designed to measure a wide variety
of observables. A cut away view of the D9 detector is shown in Figure 4.2. The

detector is made up of 4 subsystems:

o the Level Zero detector,

0 the Tracking system,

c the Calorimeter, and

40

 

The
wher.
first
New. ,
If it L
and i
detect.

the m

 

in the
and n

brieH}

4.2.1

TheL
a bun
Vertex
In re;

about

T1

the; b!

o the Muon detector.

The Level Zero detector determines whether or not an inelastic collision took place
when the proton and antiproton beams cross. A particle produced in a collision will
first pass through the Tracking system. If it is charged, its path will be detected.
Next, it will encounter the Calorimeter where it will most likely deposit its energy.
If it is a muon, however, it is unlikely to interact with the material in the calorimeter
and it will pass through the calorimeter and its path can be traced in the Muon
detector. A magnet bends the path of the muon, and from the curvature of its path,

the muon’s momentum can be inferred.

This thesis is mainly concerned with jets of hadrons which deposit their energy
in the calorimeter. Therefore, we will give only a brief description of the tracking
and muon systems and concentrate our discussion on the calorimeter. We will also

briefly discuss triggering and data taking.

4.2.1 The Level Zero Detector

The Level Zero Detector is used to determine if an inelastic collision took place during
a bunch crossing. It also provides a rough estimate of the position of the interaction
vertex. Ideally, the vertex would always occur at the center of the detector (2 = 0.0).
In reality, however, the vertex position is described by a gaussian with a width of

about 25 cm and an offset of 8 cm from the center.

The Level Zero detector consists of two scintillator based hodoscopes surrounding

the beampipe on either side of the interaction region. The hodoscopes detect charged

41

 

Muon Chambers .

4r

    
   

  
      

~\‘~ /1=/ g. \
ll

,\\_\ "Li/1’2"", I"

)3"
‘\
\

 

 

 

 

 

\.
ht

. I \P ‘ ‘
‘ C ‘
Calorimeters Tracking Chambers

Figure 4.2: Cutaway view of the D0 detector.

 

 

 

 

 

 

42

particles. When a collision takes place, the remnants of the proton and antiproton
shower close to the beamline. By taking the difference in the times that the two
hodoscopes detect particles, the interaction point can be inferred.

4.2.2 The Tracking System
The tracking system consists of 3 separate detectors:
0 a vertex detector (VTX),

o a transition radiation detector (TRD), and

0 central and forward (in pseudorapidity) drift chambers (CDC and FDC).

A side view of these detectors is shown in Figure 4.3.

e e

Central Drift Vertex Drift Transition Forward Drift

Chamber Chamber Radium Chamber
Detector

 

 

 

Ffis;

 

 

 

 

 

 

Mag.

 

 

 

L

 

 

—
_—

 

 

 

 

 

 

 

 

 

Figure 4.3: The four detectors which comprise the tracking system.

43

sure:
\T.‘
ers (
thrc
can
p05

l'f'a

Wh
me

to

ha

It

Innermost is the vertex detector (VTX) which gives a much more precise mea-
surement of the interaction point than is determined by the Level Zero detector. The
VTX has an inner radius of 3.7 cm and an outer radius of 16.2 cm. It contains 3 lay-
ers of wire chambers filled with C02(95%)-ethane(5%). As a charged particle passes
through the chamber, it ionizes the gas and a potential difference in the chamber
cause the electrons to collect on the wire and a signal is read out at both ends. The
position of the wires provide a measure of the r — 45 coordinate and the timing of the

readout gives the position along the beamline (.2) using charge division.

In the transition radiation detector (T RD), charged particles radiate photons
when passing between regions of different dielectric constants and these photons are
measured in X—ray detectors. The energy of the photons is inversely proportional
to the mass of the particle. This allows us to differentiate between electrons and
hadrons. The TRD consists of 3 layers of 393 polypropylene radiator foils and a

layer of X-ray detectors.

Just inside the Calorimeter, lie the central and forward drift chambers (CDC and

FDC). These operate on the same principle as the VTX.

4.2.3 The Calorimeter

The DC calorimeter (Figure 4.4) is a uranium liquid argon sampling calorimeter. It
provides exemplary coverage around the interaction region with fine segmentation.

It was designed for ease of calibration with linear, compensating response to energy.

44

mi LIQUID ARGON CALORIMETER

it,
it

      
   
 
  
 

 
   

END CALORIMETER \\\\\\\\\\\\
cm H a ' h‘ \\\\\\\\
l h 1 7 7 \

(Fine & Coarse)

CENTRAL
CALORIMETER

Electromagnetic

Inner Hadronic Fine Hadronic

(Fine & Coarse) Coarse Hadronic

Electromagnetic

Figure 4.4: Cutaway view of the D0 calorimeter detector.

Particles entering the calorimeter interact with depleted uranium producing a
shower of particles. These secondary particles ionize the liquid argon and a signal
is produced on a copper readout pad. A schematic diagram of a unit cell is shown
in Figure 4.5. The absorber plates are kept at ground and a readout board with a
resistive surface is kept at 2000 V. The electron drift time across the liquid argon
gap is 450 nsec. The signal is measured by a preamplifier and is then sent to a base
line subtractor (BLS) for analog shaping. At this point, the signal is split. One is
sent to the trigger framework and the other is sent to analog-to—digital converters
(ADCs) where it is translated into energy. If the energy in the cell is within 20 of
the pedestal value, it is not read out. This zero suppression significantly reduces the
number of cells read out. Otherwise, the pedestal value is subtracted and the energy
read out. The pedestal value is the average background energy measured during a
calibration run and o is the width of the distribution.

45

 

ter

tm

in

firu

the

fro;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[ Absorber Plate Pad Resistive Coat Liquid Argon \
N 010 Insulator J] Gap
7 ’- V _ _
// fl /
/A __ //2 __
I i
K H Unit Cell ‘6 j

 

 

Figure 4.5: Schematic view of a liquid argon readout cell.

The D0 calorimeter is separated into 3 cryostats containing 3 separate calorime-

ters. One covers the central pseudorapidity region (CC

V

, Inde‘I < 1.2, and the other
two cover the forward rapidity regions in the north and south respectively (EC),
1.5 < |17M| < 4.5. The calorimeter is also segmented longitudinally into 3 sections
in order of increasing distance from the interaction region: electromagnetic (EM),

fine hadronic (FH) and coarse hadronic (CH).

The EM section is comprised of 4 layers of cells with 3 mm thick uranium plates in
the CC and 4 mm plates in the EC. The thickness of the layers increases going away
from the interaction with 2, 2, 7 and 10 radiation lengths (X0). The 1st, 2nd and
4th layers are segmented in r] x ¢ by 0.1 x 0.1. The 3rd layer is where the maximum
shower deposition occurs for an electromagnetic object (i.e. electron or photon) and
has a finer segmentation of 0.05 x 0.05. A quadrant of the D0 calorimeter is shown

46

in l7

Th

lll l-llQ

 

lai’i’rs .

Thr
EC. '11
"‘“he i1

Tin
”If! Will
Was Si‘r
2” GM

”Milli

in Figure 4.6.

00 0.2 0,4 0.6 0.8 1.0

 

Figure 4.6: One quadrant of the. D0) calorimeter.

The Fll uses 6 nnn nranium-niol)ium(2"0) plates and is comprised of 3 cell layers
in the CC and 4 layers in the EC. lts total depth is about 5 interaction lengths. All

layers are segmented in 0.1 x 0.1 in 1] x «15.

The Cll uses 40.5 nnn copper plates in the CC and stainless steel plates in the
EC. This amounts to 4 interaction lengths and only the mosl. energetic particles

make it through the outer wall of the cryostats.

The calorimeter modules were. calibrated during test beam runs where sections of
the calorimeter were exposed to particles with known energy. The response to energy
was seen to be linear to within 0.5% for electrons above 10 GeV and for pions above
20 GeV. The ratio of these, e/1r, is remarkably close to unity (less than 1.05). The
energy resolution was found to be l5%/\/E and 50‘%./\/l_5 for electrons and pions

47

on

O

Olfmbmm a M

resr

The

 

 

 

Part
littl

the

end
git

ste

C0

bu

respectively.

The Inter Cryostat Region

Particles entering the area between the CC and EC cryostats may encounter very
little of the calorimetry. Two systems are placed in this region to mend this situation:

the massless gap and the inner cryostat (ICD) detectors.

The massless gap detectors are made up of signal boards placed on the steel
endplates of the calorimeters inside the cryostats. Alternating boards are set at
ground and high voltage. They detect showering in the liquid argon between the

steel endplates and the cryostat walls.

The ICD detector is positioned on the outside of the end cryostats. They are
comprised of scintillating tiles (0.1 x 0.1 in 1) x 45) and signals are read out through

bundles of wave shifting fiber.

4.2.4 The Muon Spectrometer

The Muon detector is divided into two subsystems with a total of 5 toroidal magnets.
The wide angle muon system (WAMUS) covers the central rapidity region and the
small angle muon system (SAMUS) covers the forward region. Both systems consist
of 3 layers of proportional drift tubes (PDTs). The first layer lies inside the toroids
and together with the tracking detectors, the incident path of a muon can be mea-
sured. After the muon’s path is bent by the toroid, the deflection can be measured

in the 2nd and 3rd layer PDTs and the momentum of the muon inferred.

48

def

As i
are

Jeri.

Whe

 

 

 

leve

C0115

The muon system is also used as a loose veto when a cosmic ray muon enters the

detector during data taking.

4.2.5 The D0 Trigger System

As stated in Section 4.1, mi bunch crossings occur every 3.5,usec. Most interactions
are of little interest because they generally produce low transverse momentum ob-
jects. The DC trigger system filters the events by making quick decisions about
whether or not a given event is of interest. There are four levels of decision making:
level 0, 1, 1.5, and 2. Each subsequent level is more discriminating yet more time
consuming. The first three level decisions are hardware triggers and the fourth, level

2, is a software trigger. A block diagram of these four levels is shown in Figure 4.7.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Processing 11m 132ns 900ns 10-20 as 100-200ms
From the Level Level 200 Hz Level Tape
Detector —> 0 > 1 2 —>
Level
Rate 300kHz 50kHz 10 kHz 15 100 Hz 1-2 Hz

 

 

 

Figure 4.7: Block diagram of the D0 trigger system.

Level C

The level 0 trigger is the least discriminating. It simply looks for the break up of
the proton and antiproton in the Level Zero detector. It’s efficiency is >98%. It
also provides information regarding multiple interactions occurring in a single bunch

crossing and it measures the instantaneous luminosity.

49

Level 1 and Level 1.5

The level 1 trigger is divided into two components: muon and calorimeter. The
muon trigger simply triggers on the number of muon tracks. If an event passes the
level 1 muon trigger, a level 1.5 decision is made based on the transverse momentum

of the muon. This creates a detector deadtime of one bunch crossing.

The calorimeter level 1 trigger makes fast sums of energy in towers in the calorime-
ter of 0.2 x 0.2 in n x 4). Several different reference sets are used to define energy cuts
on the trigger towers in various sections of the calorimeter. There are also reference
sets for energy summed in large groups of trigger towers. These are called large tiles

and cover regions of 0.8 x 1.6 in n x o.

After an event passes levels 1 and/or 1.5, it is passed to the level 2 system.

Level 2

The level 2 system is a farm of 50 VAXstation 4000/60 processors running identical
executables which attempt to reconstruct each event. If the event is deemed worthy
by the level 2 software, the detector information and run conditions are written to a

disk buffer and eventually transferred to tape.

4.2.6 Offline Reconstruction

The raw data on tape is taken to another facility at Fermilab for processing. A
large software package has been developed which reconstructs the data (RECO).

The RECO software uses calibration information obtained from test beam data and

50

 

 

(lat

art'-

tt'iti

 

various algorithms to piece together physical objects such as photons, electrons, jets,
muons, etc, from the raw detector data. Jets are reconstructed using the fixed cone
jet finding algorithm. It; jets must be reconstructed in a separate package after the
data has been processed through RECO. The kl and fixed cone jet finding algorithms
are described in Chapter 5. All of the data used in this thesis used data reconstructed

with version 12 of the reconstruction software (RECO v12).

51

 

 

 

 

9m I.)

A .

 

 

Chapter 5

The k_l_ and Cone Jet Algorithms

In Chapter 3, we discussed jet production in mi collisions. We showed an event
display in which two jets of hadrons deposited their energy in the DO detector
(Figure 3.4). Shown in Figure 5.1 is the same event displayed in a 3 dimensional lego
plot. The a: and y axes represent 17 and 45 coordinates shown in units of calorimeter
towers, IETA and IPHI (a calorimeter tower equals 0.1 x 0.1 in n x (b). The vertical
axis shows the amount of energy deposited in the towers and we see two large clusters

of energy in the central part of the region along with some smaller clusters at large

absolute values of IETA.

In order to relate these clusters of energy to a simple partonic interaction, we
employ jet algorithms to reconstruct the parton momenta from the energy deposited
in the calorimeter. We present here two jet finding algorithms used to analyze
DO data: the fixed cone and the [Cl jet algorithms. Compared to the fixed cone
algorithm, the kj algorithm is more amenable to jet counting, and, therefore, we

use It; jets to measure R32. The fixed cone algorithm was established prior to the

52

 

LEGO car. cup mom-1993 10:23pm 57023 Event 25191543201992 03:15

 

Max ET I 137.2 GOV

[ms
QHADE

MhE=1.GeV

 

ENERGY CAEP ETA-PHI

 

 

 

Figure 5.1: Lego plot of a 2 jet event as seen by the DO detector. The a: and y axes
represent 1) and ()5 coordinates shown in units of calorimeter towers, IETA and IPHI
(a calorimeter tower equals 0.1 x 0.1 in 17 x 45). The vertical axis shows the amount
of energy deposited in the towers.

53

Tht

 

fixe

ofa

Wht:
a 4.

int

kl algorithm, however, and much of our work calibrating the k; jet algorithm is
based on results obtained previously for cone jets. So we will begin our discussion
with a brief description of the cone jet finding algorithm. The focus of this thesis is
the implementation and calibration of the kj jet algorithm. So we will give a more

detailed account of the Is; jet algorithm.

5.1 The Fixed Cone Jet Algorithm

The fixed cone algorithm defines a jet by the sum of the 4—momenta contained in a
fixed cone of radius, R, in n—qfi space (see Figure 5.2). In other words, the 4-momenta

of all particles with AR < R are included,

 

AR.- = t/(m — 7].-)2 + (cm - a)? < R. (5.1)

where m and (15} is define the center of the jet cone and n,- and a5,- give the position of
a 4-vector inside the cone. Cone jets are found using an iterative procedure at DC

in the following way [36].

 

Figure 5.2: Fixed cone jet.

54

1. One starts with a list of 4-momenta describing partons, hadrons, or energy

deposited in a detector.
2. A reasonably high PT particle is chosen as a beginning (called a seed).
3. A cone of radius R in 17 -— <15 is drawn around the seed axis.

4. A new jet axis is found defined by the PT weighted 77 and (b of the particles in
the cone,
2;; mph

n=————— and oi:

Z?=1¢iPTi
ET '

a am

where ET is defined as the scalar sum of the PT of the particles inside the cone,

fi=iap (m)

i=1

5. Steps 3 and 4 are repeated (substituting the new jet axis for the seed axis)

until a stable jet axis is found.

6. The n, and (b of the jet are redefined by

n = — ln (tan (3)) and ¢ = tan‘1 (5%) , (5-4)

where

aum%%),m=23,mia=zgp (m)
i=1 i=1

Infrequently, two jets may be found with cones that overlap. In such cases, a
split/merge criterion must be applied to decide if the jets should be merged into one

jet or divided into two jets. At DC the jets are merged if the shared energy is less

55

 

than 50% of the ET of the lower ET jet. Otherwise, the shared energy is divided

between the two jets and their ET 77, and qfi are recalculated as in step 6.

It was mentioned in Chapter 3 that at present, the matrix element is calculated
to C(02) only. In such calculations (e.g. Jetrad Monte Carlo events), there can be
at most 2 partons produced, and at most, 2 partons can be included in a jet. In
such cases, it is possible that the two partons are separated by some distance, r, in
1) — 45 space such that R < r < 2R. Using the iterative method described above,
the two partons will not be combined into a single jet. After parton showering and
hadronization, however, it is possible that they will be merged into a single jet. We
introduce an additional parameter, Rsep. Then, we combine the two partons if they
are within Rm, x R of one another (typically Rsep ~ 1.2 — 1.3). The Rm parameter

is tuned to match what is seen experimentally in the splitting and merging of jets.

The prescription where the jet axis is defined by the PT weighted center and
the jet ET is defined by scalar summed PT (step 4) is known as the Snowmass
recombination scheme. It was agreed upon as the standard recombination scheme
for fixed cone jets during the Summer Study on High Energy Physics in Snowmass,
Colorado, in 1990. The final jet 7] and 45 definitions (step 6) were found to give
better agreement between Herwig Monte Carlo jets at the parton shower, hadron,
and detector levels and are therefore used in the DO implementation of the fixed

cone algorithm.

56

 

 

 

 

Figure 5.3: ki jet clustering.

57

ll

('0.

 

in

5.2 Clustering Algorithms for e+e‘Collisions

Unlike the cone jet finding algorithm described above, clustering algorithms begin by
considering individual pairs of particles. We start with a list of 4-vectors describing
partons, hadrons or detector information. The pairs of particles are evaluated based
on some closeness criterion in phase space and the closest pair is merged into a
single 4—vector. The merged particle is compared to all the other particles and the
process is repeated until some stopping criteria has been satisfied. This is illustrated

in Figure 5.3 and the basic steps in e+e“clustering algorithms are as follows.

1. For each pair of particles, 2' and j, we calculate some closeness function, y,,-.
2. The minimum ymm of all yij is found.
3. ymin is compared to some parameter, gm.

4. If gm,“ < you, particles 2' and j are removed from the list of 4-vectors and
merged into a new pseudo particle, k. ykj is calculated for all other particles

and we return to step 2.

5. If ymin > you, then clustering stops and we are left with a list of jets.

The first of such algorithms was introduced by the JADE collaboration [37, 38].

In this algorithm, the closeness function is the scaled invariant mass,

M,-,-2
2
Evis

 

ycut > M3” =

58

where Em is the visible energy of the event. The pair mass is calculated for massless

particles as

Mi]? 33- 2EiEj (1 - COS 6,1) (5.7)
where 9,5 is the angular separation. This can result in “fake” jets when many soft
particles belonging to unrelated parton showers are combined. This is illustrated in
Figure 5.4a where clustering begins by combining 4—vectors, 1 and 2, resulting in

4-vector, a. Since the algorithm is sensitive to soft radiation, it is not infrared safe

(as was discussed in Chapter 3).

>0:
M

 
 

(a) - - -’ a (b)

 

 

 

I
I
I
l
l
I
I

I

I

I
V
b

Figure 5.4: Jet Clustering in e+e‘Collisions. (a) The JADE algorithm. (b) The k_L

(or Durham) algorithm.

59

 

 

 

 

\V

in

3l

 

Later, the hi (or Durham) algorithm was proposed with the argument that it has
more of a tendency to be infrared and collinear safe and is less subject to hadroniza-
tion corrections[39]. It was noticed that by simply replacing EiEJ‘ in the invariant
mass equation (5.7) by min(E§,EJZ), the problem would be solved. Soft particles
would be merged with their nearest energetic neighbor instead of with other soft
particles. This is illustrated in Figure 5.4b where 4—vectors, 3 and 5, are combined
into 4-vector, b. For small angular separation, it can be shown that the new function

approximates the minimum relative transverse momentum,

kid]? 1‘ min (E32, Ej2)sin 2O

E 2min (E32, E12) (1 — COS 6,1) , for 9,5 —) 0. (5.8)

Thus, it was dubbed the hi algorithm with kl as the new closeness parameter.

5.3 Adaptation of the kl Algorithm for pp Collisions

The event structure in pp collisions differs from e+e‘ collisions and this results in
some modification of the kl jet definition. The variables used to assign particles
(final state partons, hadrons or calorimeter cells) to jets in e+e’ physics are the
energies, E, and the polar and azimuthal angles, 0 and gt. In pp collisions, the cm.
frame of the hard process is often moving with respect to the lab frame. Thus, the

variables used must be boost invariant along the beam axis, ET 2 PT, 17 and d).

k 1 can be expressed in terms of boost invariant quantities in the following way

60

 

ll

ill

be

prt

 

 

 

ha
sta
inc
Sht'

jet.

ant

SCa

for pairs of massless particles:

k1,:‘j2 '5 2 min (Eng, ET,j2) [0051] (Hi — 771‘) “ (303015 — 453)] - (5-9)
As A17, Art ——> 0, it can be expressed as

kid]? E min (ETJ'2, E7132) R2 (5.10)

ij’

where Rf]- : A772 + A452.

In e+e‘ collisions, essentially all of the hadrons in the final state are thought to
be associated with final state partons in the hard scattering process. In collisions
producing high ET jets, all particles should be assigned to a jet. The final state
hadrons in pp collisions, on the other hand, are associated not only with the final
state partons in the hard scattering process, but with radiation from partons in the
incident pp pair as well as the remnants of the pp . Therefore, not all the particles
should be assigned to the high ET jets, but many may be associated with the beam

jets (pp remnants).

In addition to this, the c.m. energy of the hard process (defined as \/§) is variable
and unknown. In the Durham algorithm described above, the closeness function is
scaled by visible energy in the event,

y” _ k1 ij
1] — a
Evis

 

(5.11)

and the stopping parameter, ywt, is dimensionless. Since Em, (J5) is not known in

pp collisions, we must provide an alternative prescription for stopping the clustering.

61

A few different modifications have been suggested to adapt the Durham algorithm
for use in pp collisions [41, 40]. The 1:; algorithm we have implemented at DC is
based on the algorithm suggested by Ellis and Soper in [41]. Below we describe the

k_L algorithm we have implemented at DC.

5.4 k_[_ Jets at DC

Before jets are reconstructed, a preclustering of calorimeter cells is performed [42].
The kl algorithm is an 0(n3) algorithm (i.e. for n particles, ~ n3 calculations must
be performed) and it is desirable to reduce the ~6000 calorimeter cells in an average
event without severely affecting the physics results. In preclustering, calorimeter cells
are first added into towers in the calorimeter. Towers with ET <0.2 GeV have their
ET redistributed in neighboring towers. The amount of ET added to neighboring
tower ET is weighted by the neighboring tower ET . Then, all towers within 0.2 of
each other in n — qi space are combined. The ET redistribution and tower merging is
done using scalar ET addition (subtraction in the case of negative ET ). In order to
have a consistent comparison to jets at the parton and hadron level, we also perform
the preclustering prior to jet reconstruction of partons and hadrons. There, parton

and hadron 4 vector information takes the place of the calorimeter towers.

After the preclustering is performed, we apply a jet reconstruction algorithm.
The jet algorithm we employ does not use a cutoff parameter, ya“. Instead, particles

are combined until all objects are separated n — (1) space by some value

Ru? > D2. (5.12)

62

 

where z' and j are jets constructed by successively combining particles. The kl jet

recombination procedure is as follows.

1. For each pair of particles (preclusters), z' and j, we calculate the function

a)?

m,- = minimum (Em-2, Em?) 732— (5.13)
where D = 1. Then we define for each particle, 2',
di = ETJ'2. (5.14)

2. The minimum dmin of all the d,- and d,,- is found.

3. If dun-n is a d,,-, particles 1' and j are merged into a new, pseudo-particle It: with

ET,k=PT,k: P2,k+P1ik’

1:

_ P,
77,, = —ln (tan 9f), and d1), = tan 1%,
with four vector Pl," 2 R” + Pj“, and 0,, = cos‘1 5335. (5.15)

kal

4. If dmin is a d, (i.e. 12,,-2 > D2 for all j ), then the particle is deemed not
”mergeable” and it is removed from the list of particles and placed in the list

of jets.

5. Return to step 1. Repeat steps 1-5 until all particles have been merged into

jets (i.e. joz > D2 for all ij ). The result is a list ofjets.

It is possible to employ alternate recombination schemes in step 3. We have derived

an energy scale only for the 4-vector recombination scheme described here.

63

 

The 4-vector recombination scheme, P1,“ = P,“+Pj", is the natural choice because
it is consistent with 4-momentum conservation. As a jet evolves from a simple
partonic interaction in the hard process to a shower of particles in the detector, its
4-momentum must be conserved. It is, therefore, most appropriate to reconstruct a
jet’s momentum and energy by summing the 4-momenta of the constituents of the jet.
Defining ET 2 PT (versus E sin0 or the scalar sum of ET of the constituents) was
decided upon because the definition of transverse energy is somewhat ambiguous for

jets with mass while transverse momentum, PT, is well defined and Lorentz invariant.

The Snowmass recombination scheme merges particles 2' and j into pseudo-particle

k with

E13501 + Emile , and m = ET,i¢i + ET,i¢i
Err ET;

9

. (5.16)

 

 

Em: = Em + Em a 77]: =

It was suggested as an approximation to 4-vector recombination because it expe-
dites theoretical calculations using the cone jet algorithm. For theoretical kl jet

calculations there is no such advantage.

We define D=1.0 partly because this roughly corresponds to R=0.7 in the cone
jet algorithm. D=1.0 was also seen to give fairly stable results in jet rate studies
on Herwig Monte Carlo data comparing jets reconstructed from the parton shower,

final state hadrons, and calorimeter cells.

Ellis and Soper examined the inclusive jet cross section for 100 GeV jet ET and
In] < 0.7 using both the Is; and cone jet algorithms [41]. At 0(a3), they found

similar results for lei jets and cone jets setting D = 1.35 x ’R. In addition, D210

64

 

and R=0.7 reduce the renomalization/ factorization scale dependence, )1, for the k 1

and cone jet cross sections respectively.

A Side Note on k] and Cone Jet Sizes

It is difficult to compare the size of a k] jet to that of a fixed cone jet. Imagine a
parton shower of 3 massless partons, all 3 at equal 77, equal momenta and separated
by 0.7 (b. They will all be included in a R=0.7 cone jet, but the D=1.0 lei jet will
only cluster two together. From this one may conclude a R=0.7 cone jet is bigger
than a D=1.0 kl jet. Now, imagine a similar shower except this time the particle
in the center is 4 times as energetic as the other two and now they are separated by
0.8 d). In this case, at most 2 will be included in a R=0.7 cone jet, but all three will

be included in a D=1.0 kl jet. In this case, the kl jet appears to be bigger.

It is difficult to extract any meaningful information from comparing kl jets to
cone jets. What is more important is that we are able to compare our experimental
results to theoretical predictions using the same jet algorithm. This is simply because
a jet is defined by the algorithm employed. The kl jet algorithm can be applied at
any level (partons, hadrons, calorimeter data) in exactly the same manner. Recall
that cone jets needed an additional parameter, Rm, in order to compare to 0(a2)
calculations. kL jets also have the feature that each 4-vector must be assigned to
one and only one jet in the clustering procedure. This avoids adding additional

split/merge criteria and makes the k_L jet algorithm more suitable for jet counting.

65

 

5.4.1 Monte Carlo Event Jet Rates

When the kl jet finding procedure described above is concluded, we have a list of
jets which are well separated in n — (,6 space. Many of these jets may be associated
with the soft interactions between the remnants of the proton antiproton pair. They
may also come from soft radiation from the partons involved in the hard interaction.
The leading-order or next-to—leading order theory cannot accommodate this soft
radiation, and if we include all the jets, we will not be able to extract a, as we
described previously. Therefore, it is necessary to make a cut to remove low PT jets

not associated with the hard process.

The probability for a parton to radiate a gluon (or split into a quark antiquark
pair) is governed by as. This splitting is a function of the fraction of the original
parton’s momentum given to the radiated gluon (or quark antiquark pair). Therefore,
we only count jets in an event if their PT is greater than some fraction of the hard
scale. To define the hard scale, we sum the PT of the 3 highest PT jets in each event,

HT31

3
HT3 = 2 PT,- . (5.17)
i=1

Then, all jets with PT below some fraction times the hard scale (PT < fem x HT3)

are dropped [44] ,

To choose a reasonable fraction cut, we study Herwig (version 5.8) Monte Carlo
data. The Monte Carlo data is generated with 2 —> 2 parton ET thresholds of 30,
60, 120, and 240 GeV. It is processed through the SHOWERLIB [48] DO detector

simulation.

66

Figure 5.5 shows fractional jet rates in Herwig Monte Carlo events as a function of
the fraction cut, fem. We compare these rates for jets found after parton showering,
hadronization, and detector simulation. If we set few too high (fem > 0.3), there
are events where only one jet passes our cut. These are events where the leading
jet carries about half the available event ET (P71 z H73 / 2) and the remaining half
is divided roughly equally between the second and third jets (P12J3 z HT3/4). On
the other hand, if we choose fwt to be small, we begin to include many jets and the
agreement between the three levels begins to break down. So a reasonable choice for
fem seems to be in the range 0.15 < fcut < 0.2. We use fwt = 0.15 because it gives

us the largest signal for R32 in this range.

67

 

PERW G V5.3 CENERATED AT 30 GEV E. PEQW'G V5.8 GENERATEO AT 60 OEV E.

 

 

 

 

   

 

 

  

    

        

 

 

Z Z
9 ‘3 ‘-
2. 2
§ :r
L" E
. =
Z Z
—— ULORWLILR
k N
PAR'CN
. «an...
0 0.05 0.1 O. i 5 O 7 0.25 0.3 0. 35
tcut
HERVIIG V5.8 GENERA'ED AT 120 GEV E, HERWIG V5.8 GENERATED AT 240 GEV E,
z 2
g o
._ a
s s i
u. r
>- ,_
... w
'3 —,
z z
0.3
0.5—
-— momma L — momuum
, ~ . , , HADRON
a ”mo“ [ ., amrou
7:5 .35
tom fcut

Figure 5.5: k; Jet Rates as a function of font in Herwig v5.8 Monte Carlo Data.

68

Chapter 6

Introduction to lei Jet Momentum

Calibration

An accurate calibration of kl jet momentum is not only necessary for a measurement
of R32, but it is necessary for almost all analyses involving kl jets. Because a
variety of studies will depend on this work, it is important that the correction we
derive be widely applicable. It will also be useful to have an understanding of the
individual uncertainties and correlations associated with the various aspects of the

kl jet momentum calibration.

Deriving a momentum correction for kl jets was an unexpectedly difficult as-
signment and as a result, we were unable to complete our analysis of R32. In many
ways, the calibration of the ki jet algorithm represents a much larger contribution
to the field than the measurement of R32 (had we completed it). Many subsequent

measurements will rely on the work decribed in the following chapters.

We will give a general overview of the jet momentum scale for kl jets. In the

69

following two chapters, we will give a full description of the offset and jet response
corrections. Following that, we will show the results of the Monte Carlo closure test
that was performed to test the method, and, finally, we will present the final lei jet

momentum scale correction with errors.

6.1 General Overview of kj Jet Momentum Cali-

bration

Almost all analyses involving the physics of jets attempt to relate the observed
jets to a simple parton interaction. Precise calibration of measured jet momentum,
therefore, is a priority. This is not a straightforward task as the evolution from
partons to jets of hadrons to clusters of energy in the calorimeter is very complex

and riddled with theoretical unknowns and detector effects.

The jet momentum scale correction is an attempt to remove effects of the detector
as well as the physics underlying event (momentum due to soft interactions between
the remnant partons of the proton and antiproton). The goal is to approximate the
sum of all the final state particle momenta incorporated into a jet resulting from
the hard parton interaction. Hadronization effects are not corrected for here. The
analysis described in the following chapters is an attempt only to correct jets to the

particle (final state hadrons) level.

The method for correcting kj jet momentum is done in two steps. First an offset

is subtracted and then a response scaling factor is applied. This can be expressed

70

 

by the to

where P
using th

the tale

Bee;
tion \Vll
comet-ti
derived
1138 the
of jet 3
the OH:

kl jets.

The
the CO,
discugS
Fro”, 1

CAFIXE

by the following relation

Pptcl _ Pjrgteas —' E0071 £2 PT)

e _ 3 6.1
,. name) ( )

where Pfgfl represents the “true” momentum of a jet found from final state particles
using the kl algorithm, E0 denotes an offset correction and RM is a correction for

the calorimeter jet response.

Because the definition of a jet is given by the algorithm employed, the calibra-
tion will depend on the choice of jet algorithm. To a certain extent, however, the
corrections can be derived generally. Previously, the jet energy scale correction was
derived for jets defined by the fixed cone jet algorithm [45, 47, 46] and we are able to
use the results of that study for detector effects that are independent of the choice
of jet algorithm. We also use results of this study to test our method for measuring
the offset and for extrapolation into regions of phase space where we lack data for

kl jets.

The cone jet energy scale is described in great detail in [45, 46]. Since much of
the correction for It; jet momentum is based on that study, we will include it in our
discussion emphasizing the material that is relevant to the kl jet momentum scale.
From here on, we will refer to the established cone jet energy scale correction as

CAFIX5.1 (Calorimeter Fix Package, version 5.1).

71

Chapter 7

kl Jet Offset Correction

The purpose of the offset correction is to subtract from the reconstructed jet the
transverse momentum which is not associated with the hard interaction itself. We
divide this into two parts: the offset due to the physics underlying event, One, and
the offset due to the experimental environment, 01b, such as noise, residual pile-up

from previous pp crossings and multiple pp interactions.

The underlying event contribution comes from soft interactions between the rem-

nant partons of the pp pair which did not take part in the hard interaction.

The noise contribution arises because the average energy of the individual cells
is not zero (even in the absence of beam) due to uranium decay and electronic noise.
Although this is corrected on average by pedestal subtraction, there remains an
effect due to zero suppression of cells at readout combined with a non symmetric

noise distribution (for further details see [46, 51]).

Pile-up is the residual contribution from previous pp crossings. It results from

the long shaping time associated with the preamplification stage. The base line

72

 

subtractor (BLS) samples the signal before the event and subtracts this amount. The
signal from previous crossings continues to decay after this sampling, and, therefore,
a residual correction is needed for a more accurate removal of the pile—up effects. The
Luminosity has some effect on the amount of signal produced by previous pp crossings

and therefore, residual pile-up will depend on luminosity.

The multiple interaction contribution is due to soft interactions between other
pp pairs that do not contribute to the hard collision. This also depends on luminosity.
While pile-up and multiple interactions contributions to the offset are luminosity

dependent, the noise and underlying event are not.

In this Chapter, we present the offset correction to be applied to jets reconstructed
with the kl algorithm. First, we will discuss the method, which is based on MC jets
with DC data overlayed. To test the method, we performed some studies using the
0.7 cone jet algorithm. We compare the results obtained using our method to the
previously obtained results from DC data [45, 46, 51]. This is shown in Appendix B.

Finally, we present the results obtained for kl jet offsets, Oz), and One.

To simulate the offset contribution to jets, we overlay DO data on Monte Carlo
data that has been processed through a DO detector simulation. The Monte Carlo
data do not include the physics underlying event and the detector simulation does not
include the effects of noise. Neither are the effects of pile-up nor multiple interaction
simulated in the Monte Carlo data. The overlayed D0 data contain these effects,
and the offsets are measured by comparing jets in the sample with no overlay to jets

with the overlay.

73

7 .1 Monte Carlo Data With Overlay

We use Herwig (version 5.9) Monte Carlo data generated with no underlying event.
Monte Carlo data (no underlying event) is generated with 2 —) 2 parton ET thresh-

olds of 30, 50, 75, 100 and 150 GeV. It is processed through the SHOWERLIB [48]

detector simulation.

Three different types of DO data are overlayed on Monte Carlo Data. They are:

ZB zero bias data.
ZBnoLQ zero bias data not passing the Level C trigger.

MB minimum bias data.

The zero bias data, ZB, have the least restrictive trigger requirements. The trigger
requires only that a bunch crossing take place and the data are taken at random
over a range of instantaneous luminosities, L. The ZBnoLO data are a subset of the

ZB data with the requirement that the event did not pass the level 0 trigger.

ZB data are taken for a range of instantaneous luminosities (.C = 0.1, 3, 5, 10
and 14 x103°cm'2sec‘1). The ZB data include the effects of noise, pile-up and
multiple interactions. ZBnoLC and MB data are used only at low luminosity only
(0.1 x103°cm’2sec‘1). ZBnoLO data includes the effects of noise and pile-up, and
MB data, in addition to noise and pile-up, include the physics underlying event. At
low luminosity, very few events pass the Level C trigger, and, therefore, ZB and

ZBnoLO are almost identical.

The DC data (ZB, ZBnoLQ, or MB) is added to the detector information in the

74

 

Monte Carlo SHOWERLIB data. As mentioned earlier (4.2.3), in data taking, cells
with energy less than 20 of the pedestal value are zero suppressed (not read out).
Therefore, the overlayed data are also zero suppressed (using 0.0 as the pedestal
value). We also use the Monte Carlo sample with no overlay. In this case, the

calorimeter cells are not zero suppressed prior to reconstruction.

The overlayed and non-overlayed data are reconstructed using version 12 of the
reconstruction package (RECO v12). Finally, we reconstruct kl jets from calorimeter

cell information as described in section 5.4.

At this time we do not have data covering all luminosities, all jet ET and all jet

1]. Shown in Table 7.1 is a summary of the data used in this thesis.

 

 

 

 

 

Type of Herwig Threshold Luminosity Jet 17

Overlay ET (GeV) (x1030cm"2sec‘l) Range
none 30, 50, 75, 100, 150 N/A 0.0< Inl <3.0
ZB 30 5 0.0< In] <3.0
ZB 30, 50, 75, 100, 150 0.1, 3, 5, 10, 14 0.0< In] <1.0

ZBnoLO 30, 50, 75, 100, 150 0.1 0.0< |n| <1.0
MB 30, 50, 75, 100, 150 0.1 0.0< [nl <1.0

 

 

 

 

Table 7.1: Availability of ET , luminosity and r) for overlayed Monte Carlo data.

7 .2 The Method

Let us define the following notation for jets reconstructed from the various data to

be used.

13:1: kj jet ET in Monte Carlo with no overlay.

m0 kl jet ET in Monte Carlo with MB overlay.

75

zn kl jet ET in Monte Carlo with ZBnoLO overlay.

zL kl jet ET in Monte Carlo with ZB overlay at luminosity .C = L ><103°cm‘2sec'1

(e.g. 25 for £ = 5 x103°cm‘2sec‘1).

As mentioned above, the ZB data include the effects of noise, pile-up and multiple

interactions. This contribution to a jet at a given luminosity, 053, is given by

05,, = 2L — mm. (7.1)

The MB data include the effects in ZBnoLO plus underlying event. Thus, the offset

due to underlying event can be measured by

One = m0 -— zn. (7.2)

These subtractions are performed on a jet by jet basis, for the two leading jets. We
ensure the same jet is selected in both samples by requesting them to be within
a distance of 0.5 in n - 45 space. Figure 7.1 shows the distribution of distances,
Run-n = [(91525 — 4533? + (7725 — 7113)]1/2, from the leading 33m jet to the closest jet in

the :45 sample.

Figure 7.2 shows a typical distribution of the energy difference between corre-
sponding jets in the noise overlayed (2:5 in this case) and no noise sample, 3:55. From

the mean and RMS of this distribution we extract the offset and its statistical error.

76

 

 

 

 

 

 

3

Figure 7.1: Distance in n —- (5 space from the leading an: kl jet to the closest z5 kl
jet.

 

 

 

 

 

.
3w ._ . .3 ................ , .................................................
- Z
.
h l
P -
.
H a
.
250 .... ................................................
.
b I
.
,. .
.
t" I
i- l
200 ._ ............................... , ................
t- Z
.
..
-
..
150 ._ ................................................................................................
it
b
)-
_
1m ...... ................................................................................................
b
)-
b
h-
so _. .......................................................
)-
b I I
b I I
. .
o 1 l L- I J.‘ Li _.l_l_l

.30 .20 .10 20 30

Figure 7.2: Distribution of ET differences between corresponding k] jets in the 25
and x1: samples

77

 

Note that leading jets in one sample do not always correspond to leading jets in
the other. Figure 7.3 plots the ET ranking number of the 25 jet associated to the
two leading 1:2: jets (jets are numbered in decreasing order according to their ET ).
Besides the expected swapping between the leading two jets due to fluctuations in the
overlayed noise, we sometimes find one of the leading 13$ jets to be associated with a

lower energy 25 jet. To reduce the effects of ET smearing, the events are weighted

 

 

 

 

 

 

 

 

 

 

 

....................... l
rlnle‘rLJlmr'TlEilrL LLILL'LLI'LL‘LL 53131111.]..R..'I'l1..'r';'.;.1.;!'IiLL'lLL]Lil.illr'li;;l;1f‘lilli;¥l

l 2 3 4 5 6 l 2 3 4 5 6

Figure 7.3: Ranking of overlayed kl jets compared to non-overlayed jets. Corre-
sponding 25 k_L jet matched to the leading (left) and second leading (right) 2:1: kl
jet. Jets are numbered in decreasing order according to their ET .

so that we have a flat jet ET distribution. The k‘L jet ET distributions without
weighting are shown in Figure 7.4. By using a flat distribution, we eliminate uneven
contributions in a given jet ET bin due to the steeply falling and rising distributions
shown in Figure 7 .4. This is discussed in more detail with respect to the 0.7 cone

jet algorithm in Appendix B.

78

 

TTTITIIIIIIIIIITITITTTTTT

 

 

 

Figure 7.4: Distribution of reconstructed ET for kl jets without noise overlay. The
different line types correspond to samples generated with parton ET thresholds of
30, 50, 75, 100 and 150 GeV.

7 .3 Verification of the Overlay Method

To ascertain whether the overlay method models the contributions to the offset
correctly, we compare the occupancies in 0.7 cone jets from our Monte Carlo with MB
overlay sample to the occupancies measured in jets in a pure MB sample. Figure 7.5
shows the occupancies measured in 0.7 cone jets taken from pure MB data, and
Figure 7.6 shows the occupancies in Monte Carlo with MB overlay data. We are
only able to compare for In] <10, and the y-axis scales are dramatically difl'erent.
However, under close examination, one can see that the occupancies for a given jet

ET are in good agreement with the exception for jet ET 340 GeV.

In an attempt to further our understanding and confidence in the overlay method,
we measured the offsets, 02b and One, for cone jets (R = 0.7) and compared our

measurement to the previous correction derived for 0.7 cone jets in the CAFIX5.1

79

 

 

 

 

>‘1“fitri'rt't'I‘THI"p‘t‘rritsfl'trrr’
o -
g _ o 7 CONE JETS ,,_.
Q .
3 r . . . 1
80'8 t. (found in Min BIOS data) a
o + «
' it Jet Eyé 4O Gev 1
. 40§JetassoCev i -
0-6 - 0 80 § Jet ET § 100 Gev a
r C 100§JetE1§ZOOGev + 1
- A 3OO§JetE1§ 400 Gev —+— .
0.; +3” 2
' 2e:
I it I
.- 1 ..
_ $4: 1
0.2 r- -_
:2: 1
h _‘_ F1 .1
0 hrrrrlrrrrlrrrrl1rrrlrrrrlrrrmlrrrrlrnmrq
0 0.5 1 1.5 2 2.5 3 3.5 4
77

Figure 7.5: 0.7 cone jet occupancy vs. jet 1] for jets found in minimum bias data.

80

 

0.7 Cone Jets (minimum bias data)

a
to

 

JethééiCE)

. . . . . .
l—-— ............... . .................. . ................. . ................................................. ................ , ................

- o 40§JetE,§80§
I i I A

Boédet 5.5-100 . :
0.16 __ ........... ,.. ........... ' ............. ............... l .............. ;.......... ,, ...........; ..... . ........
- t tongoeteszoo

Occupancy
.0
a:
o

 

 

 

 

 

 

h
. . . . a . . . .
h I c l I I o v o I
u e . . . . v . .
- . . . . . . . .
t . . . . . - . .
o.“ ._............ .........................................................................................
. t . - . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
P u o . - n u - u .
)—

L

on lllllllllllLIll11111lllllllllllllllLlllllllllllll
o

0 0.1 0.2 0.3 0.4 0.5 0.8 0.7 0.8 0.9 1

 

 

 

Figure 7.6: 0.7 cone jet occupancy vs. jet 1] for jets found in Monte Chrlo with
minimum bias overlay data.

81

 

correction package [51, 45, 46]. In that study, the densities were measured in ZB,
ZBnoLQ, and MB events. The offsets were derived by multiplying densities by the

area of a fixed cone jet, 7r x (0.7)2 ~ 1.5.

In order to compare to the CAFIX5.1 offsets, we measure the offset densities, Due
and Dzb, by dividing the offsets, One and Ozb, by the area of a 0.7 cone jet. This
study is described in detail in Appendix B. For the offset due to noise, pile-up and

multiple interactions, we compared for only one luminosity, C = 5x103°cm'2sec"1.

Our results for the offset due to underlying event, Due, are consistent with
CAFIX5.1 (see Figure B.4). For Dzb, on the other hand, we see a dependence on
0.7 cone jet ET which was not prescribed in the CAFIX5.1 correction (see Fig-
ure B.2. We believe the ET dependence that we see is due to zero suppression
effects that were not accounted for in the CAFIX5.1 correction. The zero suppression
correction used in CAFIX5.1 (Equation B.1) depends on the occupancy factor, sz
in jets. The occupancy for jets was seen to have little dependence on jet ET and,
therefore, a constant occupancy was assumed. If instead we use the small variation
in occupancy shown in Figure B5 in the CAFIX5.1 zero suppression correction, we
can explain only 30% of the 0.7 cone jet ET dependence that we measure with the

overlay method.

Because our occupancies for given jet ET agree with pure MB data, we believe the
overlay correctly models the effects of underlying event, noise, pile-up and multiple
interactions. It is possible that the zero suppression correction used in CAFIX5.1
is inexact. Because the efl'ects of zero suppression were not well understood when

CAFIX5.1 was derived, a large error was assigned. This error accommodates the

82

discrepancy between our measurement and the CAFIX5.1 value. Because the ET
dependence for 0.7 cone jets cannot be confirmed with pure DO data, we assign
an error to Ozb for kl jets. As stated above, 30% of the eflect is consistent with
CAFIX5.1. The other 70% will be assigned as a systematic error to our measurement

for the offset, 02),, for kl jets.

7 .4 Offsets for the kl Algorithm

At this time we do not have data covering all luminosities, all jet ET and all jet 1].
Shown in Table 7 .1 are the data available at this time. In the regions where we do
not have data, we will either extrapolate using the data that we have or use offset

corrections from CAFIX5. 1.

7 .4.1 Offset Due to Noise, Pile-Up and Multiple Interactions

As stated above, we measure the offset due to noise, pile-up and multiple interactions
using the relation,

05b = ZL '- $1: . (7.3)

Figs. 7.7 and 7.8 present the results for 02,, as a function Of ET at .C = 0.1
x103°cm‘2sec‘l and .C = 5 x103°cm‘2sec“1, respectively. As Opposed to the cone
case (see Appendix B), very little ET dependence is Observed for the kl algorithm
and this dependence becomes weaker as the luminosity increases. Exponential fits

were done for luminosities lower than £=5x103°cm‘2sec‘1.

83

 

Ozb(GcV)

Ozb(GcV)

OzNGeV)

 

 

_

I.

mac—oz .................
)—

Z

L:—

L- ...... ..,....... ...... ; .....................................
t o o

y-

— --------------------------------------------------------------
)-

b

)— . I .
"rrilrrrrlrrrrlrrrr

 

 

50 100 150 200

ET(GeV)

 

 

p
b-

p-

L............................77..O...4:O...6 .............
C

b

L ...... o .....................................................
P

t . O o o

I. ..............................................................
h

h I I n

y- . . .
'rrrlrrmmlrrrdrrrr

 

 

50 100 150 200

atom

 

 

h-

I

L’DOB— ...................
E

'— ..............................................................
b

3 o o 5 o

L .............. ’9 .............................
'— I

: : 5 :
”mimirrrrlnrirlrrrr

 

 

50 100 150 200

E,(GeV)

Ozb(GcV)

Ozb(GeV)

 

 

h

C

_nOZ—Q4 .............
h- u

:_ ...... ......H‘ ...... ... ................
.. : Q :

E O.

—- .............................................................
,_ I

)—

)-— . : n
i'rlrlrrrrlrignlrrri

 

 

150 200
E,(GeV)

50 100

 

 

b.-
b
)—
L’I’)06*Q 8 .............
r-
b
b
h
_ ..............................................................
p
: ' ' o o '5
L .
)_. ..............................................................
b
P I O I
l— . . .
l L l J l l l I l l l l l I L 1 L1

 

 

150 zoo
E,(CeV)

50 100

Figure 7.7: Measured Ozb vs. kl jet ET at £20.1x1030cm’2sec"1.

84

 

Ozb(GeV)

Ozb(GeV)

Ozb(GeV)

 

 

 

h

h—

I

b.- --------------------------------------------------------------
" O . O

F O .

)— ..............................................................
)—

2 s z 3
_nO—02 ................
i f i E

L- . - .
I"L11l1111l1111l1111

 

50 100 150 200

ET(GeV)

 

[- :
.
’— u
.
p I
__ .
.
)—. ..............................................................
. .
)- . .
. .
- . .
. .
_ . .
. - o
- I I
._ ...... ............................
-
h
)-
h

ITTW

 

 

llllJLJ—LJ—lliJ—JLJII

 

50 100 150 200

ET(GeV)

 

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

ITITT'IITI

 

#LlJJLJlLILJlllll

 

 

50 100 150 200

wow)

Ozb(GeV)

Ozb(GcV)

 

_n02—Q4 .............

 

 

LllllJLJJLJlllllll

 

50 100 150 200
E,(GeV)

 

 

 

'- 3

I E

'- I
h—.-coo-~--n0.-.~on~~n~.-o-o-I.......n.........> ...............
,._.. ................
F n

)-

l—

; ........................... 7; ..O..6.—..Q.8 .............
C . . .

"1_1 1 l 1 1_14_L 1 1 1 1 l 1 1 1 1

 

50 100 150 200
E,(GeV)

Figure 7.8: Measured 0,), vs. kl jet ET at £=5x103°cm‘28ec‘1.

85

 

The study of n and luminosity dependence for the central region is summarized
in Figure 7.9. The general trend is that It; offsets are 50—75% larger than for cone.
Because the kl algorithm clusters everything into jets, we would expect it to “pull”
in more noise and underlying event than a fixed cone algorithm (which excludes

energy outside the cone radius).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9 : : E e 2
£3, 3 :_ ............. g ....................... L.=Q...l .......... SE. 3 :_ ...................... L53 ...............
g I : 5 '3 E.__._ 5
: 3 i o _ +0—
2 m+ ............... 2 __ ......... ii.“ ................................
: i 50'0- 5
~ ...... = ................................................ L .......... :Q'... -.Q: ....................................
1 50"0‘0-0— l :
opilllllllllggllllil obilllLlllllLlllllLJl
0 0.5 l 1.5 2 0 0.5 l 1.5 2
7| I]
9 4 " S 4 : :
g 3 E— ............. ....................... L-;.5 ............... g 3 a.=9—....+_._ ...... L.;..l.Q ...........
5 f" ’ 9 +—o— 5 I
2 I.............-. ................................................ 2 3).. .0. ................................
C 2 -O-"O‘ : 3 3
l t__............... ................................................ 1 :_............... ................................................
o-lIlllLLljllllJlllLJl objllllllljllllllllll
0 0.5 1 1.5 2 0 0.5 1 1.5 2
'1 TI
9 4 = :6:
5 +H+ _
z 3 }W? ...................... L..-.-....14: ...........
5 z L....,.-‘O—-Q~. ................................
1 :— .............................................................
0 :LLLLI i1 1 l I l I l l l i l l l l
0 0.5 1 1.5 2
n

Figure 7 .9: 02b Offset vs 77 for Is; jets with 30<ET <50 GeV. The result for cones
(Open circles) is shown for comparison.

To study the full rapidity range, we use a high statistics sample generated with

86

 

Herwig v5.9 with the underlying event included. This sample was only gener-
ated in the low energy range, ET >30 GeV, and overlayed with ZB data with
£=5x103°cm”2sec“1. The Underlying event essentially cancels when taking the
difference zS—xx. Results are shown in Figure 7.10, for non overlayed jets with

30<ET <50 GeV.

 

Ow(GeV)

2.5

1.5

 

0.5

 

 

o L l l l 1 J l l l l l l l l I 1 l l l l l L L l l l l I 1

o 0.5 . 1 1.5 2 2.5 3
‘1
Figure 7.10: Measured Ozb vs. 17 for kl jets at £=5 and 30<ET <50 GeV (solid

symbols). The result for cones is shown for comparison (open symbols).

 

87

 

 

‘

Ozb(GeV)

1.5

 

 

 

o L l l l i L L L g j 4 1 1 l I: I J l l i l l l l j 1 l l 1
0 0.5 1 1.5 2 2.5 3

 

Figure 7.11: Parametrization of 025 vs. 1:; jet 1) for jets with 30<ET <50 GeV, for
various luminosities.

Since there is no MC available to get the offsets beyond the central region for
luminosities other than £=5, we estimate their values by extrapolating the measured
central values (Figure 7.9) with a functional form as suggested by the fit shown in

Figure 7.10.

In order to let all the points participate in the fit, the samples were divided in
two groups according to their luminosity (lower and greater than £25). Two new
distributions are obtained by making an average of the points after normalizing to

the £=5 distribution. The fits to these distributions were scaled with luminosity,

88

 

and the results are shown in Figure 7.11. Linear interpolation is used for luminosities

between the values shown in Figure 7.11.

To get the final 021,, these values must also be given an ET dependence at low
luminosity. This dependence is interpolated using a third degree polynomial between
£=0.1 and £25 so that at £=O.l, the dependence is as shown in Figure 7.7 and flat

above £=5.

Figure 7.12 shows the final Ozb vs. ET for 3 luminosities x 3 77 values (with
errors). Figure 7.13 shows the 17 dependence of Ozb for 2 values of ki jet ET and 2

luminosities.

The error arising from the disagreement in the ET dependence between our
results of 02;, for cone jets and those shown in [45] is one of the major sources
of uncertainty especially at high energies and low luminosities (around 15%). The
functional form of Ozb contributes an error of 0.2 GeV (calculated as the average of
the largest difference between the points and the fits for each curve in Figure 7 .11).
To accommodate the uncertainty for energies greater than 200 GeV, we introduce
an additional uncertainty that rises smoothly from 0.0 to .2 GeV between 120 GeV

and 270 GeV and remains fiat above 270 GeV.

7.4.2 Offset Due to Physics Underlying Event

We measure the offset due to underlying event using the relation,

One = m0 — zn. (7.4)

89

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

&

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E _ Nominal E _ Nominal E _ Nominal
>- _ High/Low L __ High/Low 3 L _ High/Low
* r- ~ _
,_ r) 1.2 .. L - 1
T. I. = 1 L. “ l .—
; n 0.0 I F ——_.._,
p u-
b L 1 1 1JLL11 L 1 b- 4 1 1 L11111 1 1 o E 1 L 1 ”1111 1 1
2 2 2
10 10 10
_ . 4 .
E _ Nominal : __ Nominal : __ Nominal
. F . .
’ _ Hugh/Low L— _ Hugh/Low 3 E_ _ High/Low
N ’- J E L 2 5
:— 2 ._ n 2.0
I L = 5 l; _ ...—l
L ' ,_. 1; 1.2 1 a"
: : E—
u- r— )-
1. l 1 1111111 1 1 h L 1 1111111 J 1 o F l 1 1 111_111 1 1
2 2 2
10 10 10
: E 4 E _ Nominal
4-4 .. » High/Low
_ 3 ..—
.. W C
p- )-
L _ Nominal '_ _ Nominal 2 "_ -—""
,2 __ High/Low I __ High/Low
L L - 9 '_ L - 9 1 L L - 9
t 1; 0.0 : n 1.2 : n 2.0
L- 1 1 1 111111 1 1 .. 1 1 1111111 1 1 o b I 1 1111111 1
2 2 2
10 10 10

E...

a,

a,

 

Figure 7.12: 0”, ET dependence and errors, for kl jets at £=1,5 and 9 and 17 =0.0,
1.2, and 2.0.

90

 

 

   

 

 

 

 

    

 

 

 

 

  

0a 4 : ca 4 3
3.5 E- L=1 3.5 :— L=5
3 E 320 GeV 3 E E. 20 GeV
2.5 E 2.5 »—
2 ’r 2 :—
1.5 E— 1.5 :—
1 :— _ Nominal l E- _ Nominal
: __ High/Low L: _ High/Low
0.5 r 0-5 I’
. : l 1 L 1 1 1 1 1 L 1 1 l 1 o : 1 1 L 1 1 LL L 1 1 1 14 1
o 1 2 o 1 2 3
n
.' ‘ fl 4 l-
o O E
3.5 L = 1 3.5 :— L = 5
3 E100 GeV 3 E_ 5,100 GeV
2.5 2.5
2 2

n—
In

1111111111111 '1' I] IIIIIIYUIUYIVIITTU

_

 

   

 

 

...
In

a YTTYIUTYTITTI’YIIIIIIYI I

~

 

 

 

 

_ Nominal _ Nominal
0.5 _ High/Low 0.5 _ High/Low
o 1 1 1 1 1 1. l 1 1 _1 1 L 0 1 1 1 1 1 1 l 1 1 1 1 1 .1 1
0 l 2 l 2 3
1‘l

 

Figure 7.13: 0,5 17 dependence and errors for It; jets with jet ET equalling 20 and
100 GeV at Liz] and £=5.

91

Figure 7.14 shows the physics underlying event offset, One, compared to the
previous result for cone. As shown in B, there is no evidence of an ET dependence
for 0.7 cone jets, and we do not see an ET dependence for kl jets. Therefore we

will apply a correction only as a function of 77.

Physics Underlying Event, One

N

 

N

 

Om(GeV)
3
C?
O
N
0m(GcV)

Illflllill
+

~
in

1111’]

. +3
+3
+§
+5

 

 

 

lll]
O

 

1111

 

 

0.51111111111111111141 05144114111141L1111L41

so 100 150 200 ' so 100 150 200
How) E,(Gev>

 

 

 

Om(GcV)
Om(GeV)

~
In
I 1 l 1 l I 1 I l 1
20-
i

I I I I

YI—FYIIIIIIIITI

 

 

 

 

0.5 1111111111111111111 0.5 lJ—LlllLllllllliriil
50 100 150 21” 50 100 150 200

wow) F..(GeV)

 

 

 

N

O kt
O cone

Ou(GeV)

 

 

 

0.; -111.
50 100 150 200
WOW)
Figure 7.14: Measured One vs ET for ki jets. The result for cones is shown for
comparison.

 

Figure 7.15 summarizes the results in One for kl and for cone jets as a function
of jet 7) compared to the offset given by CAFIX5.1. Unfortunately, there is no MC

available to get the offsets beyond the central region. Therefore we must use the

92

CAFIX5.1 result to determine the n dependence. Figure 7.15 shows One for k; jets
for |77| <1.0 compared to One given by CAFIX5.1 and the measured 0.7 cone One
(from Monte Carlo data with overlay). The good agreement in the central region
between our results for cone jets and those from CAFIX5.1 reinforces our confidence
in the overlay method. One is consistently larger for kl jets than it is for cone jets.
We normalize the CAFIX5.1 offset to our measurement for the 0.7 cone jets. Then,
we calculate the average difference between our measurements for the hi and cone
jet offsets. We add this difference to the normalized CAFIX5.1 points to get the offset
due to underlying event for kjjets. The final underlying event offset, One with errors

is shown in Figure 7.16.

We apply a 0.1 GeV statistical error that comes from the normalization process
described above. There is a systematic error of 0.1 GeV to accommodate possible
ET dependence (from Figure 7.14). Added in quadrature, this gives us about a 10%
error in the region |n| <1.0. We will inflate this to 15% above Inl >1.0 where we
have not measured 0,,e for kl jets. The 0m3 correction for kl jets (with errors) is

shown in Figure 7.16.

93

 

N

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

OudGeV)
53
I l

1.6 _ ......................... ........................ ........................

1.4

1.2

 

0.8

06 ,_.,...., ......................... ', ........................ ,..., ........................
. . . . . .
. I I . .

- D I 0 I l

04 __ .................................................
O . . . . .
P n . . . D

. . . . .
— I . o . ¢
I t D I I
. . . . .
. . . . .

-——... ........................................................................................................................................... .....
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .

 

 

 

Figure 7.15: Measured 0,,e vs kl jet 77 (solid circles) and cone jets 1) (triangles),
together with the results from the CAFIX5.1 (open circles).

94

N

 

Om(GeV)

1.6

1.4

 

1‘ —| V\

1.2

_ Nominal

_ High/Low

0.8

0.6

0.4

0.2

fif'T‘jfTTITIfiIIIIUTIIrIIlltl’ffill‘jllf?

 

 

 

E.
a
'6

Figure 7.16: 0,“, correction vs kj jet 17. The points show the measured offset for kl
jets.

95

Chapter 8

kl Jet Response Correction

The calorimeter is calibrated from Test Beam data based on charge deposition in the
liquid argon for known incident particle energies. In theory, the true jet momentum
and energy would simply be the vector sum of the energy deposited in the calorimeter.
In reality, however, the measured jet energies are reduced due to energy losses in
uninstrumented regions of the detector, variations in cryostat response to single
particles (e.g. non-linear response for low energy particles), and variations in the

e/7r response ratio [46].

The calorimeter response to jet momentum was measured for fixed cone jets [45,
46]. There, the jet response is used to correct the scalar summed cone jet energy, E.
We correct vector summed kl jet momentum, PK, jet. The method relies on trans-
verse momentum (PT) balance. It is, therefore, applicable to jet momentum. One
would expect the jet response to be identical for momentum and energy. However,
calorimeter showering effects widen jets, causing the vector summed momentum and

scalar summed energy to require different corrections. This is discussed in more

96

detail in Appendix C.

The jet response correction is described in 7 sections:

1. The Missing ET Projection Fraction (MPF) Method.
2. Cryostat Factor Correction.

3. E’ —>Pkt Mapping.

4. Jet Response vs. PM.

5. Low PM Jet Response.

6. ICR Correction.

7. Jet Response Errors.

8.1 The Missing ET Projection Fraction Method

Rm is measured using 'y-jet momentum balance in the transverse plane. To do
this, we use the missing transverse energy projection fraction (MPF) method. The
missing transverse energy, $1., is the vector momentum necessary to balance the

entire event in the transverse plane. Its a: and y components are given by

ET; = —2Pxi and $Ty = — 2133/" , (8.1)
i=1

where P3,- and P”,- are the a: and y components of 4-momenta assigned to each

calorimeter cell (assumed massless).

97

In an ideal detector, there would be no energy losses and, therefore, ET=O.0,

ET = — (1373 + fir had) = 0 , (8.2)

where RT had is the vector sum of the hadronic recoil in the transverse plane. In
reality, the electromagnetic and hadronic responses are not unity and are measured
as

”meas " ”meas _ "
T7 = Ramp“ and T had -- RhadPT had . (8.3)

ET is not zero and is now given by
ET = - (RemET'y + RhadE'jl‘ad) 5£ 0-0 - (8.4)

The electromagnetic scale, Rem, is determined very accurately. Therefore, after the

photons are calibrated, $1 is given by

ET = -ET7 - Rizal-5%“. (8.5)
From Equation 8.2, RT W = —I37~,, and we can write
ET = Em (Rhad - 1) - (8.6)

Hence, the hadronic response can be measured using

Rhad = 1 + MPF = 1 + M1, (8.7)
ET,

where inn, is the unit vector for the transverse component of the photon’s momentum.

98

 

Given that the event is balanced in transverse momentum, this gives the momentum

fraction the jet measurement has lost due to imperfections in the calorimeter.

8.1.1 The Energy Estimator, E’

Ultimately, we would like to know the response as a function of jet momentum.
However, resolution effects and reconstruction biases make the uncorrected jet mo-
mentum a poorly measured quantity. In order to avoid problems that may arise
from this, we look at the response as a function of a well measured quantity that is

strongly correlated with the true momentum of the jet of particles, 393’.

At leading order a 7—jet event should be balanced in PT. Using this and the

relation, sin0 = 1/coshn, the ideal energy of the jet, E’, is given by
E’ = 5.":“cosh(17jet) . (8.8)

The response can then be converted to a function of It; jet momentum by mapping

E” to kl jet P.

The response was derived as a function of cone jet energy in CAFIX 5.1. Only
the position of the jet is used to define the response as a function of E’. We use It;

jet momentum, PM, because the mpf method is based on momentum balance.

99

8.2 'y-Jet Data

The jet response was measured previously as a function of E’ using fixed cone jets
(R = 0.7) [45, 46]. To obtain a correction for k; jet momentum, we must provide a
mapping of E’ to PM. To do this, we use a subset of the data used to derive RM
versus E’. Below we describe the criteria applied to the 7-jet data for measuring
the jet response using cone jets. Some additional considerations were necessary for

deriving the jet response correction for kj jets, and we discuss these issues below.

8.2.1 Photon Event Requirements

In order to measure the jet response, we require a jet to be balanced by a well
calibrated object. In Section 4.2.3, we noted that the electromagnetic calorimeter is
very well calibrated for electrons and pions above a certain threshold. Therefore, we
do not actually require a pure photon sample, but we need an energetic, isolated,
electromagnetic cluster. So, although we use events passing triggers designed to
accept direct photons, we use different offline criteria to select events. Since the
majority of these electromagnetic clusters are indeed photons, throughout this thesis,

we will refer to them as photons.
Photon triggering is described in Appendix A.

Here is a list of the general offline criteria for the events used in our photon data.

2 1

0 We select events with low instantaneous luminosity, L < 5x103°cm“ sec“ .

o A multiple interaction tool, MITOOL, uses information from the level 0, track-

100

ing, and calorimeter detectors to distinguish between events where one or more
interactions took place. We select events flagged by the MITOOL as having only

one interaction.

ET, must be greater than the trigger threshold plus one 037.7, where 037.7 is

the photon energy resolution.

Where multiple photon triggers are running at once, a high ET threshold cut
prevents a photon event from passing a lower threshold trigger and fail a higher
threshold trigger. This removes photons which fluctuated to a very high energy

in the calorimeter.

Longitudinal and transverse isolation cuts demand that the EM cluster not be

contaminated by hadronic activity.

Events with photons within 0.01 radians of a (15 crack in the calorimeter are

rejected.

Photons in the inter cryostat region (ICR) are avoided by demanding that

I777| < 1.0 or 1.6 < I177] < 2.5.

Events are discarded if there is main ring activity at the time of the event. A
portion of the main ring accelerator goes through the calorimeter. When the

main ring is active, radiation leaks into the detector.

One and only one vertex must be found, and the z-vertex of the event must be

within 70 cm of the center.

101

0 Events where a noisy cell was removed are discarded. During reconstruction,
cells with a disproportionate amount of energy compared to their neighbors

are removed by the AIDA (Anomalous Isolated Deposit Algorithm) software.

0 For ET7 < 30 GeV, we demand that no muon be detected. Otherwise, we
demand that any muons detected have PT“ < 100 GeV. This is to avoid

bremsstrahlung radiated photons from cosmic ray muons.

8.2.2 Cone Jet Requirements

Here is a list of the general offline criteria for 0.7 cone jets in our 7-jet data used to

derive the CAFIX5.1 jet response.

0 We remove jets whose axes are within 0.25 (in 17 — (6 space) of the photon.
0 There must be at least one remaining jet in the event.

0 We avoid the ICR by demanding that the leading jet 1) be contained in the
central cryostat, CC, or one of the end cryostats, EC (Injetl < 0.7 for CC and

1.8 < Injetl < 2.5 for EC).
0 If the leading jet lies in the EC, we exclude the events where ET,7 < 25.0 GeV.

0 We avoid fake jets by demanding that the fractions of jet PT in the coarse
hadronic (CHF) and electromagnetic (EMF) sections of the calorimeter be

within reasonable limits:

0.05 < EMF < 0.95

CHF < 0.5.

102

o The ET ratio between the highest and the second highest ET cells in a jet

(HCF) are required to be less than 10, HCF<10.

0 We require the leading jet and '7 to be back to back in (b (2.8 < Ago < 7r).

8.2.3 Additional considerations for kl Jets

kl jets were reconstructed for a subset of the 'y-jet data described above in order to
perform the E’ to PM mapping. We use the same cuts on kl jets that were used for
0.7 cone jets in CAFIX5.1 (above) with the exceptions that we use kl jets in place
of cone jets, we require ET7 > 20 GeV (vs. 25 GeV) for EC jets, and we do not cut

on HCF (this information is not available for It; jets).

When the kl jets were reconstructed for this analysis, additional corrections were
applied to the cell energies in the calorimeter cryostats and inter cryostat region
(ICR) [52]. These corrections were not included when cone jets were reconstructed
and the CAFIX5.1 jet response was measured. The purpose of these corrections was
to scale raw EM objects. These corrections were introduced for a special reconstruc-
tion environment called DEFIX [53]. We will refer to these corrections as DOFIX

corrections from here on.

The DOFIX cryostat corrections are simple multiplicative factors which are ap-
plied at the calorimeter cell level. The DOFIX cryostat factors for the north (ECN),
central (CC), and south (ECS) cryostats are shown in Table 8.1. A kl jet in a given
cryostat will have a jet response that is higher (by the appropriate factor) than the

CAFIX5.1 jet response. To correct It; jets, therefore, we multiply the CAFIX5.1 jet

103

response by 1.0496 (the CC DOFIX factor) and adjust jet correction in the north

and south cryostats, H); and F S to accommodate the DOFIX factors.

cry,

 

DOFIX Cryostat Factors
ECN CC ECS
1.0609 1.0496 1.0478

 

 

 

 

 

 

Table 8.1: Cryostat corrections applied to the energy in the calorimeter cryostats
introduced for the DOFIX environment.
The DOFIX corrections to the inter cryostat region (ICR) are not so straightfor-

ward. So we use jet PT balance in two jet events to determine an ICR correction.

8.3 Cryostat Factor Correction

The jet response varies in the different 17 regions of the calorimeter. To eliminate
these variations, we correct the kijet momentum, PM, so that uniform (in n) jet
response correction may be applied. The CAFIX5.1 jet response we will use has been
corrected for the 1) dependent factors (cryostat and ICR) using 0.7 cone jets. The 7)
dependent corrections were applied to 0.7 cone jets and the event ET was corrected
for the change in 0.7 cone jet momentum, and the jet response, Rjet = 1 +M PF, was
measured. Once this is done, Rjet can be described by a single curve as a function

of E’.

The jet response is measured for jets found in the central calorimeter cryostat,
CC (lnl <07), and the end cryostat, EC (1.8< In] <2.5). The cryostat factor, Fay,
(not to be confused with the DOFIX factors) is defined as the ratio REC/Raf. It

Jet J

should not depend on the jet algorithm except where the jet pseudorapidity is needed

104

to determine the jet’s position in the CC or EC. The value of Fay using 0.7 cone

jets was found to be

Fay = 0.977 i 0.005 (stat) for RECO V12.

To verify that no complications arise from using a subset of the data or using
kl jets to determine pseudorapidity and to correct event ET, we remove the DOFIX
cryostat corrections from k 1 jets, correct the EC jets with Fay=0.977. We correct the
event ET for the change in kl jet momentum. The resulting jet response is consistent
with the CAFIX5.1 jet response with good agreement in the overlap region between

central and forward jets (Figure 8.1).

Because the DOFIX correction factors are different in the north and south cryostats,
we will have different jet response cryostat factors. The ratio of north to south
cryostat factors without the DOFIX corrections was measured to be Fcfi’y/ng =
0.997 i 0.003 [45]. We assume that the value Fay=0.977 is the average of F3; and
Egg. When we incorporate the DOFIX cryostat factors, we get north and south

cryostat factors of ng=0986 and ng=0.977.

8.4 E’ -—>Pkt Mapping

Before mapping E’ to PM, we subtract the offset from the jets. Then, we correct
for the cryostat factors, ng=0.986 and ng=0.977. We map jets in the CC and
EC separately and because jets in these two regions may fall partially into the ICR,

we also include the 1) dependent ICR correction. We will discuss in detail how we

105

 

 

 

 

 

 

 

 

Q)
2
O 0.9—
O- .-
U) c
(1)
(r _
O.88~
}.
~ + 42+ ll .
0.86— + + 39
0.84— &*+%
r f +
0.82: $25?
. +45) 1'
(f
0.78;%
L.
_ OCCk,JETS
076+— <> I EC k, JETS
r OCCCONEJETS
0.74— CI EC CONE JETS
’-11]]111111111lll1llllllllllillLijllllllL4L1
o 50 100 150 200 250 300 350 400 450
E’

Figure 8.1: Response versus E’. Open symbols are from the full 7—jet data sample
and solid symbols are from the smaller sample reconstructed with kl jets. The
additional DOFIX cryostat corrections were removed from kl jets.

106

derived this correction for kl jets in section 8.6. The jet response has been corrected

for the ICR using 0.7 cone jets. So this correction is only necessary for the mapping

of E’ to PM.

Once the jets have been corrected for the offset and the eta dependent jet re-
sponse corrections, the average PM is binned in E’ and plotted as a function of E’
(Figure 8.2). We fit a straight line (ax + b) to the CC and EC jets separately. The
fit parameters for the CC and EC are shown in Table 8.2. The results of the fits are

shown in Figure 8.2 with X2/d.o.f. = 2.29 in the CC and XZ/dof. = 1.11 in the EC.

 

E’ —>Pkt Mapping Parameters
CC EC
0.835 i 0.009 0.838 :l: 0.014
2.465 i 0.392 4.522 :l: 2.008

 

 

0‘93

 

 

 

 

 

 

Table 8.2: Fit parameters for E’ to Pk, mapping.

8.5 Response vs. PM

To accommodate the DOFIX corrections to the cryostats, the CAFIX5.1 jet response
is scaled by the DOFIX CC factor. Using this and the mapping parameters above,
we translate the Rjet versus E’ data to R,“ versus PM. We fit RJ-et versus Pktusing

the same functional form that was used in CAFIX5.1,

R,.,(P,.,) = a + b - 111(1),.) + c . In (19,.)2 (8.9)

107

350

 

 

 

 

 

’9 .
83 ~ 0 cc k, JETS
I <> IC was
of 300— . EC was l
250 —
200?
~ ,9"
150-
l—
L.
100—
50—
O—ILLLIllllllllllIlllllllllllLLIIIlll[MLI
O 50 100 150 200 250 300 350 400

E’(GeV)
Figure 8.2: kl jet P versus E’. Straight lines were fit to the CC and EC separately.

108

We use a Monte Carlo point to constrain the fit at high momenta. We use the
same Monte Carlo point that was used in CAFIX5.1 except we multiply both the jet
momentum and the jet response by the DOFIX CC cryostat factor. The result of

the fit is shown in Figure 8.3.

 

O?

(195
0925
09

0875

 

lTIFflTIfTITTTIITTTTITII

085

0 CC DATA

TTTT

‘
s

Q

0825
0 EC DATA

UTrrI

0.8 * MC POINT

0775

 

 

0.75 l L l l l I l I l l l l l I I l l I I l l l l l 1
O 100 200 300 400 500

PK! jet (GeV)

 

Figure 8.3: Rm versus PM. The outer band shows limits on the measured jet response
for high momentum jets based on the region in parameter space defined by the
X2 = xfnm + 3.5 surface. This region corresponds to the 68% confidence region of
parameter fluctuations from the nominal values.

The data were fit for PM > 30 GeV. The fit parameters are shown in Table 8.3.

For comparison, the fit is shown in Figure 8.4. We also show the kl RM fit divided

109

 

Jet Response Parameters
Jig-c.m.) = a + b . ln(PM) + c - ln (PM)2
a b c
0.7174 2!: 0.0518 0.0399 :t 0.0233 -.0007 :l: 0.0026

 

 

 

 

 

 

 

 

 

Table 8.3: Fit parameters for Try jet hadronic response correction.

by the DOFIX CC factor (with PM also divided by the DOFIX CC factor) for shape
comparison with the fits for the cone algorithm. The single parameter errors show

one standard deviation uncertainties as calculated from the x2 = Xian + 1 surface in

the parameter space. XZ/d.o.f. = 0.650 for the fit.

8.6 ICR Correction

The cryostat factor, Fay, is intended to put the end calorimeter cryostats on the
same footing as the central cryostat. We wish to do the same in the ICR. To do this
we use transverse momentum balance in di—jet events. The method is similar to that

used to measure the hadronic response, but here, the central jet plays the role of the

photon.

8- 7 J et-J et Data

The jet-jet data used to determine the 7) dependent correction in the ICR to the jet
I'eSponse is taken from events passing the inclusive jet triggers (triggers requiring

One or more jets in an event). These triggers are described in Appendix A.

Here is a list of the criteria for kl jets in our jet data.

110

.1 0.96

 

(194

(192

(188

 

_
L—
L
_
_
_
_
)n-
_

Of?r
_
_
_
_.
_
P
-
._
_
)—
T"
_
_
_

(186
0.84 — K, JETS (R/CCf)
’93" __ 0.3 CONE
....... 0.5 CONE
0.82 ............. 0.7 CONE
7 ....... 1.0 CONE
0.8 f
1- i:

 

 

O78 1111111111 ILPLII lllllllllLlLLI 1141

O 100 200 300 400 500 600 700
Pjet (GeV)

 

Figure 8.4: Response fit versus jet PM. Rjet(Pkt) = a + b - ln(PM) + c - ln (P)2.

111

 

 

Data Sample Pm cut (GeV)
JET-MIN 30.0
J ET_30 55.0
JET-50 90.0
JET_85 120.0
J ET-MAX 175.0

 

 

 

 

Table 8.4: Second highest jet PT requirements for triggers.

2 1

We select events with low instantaneous luminosity, [I < 5x103°cm‘ sec’ .

We select events flagged by the MITOOL as having only one interaction.

Events passing a given jet trigger must be fully efficient for the second highest
PT jet [49]. This removes resolution biases in the forward region. A list of jet

triggers and the PT cuts are shown in Table 8.4.

There can be one and only one vertex found, with |z| < 50 cm.

We demand two and only two reconstructed jets (no third jet with PT > 15

GeV.

We demand at least one jet with [17,-MI < 0.5.

The missing transverse energy in the event, ET, must be less than 70% of

the leading jet PT, < 0.7. ET is the magnitude of the vector momentum

E'rl

necessary to balance the entire event in the transverse plane. It is defined by

 

ET = -\J (,2: P...)2 + (2”: P,.-)2 . (8.10)

i=1

112

8.7.1 Measurement of F,7

We correct the hi jets for the cryostat factor and correct the event ET using the
change in kjjet momentum. The relative jet response of the forward jet with respect

to the central jet, R"’ is measured as in photon events substituting the central jet

771808 I

for the photon:

 

re E ' if tr 1 ' t
Rméas(E”7) : 1 + ngcefzitalaje-fe (811)

In a uniform detector and at leading order, the momentum of the forward jet would
be given by P" = Pficcoshn. The ideal relative jet response, R2356, for the two jets
could be calculated using the jet response as a function of PM by

Rjet(P '16" €003,177)
Rjet(PCC)

 

REAP, n) = (8.12)

Thus, the 1] dependent ICR correction, f,,, is simply the factor needed to correct

Rmeas to Route -

Using the fit to RJ-M(PM), we compare Rm“, to R0016 in Figures 8.5 and 8.6.

To parameterize the correction factor, f", we look at 17 bins of 0.1 in the regions
-2-0< n <-0.5 and 0.5< 1) <2.0. For each bin, we plot the correction factor as a
function of the average PT of the forward jet in a given bin for a given trigger. We
fit these with a straight line and these fits are used to determine f,, as a function of
jet PT for each 77 (see Figures 8.7 and 8.8). After the correction is applied, Rm“,

agrees well with Rock (see Figure 8.9).

As previously mentioned, the CAFIX5.1 jet response has been corrected for the n

113

Rjot

1.05

0.95

0.9 ,

1.1

R 5,,

1.05

—L

0.95

0.9

1.1

R...

1.05

A

0.95

0.9

Positive 77

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

111111 11
3
77
PPn>956eV #T_
T I???
— =7. + +1 -
W51 1+1 _
_ + +
b....1....1....|
1 2 3
77
L P,,>17soev
141—«11*?
Ll’f +111 ‘
hLlIMII I I Iiillil
1 2 3
77

R jet

1.05

_h

105*-

.—L

0.95

0.9

 

_ Pn>60 GeV 1

___+—— - ‘11
+++

.1,»- “
1+ 1
+++

b—

E.
++i+j++++

-1

 

 

‘17 I I

I I 1 LI 1 I I I 1 LI I I

 

1 2 3
77

 

F Pu. >1 30 GeV
1- + __ _—-"—'_—“_

 

 

1 L I 1 I I I I l I l l l l

 

1 2 3

77

Figure 8.5: Response versus 1) >00 for jet-jet data.

114

Negative 7')

 

Pu>401+ GeV

 

 

 

 

1.05—

_1I

0.95 —

0.9

1.1

R1.

1.05

0.95

0.9

 

 

 

 

 

 

 

I w)! T-
1 1 1+ 1 111 1 1 1 1.1 1.1
1 2 3
77
_P,,>95Gev T—
"+iifl fl+Tl+il
1 +++ m++
P1 1 1 1 1 1 1 1 1 111 1 1 1
1 2 3
77
. P,,>175<3ev
+ __ _ _
:44? if-
j 1’1 ii
111111111111111
1 2 3
77

u
.1
-« 1x

R jet

1.1

1.05

1

0.95

 

 

 

 

 

 

 

 

P >60 GeV _
__ 12 + ___.I- ‘l
T 1_—-—-'i+TT+ -’
+ii1tti’“—T +++ + i
E H+ +++
1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 2 3
77
L Pn>130 GeV 1:
:- ___i1,_-r _
355511; ++++i ’l
1+ +
’1 1 1 1 1.1 1 1 1 1 1 1 1 1
1 2 3
,7

Figure 8.6: Response versus 7) <0.0 for jet-jet data.

115

u31.2

 

‘n=C16

 

.—
P

h—
"--.
..—
p—

 

 

11 11 111L1 11 11 11

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 100 200 300
pl(C€V)
.1,2
m “UEO'Q ,.--1
1»:
llllLllllllllJ
0 100 200 300
p1(GeV)
v1.2
u. {-71:12
1
11 11 L111.f1‘14 L171
0 100 200 300
91(CeV)
o1.2
u 1-71“1.5
3.; ........ Q ......... 1' ...........
1 —- V
1J_l 1111111 [1 11
0 100 200 300
pr(GeV)
91.2
h.
=1_8
r-fl
1-
1 .
1J111L11411411
0 100 200 500
91(Gev)

Figure 8.7: Correction factor F,1 as a function of central jet PT for positive 17. The
SOIid straight line is a fit to the data. The dotted line is the CAFIX5.1 correction for

O~7 cone jets.

Positive 17

 

uf1'2

 

 

 

 

 

 

 

 

 

 

”77:0.7
1 »_.r+n
1 11 1 11 1 11 1 l1 1 1
0 100 200 300
P1(CeV)
912
0. .‘n=1 0
_ 1 ..... 1 _1
1’_”.
1 1 11 1 1 11 1 11 1 11
O 100 200 300
pY(GeV)
.1.2
u. _ "=1.3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1
1 1 11 1 1111 11 1 ll 1
o 100 200 300
P,(GeV)
.1.2
_‘n-1.6
1111. 11
1_+"Y ........ y ..............
111111111111ll
o 100 200 300
P,(GeV)
.1.2
u. P1n=1.9
-11 1
1 L; ....................................
11 1 11 1 11 1 L1 1411 1
o 100 200 300
P,(GeV)

116

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
 

 

 

 

 

 

 

 

 

'1.2
u _‘n=CLB
1 ::“¥‘
1 11 1 11 1 11 1 11 11
0 100 200 300
pr (GeV)
r1,2
u t n-1.1
1—
1 11 1 11 1 11 1 11 11
0 100 200 300
p1 (GeV)
o1.2
-n=1.4
MW.
1 —— 1}
11 1 1 11 1 1 11 1111 1
0 100 200 300
P, (GOV)
«1.2
h- r- "31.7
1 ;; ......
11LJ11 11 1411 11 L111
0 100 zoo 300
P1(GeV)
91.2
n _n=20
r
1 ......
1 11 1 11 1 1111 11 11
0 100 200 300
Pt (GeV)

Negotive 77

 

 

 

     

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

1 .............. .. ..............
L 1 l l 1 1 l 1 1 1 1 l 1 1 1 1 1 1 1 LL; 1 1 1 1 l 1 J 1 l 1 1 1 1 l 1 l 1 1 l 1 1
0 100 200 300 0 100 200 300 0 100 200 300
p, (GeV) p, (GeV) p, (GeV)
.1.2 .1 2
u. __ n=1.0 u. __ n=1.1
11*" 1»;- 1
1 1 i l 1 l l l l 1 1 l 1 1 1 l 1 1 1 1 l 1 1 1 l l 1 l 1 l l l 1 1 l l l 1 1 1 1 11
0 100 200 300 0 100 200 300 0 100 200 300
P, (GeV) P, (GeV) P, (GeV)
'1-2 I1.2
‘L 171:1.2 11 ~n=1-3
>- 1—
1 .“1".,__-'—‘r‘"'—"—_1 1 _ - ........... ..
111111.:1‘}-111_L11 141_1111111“1"j;1-11 11111114111111
0 100 200 300 0 100 200 300 0 100 200 300
P, (GeV) P, (GeV) P, (GeV)
.12 .1.2 .12
“ ~n=115 ‘“ ..n=1.6 “ _n=1.7
T7 .................................... ' 1. "
“ ¢ 4 ¢ ' e A. 1 '_ ..... “cw-11w: ---------- _# "" ' ‘
1 _ l 1 >-—- + V 1 — f Y Y T
11111L41111111 1’1L11111111114J 11111111111111
0 100 200 300 0 100 200 300 0 100 200 300
P, (GeV) P, (GeV) P, (GeV)
.12 .1 2
11 _ ”=19 ‘L _ n=2.o
1 1—
1 l l l 1 l L L l l l l 1 1 3L4 1 1 L l l 1 l l l l l l I l 1 LI 1 l LL14
0 100 200 300 0 100 200 300 0 100 200 300
P1 (GeV) 9. (GeV) 9. (GeV)

Figure 8.8: Correction factor F" as a function of central jet PT for negative 17. The

Solid straight line is a fit to the data. The dotted line is the CAFIX5.1 correction for
0-7 cone jets.

117

Rje1

Ric!

.J

0.95—

0.9

1.1

1.05

.J

0.95

0.9

1.1

1.05—

_b

0.951-

0.9

 

 

 

 

 

 

 

 

Pn>4o GeV 0 —
1111111111$1111 1111111 1 1
1 14 1 1 1 J 1 L 1 1 1 1 1 1
1 2 3
77
_ P,,>95 GeV 1T_
1—
_ + #:1141141 +1—
W:*‘*
'- 1 1 l 1 1 l 1 l 1 1 L 1 1 l 1
1 2 3
7?

 

IP,2>175 GeV

Wrfi 141‘:

 

 

l

l

"' I
1 l 1 1 1 1 1 1 1 1 1 1 1 L 1

 

3
77

1 2

1.1

Rjet

1.05

.__I

0.95

0.9

1.1

R jet

1.05

0.95

0.9

 

Pn> 60 GeV

——1

1

1.—

1.1111»;

b

#321:+—+ir+

W 1
1

h-

.—

 

 

11L 11L111114111

 

 

 

 

 

1 2 3
77
_ Pn>130 GeV
_ +
_ + M11
+11:t— 111-1+”
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 3
77

Figure 8.9: Response versus 1) after 1) dependent corrections.

118

dependent factors (cryostat and ICR) using 0.7 cone jets. Therefore, the corrections
derived here will have no bearing on RJ-et versus E’ . They can, in principle, effect the
Rjet versus PM fit via their effect on the mapping of E’ to Pkt(kl jets are corrected
for the offset, cryostat factor, and ICR dependencies prior to mapping). This effect

on the fit is negligible as seen in Figure 8.10

 

Rjet

(196

C194

C192

(19

(LBS

(186

(184

 

C182

....... no 77 cor

[IlTllllrlllffllflflffflllllIlTIf

(18

 

 

 

0.78 l i l l l l l J 1 l l l l L l l l L l l I I L 1 J J l l l l l 1 J 1
O 100 200 300 400 500 600 700

PK! jet (GeV)

Figure 8.10: Response fit versus jet E with and without the ICR correction.
Rje¢(E) = a + b - ln(E) + c - 1n (E)2. The two curves are virtually identical.

119

8.8 The Low ET Bias

The minimum ET reconstruction threshold for 0.7 cone jets is 8 GeV. The jet
reconstruction efficiency for this threshold does not reach 100% until 20 GeV. This,
combined with a steeply falling jet ET distribution, leads to biases in the jet response

measured using the MPF method.

To remove this bias, the jet response was measured as a function of ET7 (instead

of E’) with no jet requirements. The bias is estimated using

 

Rbias : RJet(2 l jet) (813)

1
RJet(no jet required)

where the numerator is measured as described in Section 8.1 with the jet required to
be in the CC. Since the denominator has no jet requirement, the hadronic recoil is
unrestricted and may lie in the BC or ICR making the numerator and denominator
inconsistent. To reconcile this, Rm, is normalized to unity for ET, > 20 GeV(where

the reconstruction efficiency for jets is 100%).

The jet response, RM, is corrected in the following way. First, the 0.7 cone jets
(in the CC) are corrected by the inverse of Ru“. Then, the event missing ET is

corrected for the change in the 0.7 cone jet momentum, and Rjet is measured with

the corrected Er-

The three lowest points in Figure 8.3 have been corrected for this bias. The large
error bars reflect the uncertainty determined from a Monte Carlo simulation where

the resolutions, efficiency and reconstruction parameters were varied.

120

8.9 Low Pkt Jet Response

In this study, we included kl jets with PTJ-et > 2 GeV. We hoped to avoid the Low
ET bias described above because this threshold is considerably lower than the 8 GeV
threshold used for finding cone jets. Unfortunately, it is difficult to extract a hard
2—to—2 process involving a photon and a jet at low momentum. When the jet response
is low, a jet’s position resolution is also poor. A jet and a photon resulting from a
2-to—2 process will less likely be found back to back if the jet response is low than
if it is high. This is the case for low energy events as demonstrated in Figure 8.11

where Ad), jet (A45, M = |¢7| — |¢jet|) is shown for low and high momentum kl jets.

In addition to this, we see that for ET7 < 20 GeV, the lst, 2nd and 3rd jets
appear to have similar PT distributions making it difficult to differentiate between
jets coming from the hard process and spurious jets reconstructed from underlying
event and noise. Figure 8.12 shows the PT distributions of kl jets (excluding k J_ jets

reconstructed from the photon) for a range of ET,.

Some attempt was made to pronounce the structure of these events. We tried
loosening the back-to-back cut and allowing (in addition to the leading jet) the
2nd or 3rd jet to balance the photon. While this was effective in unbiasing the
jet response, it wasn’t very useful in achieving the ultimate goal of jet momentum
calibration because it also allows events where more than one object balances the
photon. In addition, questions are raised as to how to treat jets in such events where

it is difficult to discern between a hard interaction and underlying event and noise.

121

 

 

O.25»— — ET7 > 20 GeV ——*
P ------ ET, < 20 GeV
02— A
0.15—

 

0.1—

0.05 —

 

 

 

 

O .1 .1 .1 J 1-4-4.4-1-1‘1'd‘-1-‘I-1-- 1 1 1 1 l in 1 l 1 1 1 l 1 1 1 l 1 1
1.2 1.4 1.6 1.8 2 2.2 2.4 2.5 2.8 3
v-KTAso

Figure 8.11: Act.7 jet normalized distribution for kl jets (Aqfi, M = |¢7| — |¢jet|).

122

 

 

7000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:— 100ev<E,,<150ev 40001 15GeV<E~<2006V
6000 E— 3500 :—
5000 F_ 3000 :—
E E
4000 E- 2500 f
I 2000 P .- 1
3000 :— E— f '.
: ;- 1500 r . 0.7.:
2000; _ 10003—
1000 I- 7;- '= 500 :— ? J'- I.
O :4.:I;i‘ L .1.:'l':'J_-‘.L--l.-f‘l- Jo 4-L_L_l_ QE 5);“ 11': l 1 . l'-1.':;'_"_r-.J...1:_‘1.T-J-‘r-1-JL,
0 20 30 40 0 10 20 30 40
EI (GeV) ET (GeV)
1400 :- 20 GeV < 5,, < 25 GeV 6000 :_ 20 GeV < E, < 25 GeV
1200 E- E J1
L' 5000 :-
1000 :- I
; 4000 E-
800 _— C
_. l-
. 3000 -
600 _— ...} E .
400;— a 2000;- w
: ’ t .3
200— "'5" ‘j fru'di""u-_ 1000: ; . i. , , - ,
’ ‘ -° 5’- "1- - {Um-2.. ‘ "--.
0 . LL:L-1:' 1., 1 1 .L'r- Eff-101.. 1..l I‘I‘Lflu 1:1 L.1_J-1"I Iii—1.3 ‘1---1.. . 1 1 1 I-
0 10 20 30 40 0 10 20 3O 40
E, (GeV) E, (0ev)

Figure 8.12: Er distribution of kL jets. Solid lines show ET, distributions and
dotted and dashed lines show ET distributions of the lst, 2nd and 3rd jets.

123

So, although we do not have a bias due to the reconstruction threshold, it appears
that we do introduce a topology bias at low energy by requiring the leading jet and
photon to be back to back. This causes us to reject events where the jet’s position
and/or momentum is mismeasured due to low jet response and we bias ourselves

toward higher jet response.

We do not apply a correction to the low PT kl jets as is done for cone jets. Unlike
the low ET bias for cone jets, the topology bias is apparent only when we try to
measure the response using the MPF method. Because the CAFIX5.1 jet response
at low energy was derived using data with no jet requirement (Equation 8.13), it is
considered to be free of this topology bias. We use the unbiased jet response derived
for CAFIX5.1 and assign an additional error due to the effect of unbiasing. The error

bars on the three lowest energy points in Figures 8.3 and 8.13 reflect this error.

The jet response is fit for PM above 30.0 GeV and, therefore, the low momenta
data do not affect the result of the fit. The low momenta data diverge from the
extrapolated fit (see Figure 8.13a). To correct for this, we fit the function, f(:1:) =
1+ a(a: — 35)2, to the ratio of the extrapolated fit to the low energy data, Re_f/R(0w.
Dividing the extrapolated fit by this function, Re- f/ f (:6) provides a jet response
curve for the low energy data which matches both slope and function at 35 GeV
with R“, (see Figure 8.13b). We match the fits at 35 GeV instead of 30 in order to

get a smooth match.

124

 

 

 

 

 

 

 

 

 

 

Dig
O.85~—
0.8—
0.75—
’ (G)
0.711111111lllllllLL14llLL4]111111114.L1_LL1J_1lll
10 15 20 25 30 35 40 45 50
PKHd<CeV)
“.2
0.85—
0.8—
0.75—
L (b)
0.7lLlllllllllllllllllllllllllllllllllllllllLll

10 15 20 25 30 35 4O 45 50
PK! jet (GeV)

Figure 8.13: Low momentum jet response vs. PM. (a) The solid line is the extrapo—
lated fit. Dotted lines depict errors on the fit. (b) The solid line is the jet response
used to correct jets. The dashed lines show the errors (as a function of PT).

125

8.10 The Jet Response Errors

8.10.1 Errors and Correlations of the RM Fit

To determine an error for the response function, a surface defined by X2 = Xian + 3.5
is mapped out in parameter space. For three parameters, this contains a region
with a 68% probability for parameter fluctuations [54]. The points lying on this
surface are then mapped back onto the jet response versus momentum plane. At a
given momentum, the error is determined by the parameter set giving the greatest
deviation from nominal jet response. The high and low errors are calculated for
11 points, (10, 20, 35, 50, 75, 100, 150, 200, 300, 400, and 500 GeV). The error is
interpolated for energies between these 11 points. The result for the k_L jet algorithm
is shown in Figure 8.3. The outer band represents the error on the fit to the jet

response.

The fit error described above gives the maximum deviation at each PM value
for all the fit parameters within the 68% confidence level. The parameter set that
gives this deviation at one value of PM does not necessarily induce the same effect at
another value and it is highly unlikely that one set of parameters will produce either
of the error curves shown in Figure 8.3. We do expect, however, that the errors for

two points close in PM will be largely correlated.

To quantify the correlations between different values of PM, we generate a corre-

lation matrix in the following way.

0 We map out a grid in parameter space defining the x2 S xfnm + 3.5 volume.

126

Each parameter set in this volume defines a response function contained within

the bands shown in Figures 8.3.

o The correlations are calculated for an 11 x 11 matrix. We 100p through all
the parameter sets in the volume and calculate response at eleven values of PM
(corrected for offset and n dependence) between 10 and 500 GeV. The matrix
elements are the standard correlation coefficients, r(z', j ), between the responses
measured at each energy value. r(i, j) is defined as:

= 25mm}: mime) — R—(Jj)_
[2&“(1240 — Rm)? 5mm» — mow ’

 

r(i,j) (8.14)

where N9,“ is the number of parameter sets in mapped out in the X2 S xfnm + 3.5
volume and Rn(z') is the response for the 1"” energy bin calculated with the nth

parameter set.

The correlation matrix for the jet response fit to kl jets is shown in Table 8.5.
Correlations are illustrated graphically in Figure 8.14 where four rows of the matrix
are plotted showing the error correlations relative to the errors at 35, 50, 100, and

500 GeV respectively.

8.10.2 Low Momentum Errors

For the error due to the unbiasing of the jet response (the error bars), 05, we used
the function, f (:r) = a(:r — 35)2, where a is defined such that the error decreases
from 3% to 0 from 15 GeV to 35 GeV. This comfortably accomodates the error bars.

This is added in quadrature with the errors on the extrapolated fit, Ue_f for the low

127

 

 

r35

0.75 7
0.5 ;
0.25 .

-0.25 j
-0.5 ;
-0.75 9

 

 

 

 

 

 

 

 

 

r100

0.75 i
0.5 i

1.;
0.25 .

.025 g --
-0.5 j
0.75 f

 

 

 

 

 

 

 

Figure 8.14: Error correlations for kl jet response fit. Error correlations are shown in
four slices from the full correlation matrix. The four curves show the point-to-point
correlation of fit errors relative to momentum values of 35, 50, 100, and 500 GeV
respectively.

128

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Correlations for Fit Error, 1:; Jets, Reco 12

P(GeV) 1 10 | 20 | 35 | 50 | 75 100 | 150 j 200 | 300 | 400 500
10 1.00 0.97 0.62 -032 -0.63 -0.56 -0.29 -0.06 0.23 0.37 0.45
20 0.97 1.00 0.77 -0.15 -0.57 -0.56 -O.36 -0.16 0.10 0.23 0.31
35 0.62 0.77 1.00 0.49 -0.04 -0.17 -0.20 -0.15 -0.06 0.00 0.03
50 -032 -015 0.49 1.00 0.82 0.67 0.42 0.24 0.04 -0.06 -0.12
75 -0.63 -057 -004 0.82 1.00 0.96 0.78 0.59 0.33 0.19 0.10
100 -0.56 -0.56 -0.17 0.67 0.96 1.00 0.92 0.78 0.56 0.42 0.33
150 -0.29 -0.36 -020 0.42 0.78 0.92 1.00 0.96 0.84 0.74 0.67
200 -0.06 -0.16 -015 0.24 0.59 0.78 0.96 1.00 0.95 0.89 0.84
300 0.23 0.10 -0.06 0.04 0.33 0.56 0.84 0.95 1.00 0.99 0.97
400 0.37 0.23 0.00 -0.06 0.19 0.42 0.74 0.89 0.99 1.00 1.00
500 0.45 0.31 0.03 -012 0.10 0.33 0.67 0.84 0.97 1.00 1.00

Table 8.5: Correlation matrix for error band in hadronic jet response correction for

kl jets.

error (high in jet P). The high error (high jet P) is the low error added in quadrature

with the difference between the extrapolated fit and the actual fit.

010w : V0§+U§_I

J03 +Uf2f—f +031],

 

and 0M9), = (8.15)

The correction to the extrapolated fit is applied as a function of momentum.
However, the uncertainty is applied as a function of PT rather than P to account for
forward jets whose momentum may be above 35 GeV but whose PT may be below

35 GeV.

8.10.3 77 Dependent Correction Errors

We apply a 0.6% error on ng and Egg. This is due to the 0.5% error on Fay added
in quadrature to the 0.3% error on F 6% / F 3y. No additional error need be considered

given that the DQFIX cryostat factors are known and definite.

129

 

 

77 Region Mean RMS N RMS/W
|n|<0.5 0.0028 0.0113 25 0.0023
0.5<|n|<1.0 0.0061 0.0101 25 0.0020
1.0<|n|<1.5 0.0083 0.0213 25 0.0043
1.5<lnl<2-0 -.0005 0.0186 24 0.0038
2.0<|n|<2.5 -.0146 0.0320 18 0.0076
2.5< Inl <30 -.0107 0.0500 11 0.0151

 

 

 

 

 

 

 

Table 8.6: Residuals from Figures 8.15 nd 8.16.

To measure the accuracy of the ICR correction, we apply the cryostat corrections
and the ICR correction and compare R4,...” to Ream. Figure 8.15 shows the fractional
difference. The distribution of these fractional differences is plotted in the 6 17 regions
shown in Figure 8.16. The mean, rrns, number of entries, N, and rms/x/N are shown
in Table 8.6. The correction is applied in the region for 0.5< In] <2.0. We assign
a 1% error to the correction based on these values and introduce an additional 77

dependent error that turns on at |77| 22.5 and increases linearly up to 3% at Inl =3.

130

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m7? -P,,>400ev
\ - -.-
g * +—o— + +_,_—o— -o- '0' +
0* + *fi H —o—' W -o—
l’ + + ++ +H *1
E
_O.1 l l l L l I l L L l L L l 4 I L l l l l L J L l L L L 4 LL
05 l 15 2 2.5 3
77
2 0.1
{0 :P,2>6OGeV
0: : + _._
<1 0"." .I + 1: . -o- ... 31+ . +
- -o-
_ + _._
_ -o— +
_O.1’-1 L L l I L _L L L L l I l J l l l l l l l l J L l l 1 l l L
0.5 1 15 2 25 3
77
g 0.1
m3 *P,2>95CeV
E : + ++
_ ' —o— a: :"
.. +++
_ —o—
_O.1bl l l L I l l 1 L l l l l l I l l 1 L L l L L 1T1 l _L L J
05 l 1.5 2 25 3
77
g 0.1
0:3 * P,,>130 GeV
7
\ t
CK _ -o- -o—
<1 + -O- ++++
: —o—
_O.1 l l 4 l L l l L I L l l L 1 L l 4 14L 1 L l L I l I L l l
05 1 15 2 25 3
77
g 0.1
m8 - P,,> 175 GeV +
\ .
CE
<1 0%.: + .t—r'O'a- —o—
_ + -o- _._ +
” + + 4—
—o.1r1111'*'1111111154111'111111111
05 1 15 2 25 .3
77

Figure 8.15: The fractional difference between Rm,” and R6076 for partially corrected
Jets- AR = (Rmeas ’ Realc) / Route-

131

 

 

 

 

 

 

 

 

 

 

_, Entries 25
6 __ 77<0.5 Mean 028005—02
- [RMS 0.1141E-01
: ovr1w 0.00005+00
4..
2:
OllllllfllflfllhjllfllllllL
—O.1 —0.05 0 0.05 0.1
AR/Rcolc
Entries 25
6 1.O<77 <1.5 Mean 0.84806—02
RMS 021486-01
oerw 0.0000900
4

IIIIIIITJII

   

 

 

 

 

 

 

 

 

 

O
—0.1 —0.05 0 0.05 0.1
AR/Rcmc
_ Entries 25
6— 2.O<77<2.5 Mean —0.1433£-01
E RMS 0.31906-01
ovnw 7.000

4r

2E-
0 1111 [11151111411
—O.1 —0.05 O 0.05 0.1
AR/Rcolc

 

Entries 25
6 0.5<77<1.0 Mean 0.6000E-02
RMS 010075-01
ovr1w 0.00001: +00

 

 

4:.
lITTlrrTIlT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2
OLLLLLIIIH thllllLl
—0.1 -0.05 0 0.05 0.1
AR/Rcc1|c
__ Entries 25
6 __ 1.5<n<2.0 Mean -0.3333£—05
- RMS 0.18796-01
: ovr1w 1.000
4:“
2L
0
—0.1 —0.05 0 0.05 0.1
AR/RCOIC
_ Entries 25
5 _ 2.5<n<3.0 Mean -0.2460£—01
— RMS 0.2809E—O1
: oerw 15-00
4.—
2:-
OflfllflnlfllflLfllLllll
—0.1 —0.05 0 0.05 0.1
AR/chlc

Figure 8.16: The distributions of fractional differences between Rm“, and Rock.

132

Chapter 9

K 1 Jet MPF Closure

The missing transverse energy projection fraction (MPF) method is tested using
the Monte Carlo v-jet events which are processed through a simulation of the D0
detector. kl jets are reconstructed from parton shower, hadrons, and calorimeter
information. The photon energy, E, found at the calorimeter level is corrected to

E, prior to detector simulation, and the event ET is adjusted.

A kjjet momentum correction is derived by applying the MPF method to the
Monte Carlo calorimeter information. The jet correction is applied to calorimeter
level kjjet momentum, Pam“, and the corrected momentum is compared to the

ptcl

nearest kl jet found at the particle level, Pk, . Closure is obtained when the corrected

calorimeter jet momentum agrees with the hadronic jet momentum,

Ji— = 1 . (9.1)
The closure test was performed using cone jets and closure was attained within

133

errors [45, 46]. As a reference we include comparisons to 0.7 cone jets in our analysis.
We attain closure in the central region for kl jets, but we see a small excess in the
forward region. We attribute this excess to misclustering of energy in calorimeter
jets. We are unable to measure this effect in D0 data, but we can estimate the

uncertainty.

9.1 The Data

We use Herwig (version 5.7) Monte Carlo 7-jet data generated with underlying event.
Monte Carlo data is generated with 7-jet ET thresholds of 7, 15, 30, 75, 150,
300, 500 and 700 GeV. It is processed through the SHOWERLIB [48] D0 detector
simulation and reconstructed using version 12 of the reconstruction package (RECO
v12). Then, we reconstruct kj jets as described in Chapter 5 with the requirement
that the transverse momentum, PT, must be above 4 GeV for samples generated

with ET threshold at 7 GeV and above 8 GeV for the rest of the sample.

9.2 Monte Carlo Jet Corrections

9.2.1 Monte Carlo Underlying Event Offset

The Monte Carlo data does not include the effects of noise, pile-up or multiple
interactions, but it does include a Monte Carlo physics underlying event. Therefore,

we must subtract an offset only for the Monte Carlo underlying event.

The offset due to physics underlying event for kl jets was seen to be approximately

134

 

Underlying Event Densities

CC EC

Calorimeter 0.57 0.57
Hadron 0.53 0.50

 

 

 

 

 

 

 

 

Table 9.1: Herwig v5.9 underlying event energy density.

30% larger than it was for cone jets. We estimate the offset for kl jets in Monte
Carlo data by multiplying a density by the 0.7 cone area and then scaling up by 30%.
The measured energy density due to underlying event was measured in HERWIG
v5.9 data generated with and without the underlying event present. These densities
were derived by measuring the average difference of energy in (75 rings in the detector
(divided by the area in 77 — <75) with and without the presence of underlying event.
The physics underlying event in HERWIG versions 5.7 and 5.9 are the same. The

underlying event energy densities are shown in Table 9.1.

9.3 Monte Carlo Jet Response

The jet response is measured as described in the previous chapter except we do not
apply the ICR correction, F", and we only focus on the central (|77| < 0.7) and

forward (1.8 < I77| < 2.5) regions.

9.3.1 Monte Carlo Cryostat Factor

First, we determine the cryostat factor, Fm, = Rf: / R129, for the Monte Carlo data.

Figure 9.1 shows the cryostat factors derived using 11:; and 0.7 cone jets to define E’.

F35: = 1.039 :1: 0.004 and F“ = 1.033 :1: 0.004 agree within statistical errors.

cryo

135

 

 

 

 

 

 

 

 

 

 

 

 

LLU —
~ 0 Ktjet Fcryo
E]
1.08 _ Cone7 Fcryo
1.06 —-
. :3 :3
_ C]
1.04 _____________________ g _____ Q ________________________________________ l _____
. ’ l
1.02 — .
1.
1 I L L L I l l l l l l l l ML 1 l 1 l l l l l l l L l l l
0 100 200 500 400 500 600

E

Figure 9.1: Monte Carlo Cryostat Factor. Circles are for kl jets and squares are for
cone jets. Solid line is a fit to constant for the kl jet points; dashed line is a fit to
constant for the cone jet points. Errors are statistical only.

136

 

Algorithm a b c x2 / do f
Ki 0.794 :1: 0.013 0.0244 :1: 0.0044 -0.0014 :1: 0.0004 18.8/16

 

 

 

 

 

 

 

 

Table 9.2: Fit parameters for RM vs. PM in Monte Carlo data.

9.3.2 Jet Response vs. kl Jet Momentum

The jet response, RJM, is obtained by correcting the EC jets by Fargo, adjusting the
event ETby the change in jet momentum and applying the MPF method described
in the previous chapter. The average RJM is measured in bins of E’ ranging from 10
to 450 GeV for central jets and 100 to 600 GeV for forward jets. The average k_L jet
momentum (corrected for the offset and cryostat factor) is also measured in these
E’ bins. Then, the average RJM values are plotted versus the average PM values and

the functional form,

12,-..(E) = a + b . ln(E) + c - 7712(5) , (9.2)

is fit to this data (Figure 9.2. The results of the fit are shown in Table 9.2.

9.4 Monte Carlo Closure

We apply the corrections described above to kl jets reconstructed from the Monte
Carlo calorimeter information. First we subtract the offset from PM then we divide
by the Monte Carlo cryostat factor and Rjet. We match the calorimeter (meas) and
particle (ptcl) jets to within a distance of 1.0 in 77 — (75 space. Figure 9.3 shows

the ratio of the corrected calorimeter jet momentum, P738“, to the corresponding

137

 

R jet

092*-

0.9 — #1

 

 

C188

 

(186
P 0 Ktjet CC
5 U Ktjet EC
0.84L

 

 

11LL4LLLIJLLIIILLL11111111111111llLLLLlLLLLIllIl

0 50 100 150 200 250 300 350 400 450 500
P7,,(CeV)

 

Figure 9.2: RIM vs. PMin Monte Carlo data. Circles represent CC jets and squares
represent EC jets.

138

particle jet momentum, Pfttc’, for calorimeter jets in the CC, Inmeasl < 0.7. The

average closure is determined by a constant fit and found to be 1.002 :1: 0.001
Figure 9.4 shows the ratio of the corrected calorimeter jet momentum, Pam”,

to the corresponding particle jet momentum, Pffc’, for calorimeter jets in the BC,

1.8 < Inmeasl < 2.5. The average closure is found to be 1.015 21:0.003. No out of cone

showering correction, Rome, was applied to cone jets and this can easily explain the

deficiency in Figure 9.4.

It is arguable whether the deviation from unity of the closure ratios (0.2% in the
CC and 1.5% in the EC) is significant, and there is no evidence of further excess

going farther forward as is shown in Figure 9.5.

The most plausible explanation we have for the small excess in the forward region
is that it is due to misclustering, energy incorrectly transferred from one jet to
another due to calorimeter showering. We have no direct way of determining this
effect from data. It is reasonable to expect, however, that misclustering should be a
second order effect compared with the out-of-cone showering losses observed in the
case of cone jets. This is because misclustering would only occur when two or more
jets are close to each other and by using vector summed momentum instead of scalar
summed energy, the jet PT contribution from the fraction of the shower at the edge

of a jet is greatly reduced.

As a result of this study, we assign an error of 1% in the CC, |77| <1.0, increasing
linearly to 1.5% at I77| >20, and then to 5% at 77:30. Above this the error remains

flat at 5% (see Figure 9.6).

139

L06

 

 

 

 

 

i5. .
\ 1-
60. 1.04—
1.02—
5-111- 1-1-1.1.: -1113.-- ..........
+I 1 177 7 l 1 ' q
0.98—
. 0 CC KTJet
0.96— 0 CC 0.7 Cone Jet (E)
LLLLALLLLLLLLLLILLLLLLLJLLLILllLllllLllllllLllLLLl

 

O 50 100 150 200 250 300 350 400 450 H500
P”.
jet

Figure 9.3: Monte Carlo Closure in CC. The ratio of the corrected calorimeter jet
momentum to the corresponding particle jet momentum in the central region. Circles
are for Is; jets and squares are for cone jets. Energy is compared for cone jets. The
dashed line is a constant fit to the k_L jet closure.

140

L06

 

et

sq

 

 

Eu 1—

Q.

\~ 1-

.2

§ >-

E 1—

Q_ L04
1.
_ 0

L02—-

- _______________________________ 9. .................... . ....... 1:3 ..........
. + 1’

 

 

1' m
0.98— [A] #3 Ci] %
. 0 EC KT Jet
0.96— 0 EC 0.7 Cone Jet (E)

 

 

llllllLLlLLLlllllllLllLlllllllllllllllllllllLLMLl

0 50 100 150 200 250 300 350 400 450 tl500
P".
jet

 

Figure 9.4: Monte Carlo Closure in EC. The ratio of the corrected calorimeter jet
energy to the corresponding particle jet energy in the forward region. Circles are for
k 1. jets and squares are for cone jets. The dashed line is a constant fit to the ki jet
closure.

141

L1

 

ptcl
/ P jet

.4

21.075

P

meos
I I TM I f I I I

b
01
I

1.025

Tfirrerfir
+

 

 

 

 

 

 

0.975—
0.95»—
0.925—
" OVEC KTJet
0.9-1441111111111111111llllllLLl_LllllllllllLLLLLiLLLL
0 50 100 150 200 250 500 550 400 450 500

ptcl
P jet

Figure 9.5: Monte Carlo Closure in EC. The ratio of the cOrrected calorimeter jet

energy to the corresponding particle jet energy in the far forward region, VEC,
defined by 2.5 < Inmml < 3.5.

142

L1

 

Rn

1.05 ... ...........

__ Nominal

......
7. ..
.....
aaaaaa
‘. .-
......

.. ,-

a
.......
....................................................

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

 

ooooooooooooooooooooooooooooooooooooooooooooooooooooo
. a.
.......
. o.
......
.......
.....
.e '-
. o
.....

0.95 — ...........

 

0.911 1

 

Figure 9.6: kl algorithm dependent correction, RM. Errors are shown as dotted

lines.

143

 

Chapter 10

k_l_ Momentum Calibration

Summary

To recapitulate, the method for correcting kl jet momentum uses the following re-

lation

Pptcl _ 3’35” — E007. 5, PT)

8 - 7 10.1
J t Rjet(777 P) ( )

The calibration is an average correction, integrated over all jet quantities except
energy and pseudorapidity. Jets pointing to (,0 cracks, or with average characteristics

different from those in the 7-jet sample, may need a different correction.

The correction is accurate for 1:; jets with PT >15 GeV and |77| <3. The poor
knowledge of the calibration in the range PT <15 GeV is taken into account with a

rapidly increasing error below this threshold.

The calibration is based on Run Ib data taken in p75 collisions at \/E = 1.8 TeV.

o Offset: the total offset, E0(77, LI) has contributions from physics underlying

144

event, 0,“, and an offset due to uranium noise and pile-up, 027,. One and Ozb
were derived from a sample of Monte Carlo events with DQ) data events over-
layed. One is parameterized as a function of 77. Above |77| >1.0, we apply a
correction based on the 77 dependence of the CAFIX5.1 correction but normal-
ized in the central region to our result. Ozb is parameterized as a function of
77, L, and PT. For |77| >1.0, we apply a correction based on the 77 dependence
of the sample generated at 30< PT <50 GeVat .C = 5 x 1030pb"lsec‘1 but

normalized in the central region as a function of C and PT.

Response (77 dependence): the cryostat factor is adjusted for the DOFIX
corrections, Fc’l’y20.986:l:0.006 and ng=0.977:l:0.006. The ICR 77 dependent
correction was derived using jet-jet data. It is applied to 77 bins in units of 0.1
and parametrized as a function of PT in each bin. We assign a 1% error to
the correction based on these values and introduce an additional 77 dependent

error that turns on at |77| =25 and increases linearly up to a 3% at |77| =3.

Response (energy dependence): the CAFIX5.1 jet response as a function
of E’ was taken and multiplied by the DQFIX CC factor of 1.0496 to accom-
modate this correction in the k; jet data. E’ was mapped to kl jet P and the
jet response is fit as a function of kl jet P above 30 GeV. Below 35 GeV jet
momentum, there is an additional correction to accommodate the deviation
from the extrapolated fit. Below 35 GeV jet PT, there is an additional error to

account for the uncertainty in the jet response (see Figure 8.13b).

Misclustering: No correction is applied, but an error is assigned to accom-

modate misclustering of energy.

145

0 Monte Carlo: The correction is derived from a HERWIG sample processed
through SHOWERLIB and reconstructed with RECO V12. At present, there is

no correction for variations in the ICR region.

10.1 Summary Plots of Corrections and Errors

In this section we provide some summary plots to illustrate the size of the jet correc-
tions and errors as a function of jet PT and pseudorapidity. For the following plots,

lsec—1. Figures 10.1 - 10.3 show the correction

luminosity was set to 5 x 1030 cm"
and errors as a function of kl jet PT for 3 different 77 regions. In the 77:12 plots,
Figure 10.2, the EM, CH, FH, and ICR fractions were taken as averages of values
found in D0 jet data. The fluctuations at large energies are due to low statistics
in narrow PT bins. Figures 10.4 and 10.5 show the full correction and errors as a

function of 77. Here also, the EM, CH, FH, and ICR fractions are taken as averages

of values found in data.

146

Jet Corrections and Errors

(Jet 77 = 0.0)

 

 

 

 

 

 

 

 

 

 

 

 

L 1.15
.9
U _
E 1.1-
C -
.9
5 1.05—
a)
L .—
L
o
o 1—
- —— Nominol
0.95—‘ .............. High/Low
0.9 l l l l l l L L L l l l
102
Uncorrected Jet P, (GeV)
; 0.15
o _
L
L- _
11.1
B .
C
o 0.1»—
153 1-
o
O 1—
L: _
1 __ High Error
0.05—
. .............. Low Error
’— 1 L l l l L l L L 1 l l
O 2
10

Uncorrected Jet P, (CeV)

 

Figure 10.1: Corrections and Errors for "Ktjet =0.0. Top: Nominal, high, and low
correction factors. Bottom: high and low fractional errors.

147

 

Jet Corrections and Errors (Jet 77 = 1.2)

 

 

    

 

 

 

 

 

 

 

 

4E3 - “71$"
LE 1., _ ........................
c — .......................
.9 _ "
*6 _
0) ,.
t ... ....
8 1 —
_ Nominol
_ ................ High/Low
0.9 - 1 1 l L 1 L J_1 L l
20 30 40 50 60 70 809000 200 300
Uncorrected Jet P, (GeV)
L. 0.15
o 1.
L
L b-
L1J
E) _
c
.9 0.1 _
4(4) 1-
O F-
L: _
_ High Error
0.05 -
_ ................ Low Error
r- vim—1
O p L l L L l l l l l J l
20 30 40 50 60 70 809000 200

Uncorrected Jet

Figure 10.2: Corrections and Errors for 777mg, =1.2. Top: Nominal, high, and low

correction factors. Bottom: high and low fractional errors.

148

300
P, (CeV)

Jet Corrections and Errors (Jet 77 = 2.0)

 

 

 

 

 

 

 

 

 

 

 

L
B
u _
0
LL
c
.9 I
8 1"
t
O _
Q o
_ Nomlnol
....................... High/Low
08 1 1 1 1 1 1 1 1 l
20 30 40 5O 60 7O 80 90100
Uncorrected Jet P, (GeV)
1. 0.15
o
L. 1'
L L-
11.1
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5 01~
*g t
L: _ High Error
005 2 Low Error
. 4....
1.
O L L l l I I I l l
20 30 40 50 60 70 80 90100

Uncorrected Jet P, (GeV)

Figure 10.3: Corrections and Errors for 77;“th =2.0. Top: Nominal, high, and low
correction factors. Bottom: high and low fractional errors.

149

Jet Correction 0nd Errors v.77 — (20 GeV Uncorrected P, Jets)
0.1

 

 

_ High Error

........... Low Error

 

 

 

 

 

 

 

Correction Foctor
:
Froctionoi Error
0
O
U"
I I I I I I I I I

 

 

 

 

 

 

 

 

08 I I I I I I I I I I I O I I l I I I L I I I I
-2 0 2 —2 0 2
. 77
Correction Foctor Totol Error
b P 0.01 ——.___ ___,_..__
0.02 _
O I I I I O I L L —1" I I I “I- I L L
2 —2 0 2
77 77

 

Cryo Foctor

 

 

b0.005

 

 

 

 

 

 

 

 

Residuol Bios Misclustering

Figure 10.4: Corrections and Errors versus 77mm, kl Jet PT = 20 GeV. The to-
tal correction and error are both shown as well as the eta dependence of several
individual components of the jet scale error.

150

Jet Correction ond Errors v.77 - (100 GeV Uncorrected PT Jets)

 

 

      
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 1.25— 5 ~ H. h E
P r t u rror
5 _ 11.1 0.05 9
LL M 6 f ............. Low Error
C .- C r.
.9 1 — .9
o : ‘5 —
(1L) _ E 1—
5 1 . . 1 1 1 1 1 1 LL 0 1 . 1 1 1 1 1 1 1 .
0 —2 O 2 —2 0 2
. 77
Correction Factor Totol Error
b 0.01 P 001...: __,.._._.
O 1 1 l O11I1111I’1111l1111‘I1111IL1
2 -2 —1 0 1 2
77 77
Cryo Foctor
b b 0.05
0.005 _
7 high err _
' ............. low err _
O I I 1 I I I I l I 01 I I I I I L I I I
-2 0 2 —2 0 2
. . 7i . . 7?
Resuduol BIOS Misclustering

Figure 10.5: Corrections and Errors versus ”Ktjet: kl Jet PT = 100 GeV. The to-
tal correction and error are both shown as well as the eta dependence of several
individual components of the jet scale error.

151

Chapter 11

R32 Preliminary Results

Now that we have calibrated the It; jet momentum, it is possible to make a very
preliminary experimental measurement of R32 using the kl jet algorithm. Shown in
Figure 11.1 is a measurement of R32 as a function of Hm using D0 data. Jets are
corrected for the momentum scale, and the errors reflect statistical uncertainty only.

H73 is defined as the sum of the PT of the 3 highest PT Is; jets in an event,
3
HT3 = ZPT, . (11.1)
i=1

The number of jets in a given event is equal to the number of kl jets with PT, >
fem x HT3. R32 is measured as the ratio of events with 3 or more jets to events with

2 or more jets,
023 jets

_ 022 jets °

R32 (11.2)

Because we choose fan to avoid cases where only one jet passes the cut, virtually all

events have at least 2 jets. So R32 can also be thought of as the fraction of events

152

with 3 or more jets.

 

s;
O:

0.9 i=0.15

0.8 0 DO Doto

O HW Hodrons
OJ?
()6
(15

0A.

0J3

 

C12

 

 

OJ

IIIT][IllllIII]ITTT]IIITIYIIfIIITTITTrTII—rjfilITl

 

 

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIJIII

100 200 300 400 500 600 700 800 900
H13

 

O
C

Figure 11.1: R32, vs. Hm. Errors are statistical only. Errors in Monte Carlo Data
are the weighted statistical errors.

At this time, we have not made a comparison to an 0012 calculation. For com-
parison, the R32 is measured using Herwig Monte Carlo data (version 5.8) at the
hadron level. This is the same sample of events used to determine fcut = 0.15 in
Chapter 5. The Herwig data are consistently higher than the D0 data. However,
no systematic studies (other than the momentum calibration) have been performed

on the DC data. So at this point, it is extremely difficult to draw any conclusions.

153

 

Appendix A

Photon and Jet Triggers

A.1 Photon Triggers

The photon triggers we use were designed for direct photon measurements and span
the ET range from 6 GeV through 60 GeV. At Level 1 (the hardware trigger), all
photon triggers require at least one calorimeter trigger tower (0.2 x 0.2 in 17 x 45) to
have ET above some threshold. The thresholds used for various triggers are shown
in Table A.1. When an event passes a level 1 trigger, a list of towers satisfying the

level 1 criteria is sent to the Level 2 framework for further analysis.

The Level 2 software triggers have different requirements, but they all share
the same algorithm to identify photon candidates [56]. The algorithm begins by
identifying the most energetic cell in the 3rd layer of the EM calorimeter in a tower
that passed the level 1 threshold. The ET in the cells within An x Aqb = 0.3 x 0.3
is summed in the EM and FHl (lst layer of the fine hadronic calorimeter). To

determine whether or not this is a desirable photon candidate, the following criteria

154

 

 

 

 

 

 

 

Trigger Level 1 Level 2

Name Threshold Threshold

(GeV) (GeV)

GAM.6_ISO_GAM 2.5 6.0
GAM_14_ISO_GAM 7.0 14.0
GAM.20_ISO-GAM 7.0 20.0
EMLGIS 14.0 25.0
EM1-GIS.HIGH 14.0 40.0
EM1_ESC 14.0 60.0

 

 

 

 

 

Table A.1: Triggers used in the photon event selection. Additional ET cuts are
applied offline.

are imposed on this cluster:

0 The ET of the candidate cluster must be above the thresholds shown in Ta-

ble A.1.

o The hadronic energy of the cluster (contained in FHl) must be less than 10%

of the total energy.

0 The energy deposited in the EM3 layer must be between 10 and 90 percent of

the total.

0 The shower shape of the cluster in the EM3 layer is required to be consistent
with electron shower shapes in test beam data. This is measured by taking
the difference between the radial moments in 0.5 x 0.5 and 0.3 x 0.3 windows
around the axis of the cluster. The difference is required to be below some

value which varies as a function of 77.

155

o A cut, fm, is made to ensure that the photon is isolated from other activity,

Er=.4 _ Eduster
Eduster < fiso 1

 

(A.1)

where E”:4 denotes the energy contained in a cone of radius .4 (17 — 45 space).
fiso = 15% for all level 2 filters except GAM-6_ISO-GAM where it is set to

30%

A.2 Jet Triggers

The inclusive jet triggers were designed to accept events with 1 or more jets with
jet ET above some threshold. At Level 1 (the hardware trigger), there are two types
of jet triggers. One type requires a trigger tower (0.2 x 0.2 in n x (b) to have ET

above some threshold. The other type requires a large tile (0.8 x 1.6 in 17 x 43 or
4 x 8 in trigger towers) to be above some ET threshold. All of the triggers used
in this thesis required the second type (large tiles) except for the JET.MIN trigger
which requires a trigger tower. The thresholds used for various triggers are shown
in Table A.2. When an event passes a level 1 trigger, a hot tower list is sent to the
Level 2 framework for further analysis. For J ET.MIN, the hot towers are simply all
the trigger towers with ET > 3 GeV. For the large tile type triggers, the hot towers

are the ET weighted centers of the large tiles with ET > 6 GeV.
Below is a brief overview of the workings of the level 2 jet finder software package,

L2JETS, which identifies jet candidates.

1. L2JETS receives a hot tower list from the Level 1. The hot tower list is a list

156

 

Trigger Level 1 Level 2
Name Threshold Threshold
(GeV) (GeV)

 

 

 

 

 

 

 

 

 

JET-MIN 3.0 20.0
JET_3O 15.0 30.0
J ET-50 25.0 50.0
JET-85 35.0 85.0
JET_MAX 35.0 115.0

 

Table A.2: Triggers used in jet event selection. JET-MIN required a trigger tower
(versus a large tile) at level 1. Additional ET cuts are applied offline.

of ’candidate’ trigger towers. In run 1b, there were two types of candidates:
those from trigger tower (0.217 x 0.2¢) type triggers and those from large tile
(0.817 x 1.6¢ or 4 x 8 trigger towers) type triggers. The trigger tower candidates
are simply trigger towers whose total (EM + Hadronic) ET is greater than
some set of ’seed’ thresholds The position of a large tile candidate is the trigger
tower(0.217 x 0.2¢) corresponding to the ET weighted center of a large tile(0.817x
1.6¢) whose total ET is greater than the seed threshold. These ’seed’ thresholds
are not to be confused with the thresholds necessary to pass the level 1 trigger
(i.e. JET-30 requires 1 large tile with ET > 15 GeV and the level 2 seed

requirement is large tile ET > 6 GeV). The hot tower list is ordered in ET.

2. The filters are considered in the order in which they appear in the trigger list.
For a given level 2 filter, the seed candidates in the hot tower list are considered
for this particular filter. A 1.417 x 1.4¢ box is drawn around the seed tower and

the ET weighted center of this box will become the level 2 jet center.

3. All calorimeter towers (.117 x .1¢) within .7 of the L2 jet center that are not

flagged as used in a previous jet are summed in By», EM ET and the 17 — ¢

157

RMS size is found.

. If the ET of the calorimeter tower sum is above the level 2 threshold (see
Table A.2), the event passes and all trigger towers and calorimeter towers

within .7 of the L2 jet center are flagged as used.

. Return to step 2. At any point, if the trigger tower considered has been flagged
as used, the L2 jet it is associated with is considered. If this L2 jet ET is above

threshold, the event passes.

158

Appendix B

Cone Jet Offset Comparison

The offsets for the cone algorithm implemented in CAFIX5.1 were derived using
density contributions multiplied by the area (in 17 — ¢ space) of the cone jets. The
densities were measured using the same data samples we overlayed on the Monte
Carlo data. We study the offset in cone jets, with the aim of understanding our
method, and to cross-check the results against the offset densities of CAFIX5.1. We
calculate the densities Due and Dzb as D = 0/1.5, where 1.5 is the jet area in 17 — ¢
space for an R = 0.7 cone and 0 is the offset (One or 027,) as measured using the

method described in Chapter 7.

Here we will use the same notation as is used for 11:; jets in Chapter 7, but we

will be referring to cone jets reconstructed with ’R :07 instead of It; jets.

2:2: 0.7 cone jet ET in Monte Carlo with no overlay.
m0 0.7 cone jet ET in Monte Carlo with MB overlay.

211 0.7 cone jet ET in Monte Carlo with ZBnoLQ overlay.

159

2L 0.7 cone jet ET in Monte Carlo with ZB overlay at luminosity [I = L x 103°cm‘2

(e.g. 25 for E = 5 x103°cm'2sec‘1).

B.1 Smeared Versus Unsmeared Quantities

Figure B] shows the result for 02,, obtained by two different methods:

1. for the two leading jets in sample 25 with 30 GeV<ET <50 GeV, we find the

corresponding jet in 1:2: and take the ET difference.

2. same as above but starting with the two leading jets in 132:, and then finding

the corresponding ones in 25.

Although we would like to select our jets by placing cuts on the sample with overlayed
noise, 25, method (1) is wrong because it artificially selects upwards fluctuations in
the offset, which smear jets from the Eu < 30 into the E25 > 30 region, while
rejecting the corresponding downwards fluctuations, from E“ > 30 into E25 < 30.
Method (2) does not suffer from this bias because we cut on ma: jets, which are not

subject to fluctuations in overlayed noise.

It is not however clear that Method (2) is the one we want. By selecting 2:2: jets
with 30 GeV<ET <50 GeV, we are calculating the average additional energy added
to a jet generated in this range. We will call it the “unsmeared” ofl'set. On the other
hand, by selecting 25 jets with 30 GeV<ET <50 GeV, we obtain the average oflset
for the jets actually found in this energy range. When we take into account the ET

dependence of the spectrum, we realize that this “smeared” offset will be much larger

160

SEC -

l

 

I O I l ' I O
I I I l I I I

1.8— ............... . ..................................... . ..................................... . ..................................... , ..................
1 n n I I l

0,,(Gevh1111

. . . 1 n n r
h— u . . 1 . u n
. . n . u u n
. a u 1 n . .
I - u . . . -
l6._ ............... 1 ..................................... 1 ........................................................................... . ..................
. I 1 u . u r n
. n - . u . .
o n . 1 u . u
.— n n n . n o u
- o u 4 I o .
P
I—

 

 

 

 

o IIIIIIIIIIIIIIIIIIIILIIIIIIIIIIILILIJII

0 0.5 l 1.5 2 2.5 3 3.5 4

Energy Density, D.” '0

Figure 8.1: The 0.7 cone jet ofl'set density, Dzb, as obtained by selecting the leading
jets either in the 25 (full boxes) or in the ma: sample (full circles). The open circles
are from CAFIX 5.1.

161

because many more jets are fluctuations with a positive offset from below 30 GeV,
than fluctuations with a negative offset from above 50 GeV. A prOper representation

of the physical ET spectrum is thus essential.

If we want to calculate offsets by placing cuts on the noise overlayed 25 jets, we
need to weigh the generated jets to suit our physical needs. Figure 7.4 shows the
ET distribution of the reconstructed kl jets without noise. In order to calculate the
“unsmeared” offset, weights have to be chosen so that the distribution of generated
jets without noise is flat. The resulting offsets are shown in Figure B.2 together
with those calculated using the unbiased Method (2) above, with cuts on the 2:3: jets
(and no event weighing). The results are very similar indicating that we understand
the effect of weighting, and that a flat distribution of generated jets does yield the
unsmeared offsets. This is an important cross-check of the method, before we weigh

jets to the physical ET dependence for the smeared case.

Figure 8.3 gives the results for the smeared offset. The procedure is identical
to the unsmeared case in Figure B.2, but now we weigh the events to get an ET ’5
dependence instead of a flat one. The steeply falling ET ‘5 dependence results in
the offsets being much higher. For a given smeared, Z5, jet ET there is more
contribution from low ET unsmeared, xx, jets than from high ET unsmeared jets.
Thus, the offset, 05,, = 25 - xx, (and density) will tend to be larger than in the case

2

of a flat ET distribution.

There remains to be discussed whether smeared or unsmeared offsets should be
used as the correction. Note that the approach followed in CAFIX5.1 corresponds to

unsmeared offsets, as they are obtained by subtracting energy densities in towers,

162

Energy Densitwa

 

 

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. 3 ‘ .
04 __ .......... .............. i ................
J I I I I I I I I I I I l I I I I

0.2
so 100 150 no
31‘6“”
Figure B.2: Unsmeared Dzb offset vs. ET in five 17 ranges for 0.7 cone jets. The cut
in ET is applied either to the raw xx jets (stars), or to 25 jets (full circles) weighed
to a flat distribution in ET . The result from CAFIX5.1 (open box) is shown for
comparison on the left, but no ET is associated with it.

 

163

Energy Density, D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure B3: The smeared (open circles) and unsmeared (full circles) Dzb offset for
0.7 cone jets. Both sets of points differ only by the weight assigned to the generated
jets. The open box shows for reference the result from the J ES DONote.

164

without reference to jets. To the extent that the resolution correction is performed at
a later stage in physical analyses, we will focus on this note on the unsmeared offset.
This method provides an interesting alternative to studying the effect of smearing,

and the possibility remains open for further studies with the smeared offset.

For the case of the underlying event, obtained as One 2 m0 — 211, we select the
two leading jets in xx, find the associated jets in m0 and 211, and perform the ET
subtraction, which again corresponds to the unsmeared offset. Then the offset, One

is divided by the cone jet area, 1.5, to obtain the density, Due.

B.2 Dependence of the Offset on ET

We have studied the ET dependence of Dzb and Due for the unsmeared case, as it

allows comparison with the CAFIX5.1 results.

Figure B.4 shows our results for Due as a function of 0.7 cone jet ET for several
jet 17 bins in the central region. There appears to be no ET dependence and the

values are consistent with those shown in [45].

Figure B.2 shows our results for Dzb (L = 5 xlowcm’zsec’l) as a function
of 0.7 cone jet ET for several jet 17 bins in the central region. It is somewhat
surprising to see a large dr0p with ET for Dzb, while not for the underlying event,
Due. This can be explained if the occupancy (the fraction of readout cells in a jet)
increases with energy. In this case, the noise contribution goes down because the
relative importance of zero suppression diminishes. Fig B.5 shows the occupancy as

a function of eta for various ET bins. This is consistent with occupancies measured

165

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mam

 

 

 

 

_

p-

h-

b

b

P

L-

h

b

—

h e n - a

- : : : :

- : : : :

' = ' 0 6—0 8 ‘

h..a.-..v.: ................ fl-— a ----- lA. ...-nu-u-u..:..

h U I c a

1. : : : -

_ . : : .
III III! I441 1111

L" l l l l

 

50 100 150 200

MM)

* J ES note
0 cone offset

Figure B.4: Dependence of Due on ET for cone jets. The result from CAFIX5.1 is
shown for reference

166

in MB data jets (Figure 7.5) and Monte Carlo with MB overlay (Figure 7.6).

0.7 Cone Jets (ZB Luminosity 5)

P
N

 

30$1Jet E $50

.0
a:
1

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

- <31- sosJet 13,95-

- i- 75§Jet E§100 . :

0.16 1._...........; ........ ,1 .......... ,, ..............
~ 41 1003112155125 ‘

~ 111 12Si§Jet £3170

Occupancy
0

 

 

 

 

 

 

 

 

 

 

 

 

 

7-
i- : : : : : : : : :

a.“ _.- .............. _. .............. .............. .............. ..............
L.
1' . . . . . . . . .

0“ I I I I I I I I I I I I I I I I I I I ILI I I I I I LI I I I I I I I I I I I ALIILI I I I I I

C

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

TI

Figure B.5: Jet energy dependence of occupancy for zero bias luminosity 5 and
R = 0.7 cone jets.

In CAFIX5.1, the ET density contribution of the zero suppression cut within a

jet, 61-8,, was related to the density contribution in ZB data, 623, by

F219
8 — B.
5H 528 F1111 ( 1)

 

where FZB and FM are the corresponding occupancy factors for ZB data and jets

167

respectively. In CAFIX5. 1, the occupancies were assumed to be constant as a function
of jet ET . Figure B.5 shows the occupancy in the central region on a much smaller
scale than is shown in [45] and one can see some dependence on ET . This ET

dependence can only account for 30% of the drop in Figure B2. The relation in
Equation B1 is empirical and it was checked only for low ET jets. Although
we believe our measurement to be more accurate than the empirical formula, the

remaining 70% will be taken as a systematic error to account for the discrepancy.

In CAFIX5.1, the offset is extracted from zbias events and corrected for the occu-
pancy in a jet environment assuming no change in the average energy of an occupied
cell. This assumption is probably correct between a zbias event and a low energy

jet, but only approximate as the energy of the jet increases.

If there were no zero suppression, one would certainly expect no ET dependence
in the offset for 0.7 cone jets. Because the area in 17 — ¢ space is fixed for cone jets,
the contribution should be the same regardless of jet ET . Because zero suppression
truncates both positive and negative energies and the noise is not gaussian, it is

difficult to assess its effects.

This is not the case for Due, because the underlying event energy addition is
always positive. Figures B6 and B7 show the energy densities for mO-xx and 211-
xx. Both have noise contribution and do show a drop with ET . The underlying
event contribution, Due (shown in Figure 8.4), is the difl'erence of these two, m0-
211, and, therefore, the noise contribution (including zero suppression efl'ects) cancel.

Therefore, it is reasonable that Due is ET independent.

168

Dm(Gth11¢)
.. 1': i

a
he

0,...(Gewn.¢)
E '1:

fl

0.8

.— H
to is

0,31me .1)

0.8

0.6

Minimum Bias Density, DMB

 

~JLIIIIIIIIIIIIIILII

 

 

 

50 100 150 200

E,(Gev1

 

 

............ +; .............. +..
PIIIIIIIIIIIIIIJIILL

 

 

50 100 150 200

ween

 

 

LIIIIIIIJIIIIJIIII

 

 

50 100 150 200

mew)

Dmmevmo

t"
N

fl

0.8

 

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

IIIIIIIIIIIIIIIIIII

 

 

 

50 100 150 200
now)

 

 

 

 

50

Figure B.6: Dependence of mO-xx on ET for cone jets

169

Zero Bias no LE Density, DZ,

9
he

 

 

3. r i 3. 0'8 r s z s s
'o-' 2 O a 5' I s 2 = a
E 06 :_ .......................... 27-07.02 ................... g 0.6 __ ...... .... ................ 7702-0-4
fiog Z. ................... O ..................................... Q04! E. ............ O ...... . .....................................
n F s 2 a s a E a 5 i 5
02 — ---------------- ------------ a. 0.2 — ---------------- ------------ e --------------- 1'- -

o r I I I I I I I I I I I I I I I I I I I 0 -J I_I I I I I I I J I I J I I I I I I

 

 

 

 

 

 

50 100 150 200 50 100 150 200
ween Erma)

 

 

g

M _ ................ §;_o..e-.—..o:-_8 ...........

9

a

IT I
~33

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Vin»)

(Ge

numewm)
i
I I I
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e

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7—- ..............................................................

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S
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e
+
n
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e
-e—

oooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
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..............................................................

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u e a e

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IIILLIgIILIIILIIIIII 0 IIIIIIIIIIIIIIIIIIIII
so 100 150 200 so 100 150 200

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9
ex

 

numevm .1)
i
l
c}
3
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9‘1”

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

. s : +: s
: : :
I I I I I L I J I L I I I I I I I I I

50 100 150 200
NOW)

8
1
5.

c
l

 

 

 

Figure B.7: Dependence of 2b—xx on ET for cone jets. The dependence is the same
as in the previous figure, and cancels when getting Due by taking the difference

170

B.3 Dependence of the Offset on Luminosity

We have studied the luminosity dependence of the unsmeared oflset for 0.7 cone jets
due to noise, pile-up and mulitiple interactions. Figure B.8 shows D27, as a function
of jet 17 for several luminosities. We use low ET jets for this study (30<ET <50)
to compare with CAFIX5.1. The agreement between our values and CAFIX5.1 is

excellent in this ET range.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EnergyDensity,Dzb
’5: 2 : 2 5 i 6: 2 : = i E
E : 9 5 2 E : 1 2 a
> _. ............. .............. ' ............. > .... ............. ' ...............
:3 15 : a 2 L=Ql :3 u : ; L=3
‘2 3 - 5 -. 1 Vi 3 -e.— i - ......... 5 .............
1: 1 ............ 3 ................................................ 1 g; ..........
$1." 1 a : 43,333,;
0.5 i; ............ 3 ..+. . ............... 0.5 E_ ............. . ................................
o I-I I I I LI I I I I I I I I I I I I I o I I I I I I I I I I I I I l I I J I I
0 0.5 l 1.5 2 0 0.5 l 1.5 2
"I '0
a 2 : e 2 :
E : E : 2
> 1.5 :_. .......................... _-5 ............... > 1.5 .. +e. ........ ;H?O ...........
:3. ~ 1 L” 33. 533+++e~ “‘
i 1 __ ........ *+ .. ................................ 1i 1 L-fir‘f“ ................................
a I 2 +39: 9 I §
,2 E E E t E
0.5 :— ............. . ................ ............... 0.5 r ..............................................................
ohIIIJILIIIIlIJIIIIII 0"JIJ1IIJIII1111I1111
0 0.5 l 1.5 2 0 0.5 l 1.5 2
'0 TI
’3: 2 -
E ’ ' -.-
5 1.5 W+ ......... .L..—.T.4 ...........
d. I :_ ..............................................................
0.5 E. ...............................................................
o :I I J I I l I I I I IJLI I I I I I
0 0.5 l 1.5 2
1]

Figure B8: The unsmeared offset Dzb (stars) at different luminosities for 30<ET < 50
Gev jets (our result depends on jet energy). Full circles are from CAFIX5.1, for
comparison.

171

Appendix C

Showering Effects on the Jet

Response

The MPF method uses balance of transverse momentum, PT, (not energy) to measure
the jet response of the detector. Therefore, the correction should be applied to
momentum. If there were no showering effects in the calorimeter, the correction for
energy and momentum would be identical. However, we can think of at least two
mechanisms that make this not so. In either case, the MPF method should give us

the correct momentum jet response.

First, a jet of particles (not massless) showers in the calorimeter. The particles
in the center of the shower (1 in Figure C.1a) tend to have more energy than the
particles around the perimeter of the shower (2 and 3). Particles with higher energy
have a better response, and, therefore the particle response is higher in the center
than at the edges (R1 > R2, R3). Because the response is not uniform over the entire

shower and because mpf uses PT balance (not ET ), we will tend to under correct

172

 

 

(a) (b)

Figure C.1: Showering efl'ects in the MPF method. (a) A photon is balanced by
three particles, 1, 2, and 3, in the transverse plane. E1 > E2, E3 and R1 > R2, R3.
(b) The 2nd and 3rd particles are deflected away from the jet axis in the calorimeter.

173

 

Energy using the MPF method. If the response were uniform over the shower, the
energy and momentum correction would be identical. This leads to undercorrection

when correcting energy using MPF. But the momentum is correctly corrected.

To illustrate this, Figure C.1a depicts a simple event where a photon is balanced
by a jet of 3 particles in the transverse plane. Particle 1 lies along the jet axis which
is back to back with the photon. Let us assume the 3 particles are massless (i.e.
E = P) and the event takes place in the transverse plane (i.e. ET 2 E). Then, the

particle jet’s energy can be written as

Epic! : E1+ E2 + E3 1 (0'1)

and the momentum is given by

Pptcl = E7 = E1 + E2608012 + E3603013 . ((3.2)

Given particle responses of R1 > R2, R3, the measured jet quantities are given by

Em, = R1121 + R2E2 + R3E3 (0.3)

and

Pm“, = RlEl + R2E2608012 + R3E3608013 . (0.4)

The ratio of measured to particle jet quantities is the true energy/momentum re-
sponse for the jet. If the particle response is uniform over the jet, R = R1 = R2 = R3,

the energy and momentum jet response would be identical, R.

174

The MPF jet response is given by

Rmpf=1+MPF where MPFzm.

ET,

Substituting for the event ET,

yields

ETZ—(RIISI+R2132+R3133+P;) ,

R1 E1 + R2E2608012 + R3E3608613
Rmpf =

 

E ‘7
Pmeas

R1npf P Pptcl

(0.5)

(0.1)

The jet response derived using the MPF method is identical to the true momentum

jet response.

For the energy jet response, let us assume particles 2 and 3 have equal response,

R2 = R3 = R and R1 = R + 6. Then the energy and momentum jet response will be

6E1

 

 

R = +R
and R11 = 2 1+12
Pptcl

(0.8)

Since Em, > Pptd, the energy jet response will be less than the momentum jet

response (RE < Rp = .anpf). Thus, jets will be undercorrected in energy using

Rm?! °

The second mechanism which would make the energy jet response unequal to the

175

 

momentum jet response occurs when particles get deflected in the detector and the
detector absorbs the recoil such that the recoil is not measured in the calorimeter.
The net result is a wider jet at the calorimeter level than at the particle level.
This is essentially the mechanism described in [55]. This means that the measured
Ema, — Pm“, is greater than the true Em, — Pptd. Therefore, the energy of the
jet needs less correction than the momentum. Since the MPF method measures the
momentum jet response, the energy will be over corrected using MPF method. But

again, the momentum is correctly corrected.

Figure C.1b shows an example of this where a photon is balanced by 3 show-
ered particles in the transverse plane. The true E and P are the same as above
(Equations 0.1 and C2. The measured E is also the same (Equation C.3). In this
scenario, the angles between 1 and 2, and 1 and 3, 013, are larger than in the previous
example ( 12 2‘ > 0:3“ and 01’5““ > 0:3”). Therefore, the measured P will be less

than it was in the previous example.

A similar exercise will also show that Rmpf = Rp and that RE > HP. In this
case, jets will be overcorrected in energy using Rmpf- And again, Rm, gives us the

correct jet momentum response.

Both these showering effects come into play with cone jets because they use scalar
sum Et. Because we use vector sum momentum for kt jets, we should not be aflected
by these biases. We do use Snowmass recombination in the preclustering, however,

so there may be a small efl'ect. This is discussed in section 9.4.

176

 

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181