Using MAX/MIN transverse regions to study the underlying event in Run 2 at the Tevatron

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Using MAX/MIN transverse regions to study the underlying event in Run 2 at the Tevatron
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Cruz, L. Alberto
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Thesis (Ph. D.)--University of Florida, 2005.
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by L. Alberto Cruz.
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USING MAX/MIN TRANSVERSE REGIONS TO STUDY THE UNDERLYING
EVENT IN RUN 2 AT THE TEVATRON














By

L. ALBERTO CRUZ


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE
UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2005











I dedicate this work to my wife Rachel and my parents, Rose "Shelley" and Luis

Cruz.















ACKNOWLEDGMENTS

I am very grateful to my advisor, Prof. Richard Field, for his guidance and support

throughout my research.

I also thank Craig Group for all of his invaluable help and patience, Bobby

Scurlock and Mike Schmitt for the basketball breaks, and Brendan Lyden for the business

class ticket back from China.















TABLE OF CONTENTS

page
ACKNOWLEDGMENTS...................................................................... ....iii

LIST OF TABLES........................................................................................vi

LIST OF FIGURES..................................... .........................................vii

A BSTRA CT........................................................ ...................................xx

CHAPTER

1 INTRODUCTION..... ................................................................. .... 1

1.1 Forces and Particles................................. ............................ 3
1.2 The Standard Model .................................................. ......... 6
1.3 QCD and the Structure of Hadrons..... ............ .............. ........... 8
1.4 Hadron Hadron Interactions..................................................11
1.4.1 Parton Model and Large PT Processes...............................12
1.4.2 The "Underlying Event" in Proton-Antiproton Collisions: Pythia
and Herwig................................... ...........................14

2 ACCELERATOR AND DETECTOR.................................................17

2.1 The Accelerator Complex...... ............................................... 17
2.2 The Collider Detector at Fermilab............................................ 22
2.2.1 The CDF Coordinate System ....................... .................. 23
2.2.2 Tracking.................................................................. 26
2.2.3 Calorim eters................................ ............................ 30
2.3 The CDF Trigger System .................. ..... ........ .... .... ....... 34

3 JETS AT CDF............. ................................................................36

4 MONTE-CARLO GENERATION AND CORRECTION FACTORS............38

4.1 Monte-Carlo Generation.......................................................38
4.2 Correcting the Data to the Particle Level .................................... 39

5 DATA SELECTION AND SYSTEMATIC ERRORS.............................69















5.1 Data Selection................................................................69
5.2 Systematic Uncertainty.......................................................... 70

6 DISCUSSION OF RESULTS........................................................73

6.1 The MAX/MIN Transverse Regions........................................ 76
6.2 "Leading Jet" Events................ .............. .........................77
6.3 "Back-to-Back" Events....................................................... 87
6.4 "Leading Jet" versus "Back-to-Back" Events............................. 98

7 SUMMARY AND CONCLUSIONS.............................................. 108

REFERENCES................................................................................ .. 111

BIOGRAPHICAL SKETCH....................................................................115

































v














LIST OF TABLES

Table page

1-1 Gauge bosons and forces of the Standard Model. There are eight different
species of gluons each corresponding to a particular color charge........................4

1-2 Propeties of leptons.............................................................................................. 5

1-3 Properties of quarks............................................................................................ 5

4-1 PYTHIA Tune A (5.3.3nt) at 1.96 TeV.............................................................. 38

4-2 HERW IG (5.3.3nt) at 1.96 TeV................................ ...........................................39

4-3 Observables examined in the "transverse" region (see Fig. 6-2) as they are
defined at the particle level and the detector level. Charged tracks are
considered "good" if they pass the selection criterion given in Table 5-2. The
mean charged particle and the charged fraction PTsum/ETsum are
constructed on and event-by-event basis and then averaged over the events.
There is one PTmax per event with PTmax = 0 if there are no charged particles ...40

4-4 Correction factors for Method 1. PYTHIA Tune A and HERWIG are used to
calculate the observables in Table 2 at the particle level in bins of particle jet#l
PT (GEN) and at the detector level in bins of calorimeter jet#l PT (uncorrected).
The detector level data in bins of calorimeter jet#1 PT (uncorrected) are
corrected by multiplying by QCD Monte-Carlo factor, GEN/CDFSIM..................41

5-1 Data sets (5.3.3nt) and event selection criterion used (L ~ 380 pb.').....................69

5-2 Track selection criterion ....................................................................................70

5-3 Range of PT(jet#1) used for each data set......................................... ................ 70

5-4 The errors on the corrected observables in Table 4-3 include both the statistical
error and the systematic uncertainty (added in quadrature). The systematic
uncertainty consists of oI and 02 (added in quadrature)........................................71















LIST OF FIGURES


Figure page

1-1 Illustration of the way QCD Monte-Carlo models simulate a proton-antiproton
collision in which a "hard" 2-to-2 parton scattering with transverse momentum,
PTard, has occurred. The resulting event contains particles that originate from
the two outgoing partons (plus initial and final-state radiation) and particles that
come from the breakup of the proton and antiproton (i.e. "beam-beam
remnants"). The "underlying event" is everything except the two outgoing hard
scattered "jets" and consists of the "beam-beam remnants" plus initial and final-
state radiation. The "hard scattering" component consists of the outgoing two
jets plus initial and final-state radiation............................................. ................ 2

1-2 Relative strength of the strong and electromagnetic forces ...................................11

1-3 The parton structure functions extracted from an analysis of deep inelastic
scattering data at Q2=10GeV2.......................................................................... ... 13

1-4 Hard "two-body" parton interaction producing a di-jet event in a proton-
antiproton collision............................................................................................... 14

1-5 Illustration of the way PYTHIA models the "underlying event" in proton-
antiproton collision by including multiple parton interactions. In addition to the
hard 2-to-2 parton-parton scattering with transverse momentum, PT(hard), there
is a second "semi-hard" 2-to-2 parton-parton scattering that contributes particles
to the "underlying event"................................................................. ............. 16

2-1 Overview of the accelerator complex at Fermilab. H- ions are injected into the
linac from the Cockcroft-Walton, to travel to the Booster, then to the Main Ring,
and finally to the Tevatron. Some protons are extracted from the Main Ring and
are used to make anti-protons. The anti-protons are re-injected into the Main
Ring and then into the Tevatron. The final proton-antiproton center of mass
energy is v -=1.96 TeV ......... ......................................................................... .... 18

2-2 Run II instantaneous initial luminosity ..................................................... ...........20

2-3 Run II integrated luminosity .................................................. .......................... 21

2-4 Solid cutaway view of the CDF II detector .....................................................22

2-5 Elevation view of the CDF II detector................................................................... 23









2-6 The CDF coordinate system ....................................................................................24

2-7 A quarter of the CDF detector. Only the central and end-plug subsystems are
show n ......................................................................................................................26

2-8 The CDF II tracking volume............................................................. ...................27

2-9 Schematic layout of the silicon tracking system. The The innermost layer,
Layer00 consists of 6 sensors in z ...........................................................................28

2-10 End view of the three components of the silicon microsrtip detector system..........29

2-11 The COT sense wires and potential wires are alternated and arranged in 8
'superlayers' ...........................................................................................................30

2-12 Calorimeter tower segmention in r1-( space ......................................................32

2-13 CEM/CES/CHA wedge. ....................................................... ....................33

2-14 CES strip and wire................................................................................................ 33

4-1 Example of fits to the QCD Monte-Carlo results. Shows the particle level
predictions at 1.96 TeV for the density of charged particles, dNchg/drldo, with
PT > 0.5 GeV/c and hi < 1 in the "transMAX" and "transMIN" regions for
"leading jet" events defined in Fig. 6-3 as a function of the leading particle jet PT
for PYTHIA Tune A (top) and HERWIG (bottom)..............................................42

4-2 Particle level predictions from PYTHIA Tune A and HERWIG for average
density of particles dNall/drld) (top), the average charged particle PTsum
density, dPTsum/dild) (middle), and the average charged particle (bottom)
for particles with |r| < 1 in the "transverse" region for "leading jet" events
defined in Fig. 6-3 as a function of the leading particle jet PT.................................43


4-3 Particle level predictions from PYTHIA Tune A and HERWIG for average
density of particles dNall/drld (top), the average charged particle PTsum
density dPTsum/drld) (middle), and the average charged particle (bottom)
for particles with |h < 1 in the "transverse" region for "back-to-back" events
defined in Fig. 6-3 as a function of the leading jet PT..............................................44

4-4 Method 1 response factors for the density of charged particles, dNchg/dTrd), with
PT > 0.5 GeV/c and |l| < 1 in the "transMAX" region for "leading jet" events
defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle level
prediction (GEN) versus the leading particle jet PT and the detector level result
(CDFSIM) versus the leading calorimeter jet PT (uncorrected) with h|(jet#1)I < 2
for PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the









detector level to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e.
response factor).................................................................................................46

4-5 Method 1 response factors for the density of charged particles, dNchg/drldo,
with pr > 0.5 GeV/c and Ir|l < 1 in the "transMIN" region for "leading jet"
events defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle
level prediction (GEN) versus the leading particle jet PT and the detector level
result (CDFSIM) versus the leading calorimeter jet PT (uncorrected) with
h(jet#l)I < 2 for PYTHIA Tune A (top) and HERWIG (middle). Also shows
the ratio of the detector level to the particle level, CDFSIM/GEN, versus the
leading jet PT (i.e. response factor). ............................................................ ..48

4-6 Method 1 response factors for the PTsum density of charged particles,
dPTsum/drld), with pr > 0.5 GeV/c and I|ll < 1 in the "transMAX" region for
"leading jet" events defined in Fig. 6-3 as a function of the leading jet PT.
Shows the particle level prediction (GEN) versus the leading particle jet PT and
the detector level result (CDFSIM) versus the leading calorimeter jet PT
(uncorrected) with h(jet#l)l < 2 for PYTHIA Tune A (top) and HERWIG
(middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor). ............................49

4-7 Method 1 response factors for the PTsum density of charged particles,
dPTsum/drld), with pr > 0.5 GeV/c and hi < 1 in the "transMIN" region for
"leading jet" events defined in Fig. 6-3 as a function of the leading jet PT.
Shows the particle level prediction (GEN) versus the leading particle jet PT and
the detector level result (CDFSIM) versus the leading calorimeter jet PT
(uncorrected) with h(jet#l)l < 2 for PYTHIA Tune A (top) and HERWIG
(middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor). ............................50

4-8 Method 1 response factors for the average of charged particles with pr >
0.5 GeV/c and |Irl < 1 in the "transverse" region for "leading jet" events defined
in Fig. 6-3 as a function of the leading jet PT. Shows the particle level prediction
(GEN) versus the leading particle jet PT and the detector level result (CDFSIM)
versus the leading calorimeter jet PT (uncorrected) with |(jet#l)l < 2 for
PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the
detector level to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e.
response factor).................................................................................................51

4-9 Method 1 response factors for the average maximum pr, PTmax, for charged
particles with pr > 0.5 GeV/c and hi < 1 in the "transverse" region for "leading
jet" events defined in Fig. 6-3 as a function of the leading jet PT. Shows the
particle level prediction (GEN) versus the leading particle jet PT and the detector
level result (CDFSIM) versus the leading calorimeter jet PT (uncorrected) with
h|(jet#1)l < 2 for PYTHIA Tune A (top) and HERWIG (middle). Also shows









the ratio of the detector level to the particle level, CDFSIM/GEN, versus the
leading jet PT (i.e. response factor). ....................................................... .............52

4-10 Method 1 response factors for the ETsum density of all particles, dET/dldd),
with |h < 1 in the "transMAX" regions for "leading jet" events defined in Fig.
6-3 as a function of the leading jet PT. Shows the particle level prediction
(GEN) versus the leading particle jet PT and the detector level result (CDFSIM)
versus the leading calorimeter jet PT (uncorrected) with hr(jet#l)l < 2 for
PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the
detector level to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e.
response factor).................................................................................................53

4-11 Method 1 response factors for the ETsum density of all particles, dET/drldo,
with ||I < 1 in the "transMIN" regions for "leading jet" events defined in Fig. 6-
3 as a function of the leading jet PT. Shows the particle level prediction (GEN)
versus the leading particle jet PT and the detector level result (CDFSIM) versus
the leading calorimeter jet PT (uncorrected) with [r(jet#l)J < 2 for PYTHIA
Tune A (top) and HERWIG (middle). Also shows the ratio of the detector level
to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e. response
factor)...................................................... .............................................. ...........54

4-12 Method 1 response factors for the charged fraction, PTsum/ETsum, in the
"transverse" region for "leading jet" events defined in Fig. 6-3 as a function of
the leading jet PT, where PTsum includes charged particles with pr > 0.5 GeV/c
and hi < 1 and the ETsum includes all particles with 1h < 1. Shows the particle
level prediction (GEN) versus the leading particle jet PT and the detector level
result (CDFSIM) versus the leading calorimeter jet PT (uncorrected) with
[h(jet#l)l < 2 for PYTHIA Tune A (top) and HERWIG (middle). Also shows
the ratio of the detector level to the particle level, CDFSIM/GEN, versus the
leading jet PT (i.e. response factor). ....................................................... .............55

4-13 Shows the ratio of the detector level to the particle level, CDFSIM/GEN, versus
the leading jet PT (method 1 response factors) for PYTHIA Tune A for the
"transMAX", "transMIN", and "transverse" regions for "leading jet" events
defined in Fig. 6-3 as a function of the leading jet PT. Shows the density of
charged particles dNchg/drld) with pr > 0.5 GeV/c and hi < 1 (top), the PTsum
density of charged particles dPTsum/dTldo with pr > 0.5 GeV/c and hi < 1
(middle), and ETsum density of all particles dET/drTd4 with tr < 1 (bottom).........56

4-14 Method 1 response factors for the density of charged particles, dNchg/dld),
with pT > 0.5 GeV/c and 1h < 1 in the "transMAX" region for "back-to-back"
events defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle
level prediction (GEN) versus the leading particle jet PT and the detector level
result (CDFSIM) versus the leading calorimeter jet PT (uncorrected) with
hr(jet#1)l < 2 for PYTHIA Tune A (top) and HERWIG (middle). Also shows









the ratio of the detector level to the particle level, CDFSIM/GEN, versus the
leading jet PT (i.e. response factor). ....................................................................57

4-15 Method 1 response factors for the density of charged particles, dNchg/drld),
with pr > 0.5 GeV/c and ||I < 1 in the "transMIN" region for "back-to-back"
events defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle
level prediction (GEN) versus the leading particle jet PT and the detector level
result (CDFSIM) versus the leading calorimeter jet PT (uncorrected) with
h(jet#l)l < 2 for PYTHIA Tune A (top) and HERWIG (middle). Also shows
the ratio of the detector level to the particle level, CDFSIM/GEN, versus the
leading jet PT (i.e. response factor). ................................................................58

4-16 Method 1 response factors for the PTsum density of charged particles,
dPTsum/drldo, with pr > 0.5 GeV/c and hi < 1 in the "transMAX" region for
"back-to-back" events defined in Fig. 6-3 as a function of the leading jet PT.
Shows the particle level prediction (GEN) versus the leading particle jet PT and
the detector level result (CDFSIM) versus the leading calorimeter jet PT
(uncorrected) with h(jet#l)l < 2 for PYTHIA Tune A (top) and HERWIG
(middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).............................59

4-17 Method 1 response factors for the PTsum density of charged particles,
dPTsum/dTld(, with pr > 0.5 GeV/c and I1|I < 1 in the "transMIN" region for
"back-to-back" events defined in Fig. 6-3 as a function of the leading jet PT.
Shows the particle level prediction (GEN) versus the leading particle jet PT and
the detector level result (CDFSIM) versus the leading calorimeter jet PT
(uncorrected) with o(jet#l)l < 2 for PYTHIA Tune A (top) and HERWIG
(middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor). ............................60

4-18 Method 1 response factors for the average of charged particles with pr >
0.5 GeV/c and Irll < 1 in the "transverse" region for "back-to-back" events
defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle level
prediction (GEN) versus the leading particle jet PT and the detector level result
(CDFSIM) versus the leading calorimeter jet PT (uncorrected) with q(jet#l)l < 2
for PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the
detector level to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e.
response factor).................................................................................................61

4-19 Method 1 response factors for the average maximum Pr, PTmax, for charged
particles with pr > 0.5 GeV/c and |ri < 1 in the "transverse" region for "back-to-
back" events defined in Fig. 6-3 as a function of the leading jet PT. Shows the
particle level prediction (GEN) versus the leading particle jet PT and the detector
level result (CDFSIM) versus the leading calorimeter jet PT (uncorrected) with
ri(jet#l)l < 2 for PYTHIA Tune A (top) and HERWIG (middle). Also shows









the ratio of the detector level to the particle level, CDFSIM/GEN, versus the
leading jet PT (i.e. response factor). ........................................................................62

4-20 Method 1 response factors for the ETsum density of all particles, dET/drldo,
with hrl < 1 in the "transMAX" regions for "back-to-back" events defined in Fig.
6-3 as a function of the leading jet PT. Shows the particle level prediction
(GEN) versus the leading particle jet PT and the detector level result (CDFSIM)
versus the leading calorimeter jet PT (uncorrected) with h(jet#l)| < 2 for
PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the
detector level to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e.
response factor).................................................................................................63

4-21 Method 1 response factors for the ETsum density of all particles, dET/dTldO,
with IT| < 1 in the "transMIN" regions for "back-to-back" events defined in Fig.
6-3 as a function of the leading jet PT. Shows the particle level prediction
(GEN) versus the leading particle jet PT and the detector level result (CDFSIM)
versus the leading calorimeter jet PT (uncorrected) with h(jet#l)| < 2 for
PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the
detector level to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e.
response factor).................................................................................................64

4-22 Method 1 response factors for the charged fraction, PTsum/ETsum, in the
"transverse" region for "back-to-back" events defined in Fig. 6-3 as a function
of the leading jet PT, where PTsum includes charged particles with pr > 0.5
GeV/c and |I < 1 and the ETsum includes all particles with hi < 1. Shows the
particle level prediction (GEN) versus the leading particle jet PT and the detector
level result (CDFSIM) versus the leading calorimeter jet PT (uncorrected) with
Ih(jet#l)l < 2 for PYTHIA Tune A (top) and HERWIG (middle). Also shows
the ratio of the detector level to the particle level, CDFSIM/GEN, versus the
leading jet PT (i.e. response factor). ....................................................... .............65

4-23 Leading jet PT correction used in method 2 for "leading jet" events. Shows the
difference in the observed leading jet PT at the detector level (i.e. in the
calorimeter) compared with the true PT (i.e. corrected) of matched leading
particle jets using PYTHIA Tune A and HERWIG.................................... ..66

4-24 Method 2 response factors from PYTHIA Tune A for "leading jet" events
defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle level
prediction (GEN) versus the leading particle jet PT and the detector level result
(CDFSIMcor) versus the leading calorimeter jet PT (corrected) with h(jet#1)| <
2. Also shows the ratio of the detector level to the particle level,
CDFSIMcor/GEN, versus the leading jet PT (i.e. response factor)..........................67

4-25 Compares the method 1 response factors versus the leading jet PT (uncorrected)
with the method 2 response factors versus the leading jet PT (corrected) from
PYTHIA Tune A ...............................................................................................68









5-1 Data at 1.96 TeV corrected to the particle level using method 1 and method 2
compared with PYTHIA Tune A and HERWIG at the particle level. Shows the
density of charged particles, dNchg/drld4 (top), the PTsum density of charged
particles, dPTsum/drld) (middle), (pr > 0.5 GeV/c and I|ll < 1), and the ETsum
density, dET/drld) (bottom), for particles with hi < 1 in the "transverse" region
(average of "transMAX" and "transMIN") for "leading jet" events defined in
Fig. 6-3 as a function of the leading jet PT.............................................................. 72

6-1 Illustration of correlations in azimuthal angle A) relative to the direction of the
leading jet (MidPoint, R = 0.7) in the event, jet#l. The angle A) = 4 )jet#1 is
the relative azimuthal angle between charged particles and the direction of jet#l.
The "toward" region is defined by IA|) < 600 and hr < 1, while the "away"
region is I|A| > 1200 and hi < 1. The "transverse" region is defined by 600 <
JA I < 1200 and hi| < 1. Each of the three regions "toward", "transverse", and
"away" and has an overall area in Trl- space of ATrlA = 47/3. We examine
charged particles in the range pT > 0.5 GeV/c and hi < 1, but allow the leading
jet to be in the region h(jet#l)l < 2. ...................................................................75

6-2 Illustration of correlations in azimuthal angle A) relative to the direction of the
leading jet (highest ET jet) in the event, jet#1. The angle A) = ) )jet#1 is the
relative azimuthal angle between charged particles and the direction of jet#l.
The "toward" region is defined by I|A| < 600 and [h < 1, while the "away"
region is |A | > 1200 and hil < 1. The two "transverse" regions 600 < A) < 1200
and 600 < -A) < 1200 are referred to as "transverse 1" and "transverse 2". Each
of the two "transverse" regions have an area in rl-o space of ArlAo) = 4n/6. The
overall "transverse" region defined in Fig. 3 corresponds to combining the
"transverse 1" and "transverse 2" regions. Events in which there are no
restrictions placed on the on the second highest ET jet, jet#2, are referred to as
"leading jet" events (left). Events with at least two jets where the leading two
jets are nearly "back-to-back" (A)12 > 1500) with ET(jet#2)/ET(jet#l) > 0.8 are
referred to as "back-to-back" events (right). .........................................................76

6-3 Illustration of correlations in azimuthal angle A) relative to the direction of the
leading jet (highest PT jet) in the event, jet#l for "leading jet" events (left) and
"back-to-back" events (right) as defined in Fig. 4. The angle A) = 4 Ojet#1 is
the relative azimuthal angle between charged particles (or calorimeter towers)
and the direction of jet#l. On an event by event basis, we define "transMAX"
("transMIN") to be the maximum (minimum) of the two "transverse" regions,
600 < A) < 1200 and 60 < -A) < 1200. "TransMAX" and "transMIN" each have
an area in rl-4 space of ATlA) = 4i/6. The overall "transverse" region defined in
Fig. 3 includes both the "transMAX" and the "transMIN" region ..........................76

6-4 Illustration of the topology of a proton-antiproton collision in which a "hard"
parton-parton collision has occurred. The "toward" region as defined in Fig. 6-1
contains the leading "jet", while the "away" region, on the average, contains the









"away-side" "jet". The "transverse" region is perpendicular to the plane of the
hard 2-to-2 scattering and is very sensitive to the "underlying event". For events
with large initial or final-state radiation the "transMAX" region defined in Fig.6-
3 would contain the third jet while both the "transMAX" and "transMIN"
regions receive contributions from the beam-beam remnants (see Fig. 1-1).
Thus the "transMIN" region is very sensitive to the beam-beam remnants, while
the "transMAX" minus the "transMIN" is very sensitive to initial and final-state
radiation. ..................................................................................................................77

6-5 Data at 1.96 TeV on the density of charged particles, dNchg/drldo, with pr > 0.5
GeV/c and [h < 1 in the "transMAX" and "transMIN" regions for "leading jet"
events defined in Fig. 6-3 as a function of the leading jet PT compared with
PYTHIA Tune A and HERWIG. (top) Shows the uncorrected data (with
statistical errors only) compared with the theory after detector simulation
(CDFSIM). (bottom) Shows the data corrected to the particle level (with errors
that include both the statistical error and the systematic uncertainty) compared
with the theory at the particle level (i.e. generator level). .....................................79

6-6 Data at 1.96 TeV on the density of charged particles, dNchg/drldO, with pr > 0.5
GeV/c and |h < 1 in the "transverse" region (average of "transMAX" and
"transMIN") for "leading jet" events defined in Fig. 6-3 as a function of the
leading jet PT compared with PYTHIA Tune A and HERWIG. (top) Shows the
uncorrected data (with statistical errors only) compared with the theory after
detector simulation (CDFSIM). (bottom) Shows the data corrected to the
particle level (with errors that include both the statistical error and the
systematic uncertainty) compared with the theory at the particle level (i.e.
generator level)................................................................................................. 80

6-7 Data at 1.96 TeV on the PTsum density of charged particles, dPTsum/d1ldo,
with pr > 0.5 GeV/c and r1" < 1 in the "transMAX" and "transMIN" regions for
"leading jet" events defined in Fig. 6-3 as a function of the leading jet PT
compared with PYTHIA Tune A and HERWIG. (top) Shows the uncorrected
data (with statistical errors only) compared with the theory after detector
simulation (CDFSIM). (bottom) Shows the data corrected to the particle level
(with errors that include both the statistical error and the systematic uncertainty)
compared with the theory at the particle level (i.e. generator level)........................ 81

6-8 Data at 1.96 TeV on the charged PTsum density, dPTsum/drldo, with pr > 0.5
GeV/c and |rl < 1 in the "transverse" region (average of "transMAX" and
"transMIN") for "leading jet" events defined in Fig. 6-3 as a function of the
leading jet PT compared with PYTHIA Tune A and HERWIG. (top) Shows the
uncorrected data (with statistical errors only) compared with the theory after
detector simulation (CDFSIM). (bottom) Shows the data corrected to the
particle level (with errors that include both the statistical error and the
systematic uncertainty) compared with the theory at the particle level (i.e.
generator level). ................................................................................................. 82









6-9 Data at 1.96 TeV on the average of charged particles with pr > 0.5 GeV/c
and hi < 1 in the "transverse" region for "leading jet" events defined in Fig. 6-3
as a function of the leading jet PT compared with PYTHIA Tune A and
HERWIG. (top) Shows the uncorrected data (with statistical errors only)
compared with the theory after detector simulation (CDFSIM). (bottom) Shows
the data corrected to the particle level (with errors that include both the
statistical error and the systematic uncertainty) compared with the theory at the
particle level (i.e. generator level). ........................................................ .............83

6-10 Data at 1.96 TeV on the average maximum pr, PTmax, for charged particles
with pT > 0.5 GeV/c and Jill < 1 in the "transverse" region for "leading jet"
events defined in Fig. 6-3 as a function of the leading jet PT compared with
PYTHIA Tune A and HERWIG. (top) Shows the uncorrected data (with
statistical errors only) compared with the theory after detector simulation
(CDFSIM). (bottom) Shows the data corrected to the particle level (with errors
that include both the statistical error and the systematic uncertainty) compared
with the theory at the particle level (i.e. generator level). .....................................85

6-11 Data at 1.96 TeV on the ETsum density, dET/drld), for particles with ITrl < 1 in
the "transMAX" and "transMIN" regions for "leading jet" events defined in Fig.
6-3 as a function of the leading jet PT compared with PYTHIA Tune A and
HERWIG. (top) Shows the uncorrected data (with statistical errors only)
compared with the theory after detector simulation (CDFSIM). (bottom) Shows
the data corrected to the particle level (with errors that include both the
statistical error and the systematic uncertainty) compared with the theory at the
particle level (i.e. generator level). ........................................................ .............86

6-12 Data at 1.96 TeV on the ETsum density, dET/dTrdO, for particles with |ill < 1 in
the "transverse" region (average of "transMAX" and "transMIN") for "leading
jet" events defined in Fig. 6-3 as a function of the leading jet PT compared with
PYTHIA Tune A and HERWIG. (top) Shows the uncorrected data (with
statistical errors only) compared with the theory after detector simulation
(CDFSIM). (bottom) Shows the data corrected to the particle level (with errors
that include both the statistical error and the systematic uncertainty) compared
with the theory at the particle level (i.e. generator level). .....................................87

6-13 Data at 1.96 TeV on the charged fraction, PTsum/ETsum, in the "transverse"
region for "leading jet" events defined in Fig. 6-3 as a function of the leading jet
PT, where PTsum includes charged particles with pr > 0.5 GeV/c and hi < 1 and
the ETsum includes all particles with Jrli < 1. The data are compared with
PYTHIA Tune A and HERWIG. (top) Shows the uncorrected data (with
statistical errors only) compared with the theory after detector simulation
(CDFSIM). (bottom) Shows the data corrected to the particle level (with errors
that include both the statistical error and the systematic uncertainty) compared
with the theory at the particle level (i.e. generator level). .....................................88









6-14 Data at 1.96 TeV on the density of charged particles, dNchg/drld with pr > 0.5
GeV/c and hi < 1 in the "transMAX" and "transMIN" regions for "back-to-
back" events defined in Fig. 6-3 as a function of the leading jet PT compared
with PYTHIA Tune A and HERWIG. (top) Shows the uncorrected data (with
statistical errors only) compared with the theory after detector simulation
(CDFSIM). (bottom) Shows the data corrected to the particle level (with errors
that include both the statistical error and the systematic uncertainty) compared
with the theory at the particle level (i.e. generator level). .....................................90

6-15 Data at 1.96 TeV on the density of charged particles, dNchg/dTld), with pr > 0.5
GeV/c and I|r < 1 in the "transverse" region (average of "transMAX" and
"transMIN") for "back-to-back" events defined in Fig. 6-3 as a function of the
leading jet PT compared with PYTHIA Tune A and HERWIG. (top) Shows the
uncorrected data (with statistical errors only) compared with the theory after
detector simulation (CDFSIM). (bottom) Shows the data corrected to the
particle level (with errors that include both the statistical error and the
systematic uncertainty) compared with the theory at the particle level (i.e.
generator level). ................................................................................................. 91

6-16 Data at 1.96 TeV on the PTsum density of charged particles, dPTsum/drld),
with pr > 0.5 GeV/c and Irll < 1 in the "transMAX" and "transMIN" regions for
"back-to-back" events defined in Fig. 6-3 as a function of the leading jet PT
compared with PYTHIA Tune A and HERWIG. (top) Shows the uncorrected
data (with statistical errors only) compared with the theory after detector
simulation (CDFSIM). (bottom) Shows the data corrected to the particle level
(with errors that include both the statistical error and the systematic uncertainty)
compared with the theory at the particle level (i.e. generator level)......................92

6-17 Data at 1.96 TeV on the PTsum density, dPTsum/drldo, with pr > 0.5 GeV/c and
h1 < 1 in the "transverse" region (average of "transMAX" and "transMIN") for
"back-to-back" events defined in Fig. 6-3 as a function of the leading jet PT
compared with PYTHIA Tune A and HERWIG. (top) Shows the uncorrected
data (with statistical errors only) compared with the theory after detector
simulation (CDFSIM). (bottom) Shows the data corrected to the particle level
(with errors that include both the statistical error and the systematic uncertainty)
compared with the theory at the particle level (i.e. generator level).......................93

6-18 Data at 1.96 TeV on the average of charged particles with pr > 0.5 GeV/c
and I ll < 1 in the "transverse" region for "back-to-back" events defined in Fig.
6-3 as a function of the leading jet PT compared with PYTHIA Tune A and
HERWIG. (top) Shows the uncorrected data (with statistical errors only)
compared with the theory after detector simulation (CDFSIM). (bottom) Shows
the data corrected to the particle level (with errors that include both the
statistical error and the systematic uncertainty) compared with the theory at the
particle level (i.e. generator level). .....................................................................94









6-19 Data at 1.96 TeV on the average maximum pr, PTmax, for charged particles
with PT > 0.5 GeV/c and ri| < 1 in the "transverse" region for "back-to-back"
events defined in Fig. 6-3 as a function of the leading jet PT compared with
PYTHIA Tune A and HERWIG. (top) Shows the uncorrected data (with
statistical errors only) compared with the theory after detector simulation
(CDFSIM). (bottom) Shows the data corrected to the particle level (with errors
that include both the statistical error and the systematic uncertainty) compared
with the theory at the particle level (i.e. generator level). .....................................95

6-20 Data at 1.96 TeV on the ETsum density, dET/drldo, for particles with I|ri < 1 in
the "transMAX" and "transMIN" regions for "back-to-back" events defined in
Fig. 6-3 as a function of the leading jet PT compared with PYTHIA Tune A and
HERWIG. (top) Shows the uncorrected data (with statistical errors only)
compared with the theory after detector simulation (CDFSIM). (bottom) Shows
the data corrected to the particle level (with errors that include both the
statistical error and the systematic uncertainty) compared with the theory at the
particle level (i.e. generator level). ........................................................ .............97

6-21 Data at 1.96 TeV on the ETsum density, dET/drld), for particles with I|ll < 1 in
the "transverse" region (average of "transMAX" and "transMIN") for "back-to-
back" events defined in Fig. 6-3 as a function of the leading jet PT compared
with PYTHIA Tune A and HERWIG. (top) Shows the uncorrected data (with
statistical errors only) compared with the theory after detector simulation
(CDFSIM). (bottom) Shows the data corrected to the particle level (with errors
that include both the statistical error and the systematic uncertainty) compared
with the theory at the particle level (i.e. generator level) ......................................98

6-22 Data at 1.96 TeV on the charged fraction, PTsum/ETsum, in the "transverse"
region for "back-to-back" events defined in Fig. 6-3 as a function of the leading
jet PT, where PTsum includes charged particles with pr > 0.5 GeV/c and hi < 1
and the ETsum includes all particles with h|ll < 1. The data are compared with
PYTHIA Tune A and HERWIG. (top) Shows the uncorrected data (with
statistical errors only) compared with the theory after detector simulation
(CDFSIM). (bottom) Shows the data corrected to the particle level (with errors
that include both the statistical error and the systematic uncertainty) compared
with the theory at the particle level (i.e. generator level). .....................................99

6-23 Data at 1.96 TeV on the density of charged particles, dNchg/drldo, with pr > 0.5
GeV/c and hi| < 1 in the "transMAX" region (top), "transMIN" region (middle),
and "transverse" region (average of "transMAX" and "transMIN") (bottom) for
"leading jet" and "back-to-back" events defined in Fig. 6-3 as a function of the
leading jet PT compared with PYTHIA Tune A and HERWIG. The data are
corrected to the particle level (with errors that include both the statistical error
and the systematic uncertainty) and compared with the theory at the particle
level (i.e. generator level) ......................................................................................101


xvii









6-24 Data at 1.96 TeV on charged PTsum density of charged particles, dPTsum/dTld4,
with pT > 0.5 GeV/c and |Ir < 1 in the "transMAX" region (top), "transMIN"
region (middle), and "transverse" region (average of "transMAX" and
"transMIN") (bottom) for "leading jet" and "back-to-back" events defined in
Fig. 6-3 as a function of the leading jet PT compared with PYTHIA Tune A and
HERWIG. The data are corrected to the particle level (with errors that include
both the statistical error and the systematic uncertainty) and compared with the
theory at the particle level (i.e. generator level). ...................................... ...102

6-25 Figure 6-25: Data at 1.96 TeV on the average of charged particles (top)
and the average maximum pr, PTmax, for charged particles (bottom) with pr >
0.5 GeV/c and hi| < 1 in the "transverse" region for "leading jet" and "back-to-
back" events defined in Fig. 6-3 as a function of the leading jet PT compared
with PYTHIA Tune A and HERWIG. The data are corrected to the particle
level (with errors that include both the statistical error and the systematic
uncertainty) and compared with the theory at the particle level (i.e. generator
level)............................................................................................................ 104

6-26 Data at 1.96 TeV on the ETsum density, dET/dld#, for particles with |h < 1 in
the "transMAX" region (top), "transMIN" region (middle), and "transverse"
region (average of "transMAX" and "transMIN") (bottom) for "leading jet" and
"back-to-back" events defined in Fig. 6-3 as a function of the leading jet PT
compared with PYTHIA Tune A and HERWIG. The data are corrected to the
particle level (with errors that include both the statistical error and the
systematic uncertainty) and compared with the theory at the particle level (i.e.
generator level). ............................................................................................... 105

6-27 Data at 1.96 TeV on the charged fraction, PTsum/ETsum, in the "transverse"
region defined in Fig. 6-3 for "leading jet" events (top) and "back-to-back"
events (bottom) as a function of the leading jet PT, where PTsum includes
charged particles with pr > 0.5 GeV/c and Irll < 1 and the ETsum includes all
particles with hi < 1, compared with PYTHIA Tune A and HERWIG. The data
are corrected to the particle level (with errors that include both the statistical
error and the systematic uncertainty) and compared with the theory at the
particle level (i.e. generator level). ..................................................... .............106

6-28 Data at 1.96 TeV on the density of charged particles, dN/dTrdO and the PTsum
density, dPTsu/J dr1d for charged particles with pr > 0.5 GeV/c and hi < 1 for
the "transMAX" minus the "transMIN" region defined in figure 6-3 for "leading
jet" and "back-to-back" events defined in Fig. 6-2 as a function of the leading jet
PT compared with PYTHIA Tune A and HERWIG. The "transDIF" ETsum
density, dETsun/ddid for particles with hi < 1 is also presented. The data are
corrected to the particle level (with errors that include both the statistical error
and the systematic uncertainty) and compared with the theory at the particle
level (i.e. generator level) .................................. ....................................... 108


xviii








7-1 A comparison between the Run I and Run II analysis on the PTsum density in
the "transverse" region. (top) Data uncorrected (with errors that include both
statistical and the systematic uncertainty) at 1.8 TeV on the charged PTsum
density, dPTsum/dTrdO, with PT > 0.5 GeV/c and I|ll < 1.0 for leading jet events
defined in Fig. 6-3 as a function of leading jet PT compared PYTHIA set A,
PYTHIA set B, and HERWIG. (bottom) Data corrected (with errors that include
both statistical and the systematic uncertainty) at 1.96 TeV on the charged
PTsum density, dPTsum/drldo, with PT > 0.5 GeV/c and I|ll < 1.0 for "leading
jet events" defined in Fig. 6-3 as a function of leading jet PT compared PYTHIA
Tune A and HERW IG. ................................................. ................................. 11














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

USING MAX/MIN TRANSVERSE REGIONS TO STUDY THE UNDERLYING
EVENT IN RUN 2 AT THE TEVATRON

By

Luis Alberto Cruz

August 2005

Chair: Richard Field
Major Department: Physics

We study the behavior of the charged particle (pr > 0.5 GeV/c, I|ll < 1) and energy

(|r11 < 1) components of the "underlying event" in hard scattering proton-antiproton

collisions at 1.96 TeV. We use the direction of the leading calorimeter jet in each event to

define two "transverse" regions of rl-0 space that are very sensitive to the "underlying

event". Defining a variety of MAX and MIN "transverse" regions helps separate the

"hard component" (initial and final-state radiation) from the "beam-beam remnant" and

multiple parton interaction components. In addition, selecting events with at least two

jets that are nearly back-to-back (A4 2 > 1500) with PT(jet#3) < 15 GeV/c suppresses the

hard initial and final-state radiation, thus increasing the sensitivity of the "transverse"

region to the "beam-beam remnant" and the multiple parton scattering components of the

"underlying event." In this analysis we use the MidPoint algorithm (R = 0.7, fmerge = 0.75)

and correct the observables to the particle level. The corrected observables are then

compared with PYTHIA Tune A and HERWIG at the particle level (i.e., generator level).














CHAPTER 1
INTRODUCTION

Elementary particle physics is concerned with the understanding of the

fundamental constituents of matter. Our current understanding of nature reveals only a

small number of fundamental particles. Furthermore, the taxonomy is greatly simplified

because these particles are perfectly replicated in indistinguishable copies. It should then

be sufficient to simply list these particles and describe their interactions. Unfortunately,

due to their size, we are left to discover how they interact via indirect measurements.

Classically this requires the study of decay rates, bound states, and scattering

experiments. To fix the laws of physics in a formulated phrase, the traditional approach

is to guess a form of the interaction and compare the resulting theoretical calculations to

experimental measurements.

One important quantity measured by the experimentalist and calculated by the

theorist is the differential scattering cross section. Suppose particles 1 and 2 collide,

producing particles 3,4,...,n, the cross section is given by formula 1.1,

de 2 = I S d_ d'f z. d d3(2 r) dy4'34 (+ 1)
I i4 (p p2)2p-(m,m) ,(2x)2E, (2) 2E, ) (2x)2E, jx(2)46(p + p34 ) )

where M is the invariant amplitude (matrix element) for the process, p, = (E,, pi) is the

four-momentum of particle i (mass mi), Ei = mn + pi and S is a statistical factor

The inclusive jet cross section at the Tevatron, do/dET averaged over a small range

of pseudorapidity, rI = -In(tan 0/2), is an important object for study because it tests









perturbative QCD at the highest Q2 (Q2 = -q2 =(pi-pf)2) scale currently possible [1,2].

This measurement continues to substantiate QCD and contributes to its global data fitting

used to measure parton distribution functions [3]. It is imperative that we consider all

systematic effects that influence our interpretation of the measurement.

One of the contributing effects results from the "underlying event" that is present in

all proton-antiproton collisions. Figure 1-1 illustrates a "hard" 2-2 parton scattering with

transverse momentum, PThard. The "hard" scattering component is comprised of the two

outgoing jets plus initial and final-state radiation. Removal of the two outgoing jets

leaves only the "underlying event."


"Hard" Scattering ao

PTb(hard)

Proton AntiProton

Underlying Event ...Udeing Event
*..... Initial-State

Final-State
SRadiation
Outgoing Parton /


Figure 1-1: Illustration of the way QCD Monte-Carlo models simulate a proton-
antiproton collision in which a "hard" 2-to-2 parton scattering with transverse
momentum, p,,, has occurred. The resulting event contains particles that originate from
the two outgoing partons (plus initial and final-state radiation) and particles that come
from the breakup of the proton and antiproton (i.e. "beam-beam remnants"). The
"underlying event" is everything except the two outgoing hard scattered "jets" and
consists of the "beam-beam remnants" plus initial and final-state radiation. The "hard
scattering" component consists of the outgoing two jets plus initial and final-state
radiation.

Theoretical analysis of such a process uses simulations based on QCD Monte Carlo

models. The justification lies in the factorization theorem [4-6], which, roughly, states

that physical observables are the product of short distance functions and long distance









functions. The short distance functions are calculable in perturbation theory, where the

usual perturbative expansion in terms of Feynman diagrams is used to calculate matrix

elements. The long distance functions are fit at a scale, but their evolution to any other

scale is also calculable in perturbation theory. Of course, due to the nature of Quantum

mechanics it is impossible to distinguish initial state radiation from final state radiation.

However, in the Leading Log Approximation Figure 1-1 can be factorized into the

following subprocesses: (1) final state emission; (2) initial state emission; (3) the

elementary hard subprocess, which can be computed exactly to finite order in

perturbation theory; and (4) The hadronization process.

Refinement of each of these subprocesses extends the comparative scale of high

energy physics. The work presented here extends to higher energies the previous

characterization of the "underlying event" [7-13]. Unlike the previous analysis we

examine the energy in the transverse regions and correct the data back to the particle

level.

1.1 Forces and Particles

Four known forces serve as the impetus of our physical theories: strong,

electromagnetic, weak, and gravitational. Intimately related to these forces are the

relatively few "elementary" particles on which they act: leptons, quarks, and bosons.

Our current understanding of gravity started with Sir Isaac Newton's law of

universal gravitation. This classical theory of gravity saw its relativistic generalization to

the general theory of relativity by Albert Einstein. However, gravitational forces are the

weakest, and they are important for massive bodies but negligible for nuclear and

subnuclear particles.









Electrodynamics, the theory describing electromagnetic forces, owes its classical

formulation to the Scottish physicist James Clerk Maxwell. It was not until the 1940's

that Tomonaga, Feynman, and Schwinger would perfect the quantum theory of

electrodynamics. The theory of weak interactions or flavordynamics was originally

formulated by Fermi in 1933, but in the 1960's Glashow, Wienberg, and Salam (GWS)

put it into its present form. In the GWS model the weak and electromagnetic interactions

are treated as different manifestations of a single electroweak force. This electroweak

force provides for the attraction between charged particles and is responsible for the P

decay of nuclei.

Chromodynamics emerged in the mid-seventies to support the pioneering work of

Yukawa on the strong force. The work of Gross, Politzer, and Wilczek on a strong force

earned them recent recognition in the form of the 2004 Nobel Prize in physics. Strong

forces act only at very small distances: they bind quarks into nucleons and nucleons

together to make nuclei.

All of these apparently different forces are each mediated by the exchange of an

integer-spin particle, called a boson. Table 1-1 summarizes the properties of the gauge

bosons of the Standard Model.

Table 1-1: Gauge bosons and forces of the Standard Model. There are eight different
species of gluons each corresponding to a particular color charge.
Boson Force Spin Charge [e] Mass [GeV/c2] Range [fm]

g strong 1 0 0 <~1
y electromagnetic 1 0 0 o
W weak 1 1 80.425+0.038 = 10-3
Z weak 1 0 91.18760.0021 = 10-3









The Standard Model [14, 15] classifies elementary particles as structureless at all

scales presently accessible. Furthermore, it states that all visible matter consists of

elementary particles of two kinds: leptons and quarks. These particles are interpreted as

quantum excitations of a field and are characterized by having spin V2 intrinsic angular

momentum in units of h. They obey the Pauli Exclusion Principle and are called

fermions. There are six types of leptons and six types of quarks which are each grouped

into three generations according to their mass, the properties of which are summarized in

Tables 1-2 and 1-3. Each has an associated antiparticle with the same mass and spin but

opposite charge.

Table 1-2: Properties of leptons.
Lepton Spin Charge [e] Mass [MeV/c2]
1stgeneration e" 1/2 -1 0.510998920.00000004
Ve 1/2 0 < 3*10-6
2d generation 9- 1/2 -1 105.6583690.000009

v4 1/2 0 < 0.19
3rd generation z 1/2 -1 1776.9929
v, 1/2 0 < 18.2


Table 1-3: Properties of quarks.
Quark Spin Charge [e] Mass
1st generation u 1/2 +2/3 1.5-4 MeV/c2
d 1/2 -1/3 4-8 MeV/c2
2"d generation c 1/2 +2/3 1.15-1.35 GeV/c2
s 1/2 -1/3 80-130 MeV/c2
3rd generation t 1/2 +2/3 178.04.3 GeV/c2
b 1/2 -1/3 4.1-4.4 GeV/c2









1.2 The Standard Model

The Standard Model of strong, weak, and electromagnetic interactions is based on

the symmetry group SU(3)cxSU(2)LXU(l)Y [16] where the subscripts denote special

features of a given symmetry which act on the quark and lepton fields. The C in SU(3)c

stands for color. Each quark has three color components and SU(3)c transforms them

into one another. SU(3)c, the basis of quantum chromodynamics (QCD), is an exact

symmetry of nature. There are eight massless gluons which correspond to the eight

gauge fields of SU(3)c. This description requires a new quantum number: color charge.

By convention, the three colors are red, green, and blue and each quark is supposed to

carry one of these colors. The gluons, the quanta of color fields, also carry color. Quarks

are bound together in hadrons by the strong color force via the exchange of colored

gluons. All observed hadrons are described in the parton model as color singlet states

(referred to as "colorless") composed of three quarks baryonss: qqq) or of a quark-

antiquark pair (mesons: qq). The quarks of these configurations are called valence

quarks because they are responsible for the charge and other quantum numbers of

hadrons.

The L on SU(2)L, the weak isospin group, denotes the fact that only left-handed


components, TL, of spinor fields, L = 2 transform as doublets under that



group. The right-handed spinor components Y/R -2- are isosinglets under


SU(2)L; i.e., they are unchanged under SU(2)L transformations and therefore do not

WI +W2
couple to its three gauge fields which we denote by W, and W The fact
J2 n 3.Tefc









that only left-handed quarks and leptons couple to those gauge fields makes their (weak)

interactions maximally parity violating [17].

The Y on U(l)y stands for weak hypercharge, the charge associated with that

Abelian group. That gauge group has one gauge field B, that couples to quarks and

leptons via their hypercharge Y. It couples to left and right handed components of these

particles differently and therefore also violates parity, but not maximally. The

SU(2)LXU(l)y part of the standard model is not an exact symmetry. If it were, the W,

W3, and B, would all be massless gauge bosons. That is not the case. To accommodate

electroweak phenomenology, a scalar (spin 0) field is introduced which breaks the

symmetry SU(2)LXU(l)y down to the U(1) symmetry of QED. That breaking gives mass

to the W:, and the combination of fields Z, = W3 cos 9 B, sin 0, which is called the

Z boson. The orthogonal combination A, = B, cos 8, + W3 sin 0, remains massless and

is identified as the photon. The angle 0,, called the weak mixing angle, is

experimentally found to be sin2 0, = 0.23. That leads to standard model predictions

Massw = 80GeV/c2 and Massz = 91GeV/c2. The discoveries of the W [18, 19] and Z [20,

21] bosons by the UAl and UA2 collaborations at Cern substantiate the validity of the

Standard Model. The search for the spin 0 Higgs Boson continues to be one of the most

important problems to be addressed during Run 2 at the Tevatron and future LHC

experiments.


1.3 QCD and the Structure of Hadrons









QCD is a non-Abelian' gauge theory that is based on the SU(3)c group of

transformations which relate quarks of different colors. The gauge bosons associated

with the eight group generators, known as gluons, can be emitted or absorbed by quarks

in transition in which the color (but not flavor) can change. Since the gluons themselves

carry color they can interact with each other as well.

In quantum field theories like QED and QCD any charge (color or electromagnetic)

is shielded by a cloud of polarized charges: a quark can emit a gluon which can convert

into qq or gg pairs which in turn can radiate gluons and we have a branching tree of

quarks and gluons (this effect is called vacuum polarization). Because of the effect of

charge screening the charge one measures depends on the distance (or wavelength, or

transferred momentum Q2) with which one is probing the charge itself. We thus have a

"running" coupling constant which changes with the transferred momentum:

a=a(Q2) with Q2 =-q2 >0 (1-2)

where q is the four-momentum of the virtual boson exchanged between charges.

For both QED and QCD the effective coupling constant a depends on the

momentum (or distance) scale at which it is evaluated, and takes the general form of

equation 1-3.

(Q2) a(O) (1-3)
S-X(Q2)

Where a(0) for QED is the fine structure constant and is approximately equal to 1/137.

For QED it can be shown that X(Q2) takes the form of equation 1-4.


' A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold.









X(Q2) f Inf( (1-4)
t,.te 3u2 t)

Here Nf is the number of fundamental fermions with masses below V1QI and gA is the

mass of the heaviest fermion in the energy region being considered. Clearly, X(Q2) for

QED is > 0, and the coupling constant grows with energy. At some energy scale the

coupling of QED becomes strong and perturbation theory no long applies. Due to this

behavior, the bare charge in QED is said to be "ultraviolet divergent."

The coupling constant in QCD exhibits the opposite behavior. It can be shown that

X(Q2) for QCD takes the form of equation 1-5.

( 2) In ,1N (1-5)
X(Q 1 2 f -


Here Nf is the number of quark flavors with masses below V21QI and g. is the mass of the

heaviest quark in the energy region being considered, and Nc is the number of colors. In

contrast to the form of the QED term, for 6 flavors and 3 colors 2N-llNc < 0 and

therefore a(Q2) decreases with increasing momentum (or shorter distances). Only in a

world with more than 16 quark flavors (we are safely below this number at present

energies) is the sign of X(Q2) the same as in QED. This results in an antiscreening of the

color charge: by moving closer to the original quark the amount of the measured color

charge decreases.

The QCD "running coupling constant" (Eq. 1-6) is usually expressed in terms of a

parameter, AQCD, that indicates the magnitude of the scale at which as(Q2) becomes


1s (Q2)= 4r
N3 N, In (1-6)
3 c3 A2CD









strong; it is determined experimentally to be about 0.2 GeV.

Figure 1-2 compares the relative strength of the strong and electromagnetic forces

at different energy scales. With three colors and six flavors we can see that as(Q2) in eq.

1-6 goes to zero as Q2 goes to infinity. This results in quarks and gluons appearing

almost like free particles when probed at very high energies or short distances. This

behavior is called asymptotic freedom and allows perturbation theory to be applied to

theoretical QCD calculations to produce experimentally verifiable predictions for hard

scattering processes.

Asymptotic freedom is quickly overcome by the strong force as color charges

separate. In contrast, as two electrically charged particles separate, the electric fields

between them quickly diminish, allowing electrons to become unbound from nuclei.

However, the gluon field lines associated with color charges do not radially fan out but

remain confined to a narrow cylindrical region. This leads to an interaction energy that is

proportional to the separation distance of the sources of the field lines. When quarks

become separated, as happens in high energy hadron collisions, at some point it is

energetically favorable for a new quark/antiquark pair to "pop" out of the vacuum than to

allow the quarks to separate further. As a result of this, when quarks are produced in

collisions, instead of seeing the individual quarks, we see an avalanche of colorless

particles clustered together moving in roughly the same direction known as jets. This

process is called hadronization, fragmentation or string-breaking.










0.1B -. | |ji



0.10




oto electromagnetic -



0.00oo I I I
100 104 10s 1012 1016 1020
Energy in GeV
Figure 1-2: Relative strength of the strong and electromagnetic forces


1.4 Hadron Hadron Interactions

From a phenomenological point of view, we can consider two hadrons colliding at

high energies, such as we have at the Tevatron Collider, to be colliding broad-band

beams of quarks, antiquarks, and gluons. An average hard scattering event consists of a

collection (or burst) of hadrons traveling roughly in the direction of each of the initial

beam particles and two collections of hadrons with large transverse momentum. The two

large transverse momentum jets are roughly back to back in azimuthal angle. One can

use the topological structure of hadron-hadron collisions to study the "underlying event"

[13, 22-24]. Of course, from a certain point of view there is no such thing as an

"underlying event" in a proton-antiproton collision. There is only an "event" and one

cannot say where a given particle in the event originated. On the other hand, hard

scattering collider "jet" events have a distinct topology. On the average, the outgoing

hadrons "remember" the underlying 2-to-2 hard scattering subprocess.









1.4.1 Parton Model and Large PT Processes

Hadronic collisions which involve a short distance scattering can be described, in

first approximation, by the Parton Model. Since the transferred momentum is the

conjugate variable of the (quark-quark) impact parameter, larger Q2 implies that partons

have scattered at small distances where as is small. In order to be able to apply

perturbation theory one needs a momentum transfer of about 10 GeV: from the

uncertainty principle we calculate that the associated distance is in the order of 10-7m.

From the experimental point of view there is no certain way to separate such rare events

but intuition suggests that large Pt final state particles should be a good indication and

experiments fully support this.

We can picture this scattering process as a sequence of three different phases

occurring at different time scales. Partons approach each other carrying a fraction, x, of

the momentum of their parent hadrons. The transverse moment of the partons are

neglected. "Parton Distribution Functions" (PDF) f, (x,/2 ) are so introduced giving the

probability for parton i to have fractional momentum between x and x + dx (gi is a

factorization scale). Figure 1-3 is an example of such parton distribution functions.

These functions are extracted from experimental data in deep inelastic scattering (DIS) of

leptons on nucleons [25]. These parton distribution functions of the proton are a result of

the work done by the H1 [26-28] and ZEUS [29] collaborations at HERA, and of the

inclusive jet distribution by DO [30] and CDF [31] collaborations at the Tevatron. As the

data only cover a finite range of Q2, the evolution of such functions with Q2 is computed,

using perturbation theory, with the Altarelli-Parisi equation [32].






13


1.2
MRST2001 up
1.0- Q= 10GeV2 down
-- antiup
-- antidown
0.8
0.8 -- strange
charm
0 0.6 -- gluon


0.4


0.2


0.0
10"3 102 101 100
X
Figure 1-3: The parton structure functions extracted from an analysis of deep inelastic
scattering data at Q2=10GeV2.


A hard collision then takes place between a pair of partons regarded as free

particles. Predictions for jet production are given by folding the parton distribution

functions with perturbatively calculated "two-body" scattering cross sections d'i. Any

cross section of interest is calculated using equation (1-7).


a= fi ,(x "k f2,,p2 ij p1 2 2 (1-7)


Figure 1-4 shows the representation of an elementary "two-body" interaction

between two partons in a ppj collision producing a di-jet event.






14



PP




Jets

P2 "
fi (x2) P2=X2P2




Figure 1-4: Hard "two-body" parton interaction producing a di-jet event in a proton-
antiproton collision.

The factorization scale g discriminates whether a parton, inside the incoming

hadron, takes part or not in the hard scattering: if the momentum of a parton is greater

than the scale g, it contributes to the short-distance cross section (as the partons i and j in

fig. 1-4); if its momentum is less than the scale g, it is considered part of the hadron

structure not involved in the hard interaction (spectator parton).

1.4.2 The "Underlying Event" in Proton-Antiproton Collisions: Pythia and Herwig

Fig. 1-1 illustrates the way QCD Monte-Carlo models simulate a proton-antiproton

collision in which a "hard" 2-to-2 parton scattering with transverse momentum, PT(hard),

has occurred. The resulting event contains particles that originate from the two outgoing

partons (plus initial andfinal-state radiation) and particles that come from the breakup of

the proton and antiproton (i.e., "beam-beam remnants"). The "underlying event" is

everything except the two outgoing hard scattered "jets" and receives contributions from

the "beam-beam remnants" plus initial and final-state radiation. The "hard scattering"

component consists of the outgoing two jets plus initial and final-state radiation. Any

measured observable of the underlying event necessarily receives contributions from









initial and final state radiation. It is possible to reduce these contributions by placing

constraints on event topology and jet energy.

The "beam-beam remnants" are what is left over after a parton is knocked out of

each of the initial two beam hadrons. It is the reason hadron-hadron collisions are more

"messy" than electron-positron annihilations and no one really knows how it should be

modeled. For the QCD Monte-Carlo models the "beam-beam remnants" are an important

component of the "underlying event." Also, it is possible that multiple parton scattering

contributes to the "underlying event." Figure 1-5 shows the way PYTHIA [33] models

the "underlying event" in proton-antiproton collision by including multiple parton

interactions. In addition to the hard 2-to-2 parton-parton scattering and the "beam-beam

remnants," sometimes there is a second "semi-hard" 2-to-2 parton-parton scattering that

contributes particles to the "underlying event."

For the hadronization process we have three types of non-perturbative contributions

to consider: (1) representation of the incoming partons as constituents of the incident

hadrons via parton distribution functions; (2) the conversion of the emitted partons into

outgoing hadrons using quark and gluon fragmentation functions; and (3) the "soft"

component to the "underlying event" generated by spectator partons. The "underlying

event" receives contributions from the original ppj system ("beam-beam remnants"),

initial and final-state radiation, and possibly hadrons resulting from multiple parton

interactions, as in Figure 1-5.










Multiple Parton



Proton


Parton


SEvent


Fig. 1-5. Illustration of the way PYTHIA models the "underlying event" in proton-
antiproton collision by including multiple parton interactions. In addition to the hard 2-to-
2 parton-parton scattering with transverse momentum, PT(hard), there is a second "semi-
hard" 2-to-2 parton-parton scattering that contributes particles to the "underlying event".

Both of the QCD Monte Carlo models, HERWIG [34] and PYTHIA, include a

"soft" underlying event structure that is modeled by a parameterization of minimum bias

data, and creates jets from the beam remnants. This is an imperfect model of the

"underlying event," since it always contains particles, yet the soft underlying event can

be absent, as shown by the finite survival probabilities for inelastic events with large

rapidity gaps [35-38]. PYHTIA has added multiple parton interactions to enhance the

activity of the "underlying event," and Tune A [22-23] was specifically tuned to fit the

"underlying event" in the Run I data.

The QCD perturbative 2-to-2 parton-parton differential cross section diverges as the

transverse momentum of the scattering, PT, goes to zero (see figure 1-1). PYTHIA uses a

tunable parameter to prevent divergences at low PT. Tune A was tuned to fit the Run I

data, and the low PT region was an area of focus. HERWIG does not allow for this, and a

suitable PT cutoff most be chosen. We use PT > 5 GeV/c for all 2-to2 hard scattering

events in HERWIG.














CHAPTER 2
ACCELERATOR AND DETECTOR

The Tevatron [39] ppj Collider is currently the world's highest energy particle

accelerator in operation. It is the largest in a chain of five accelerators at the Fermi

National Accelerator Laboratory (FNAL, Fermilab) and is capable of producing proton-

antiproton collisions at a center of mass energy -s =1.96 TeV. The Collider Detector at

Fermilab (CDF) [40] and DO [41] are the multipurpose detectors built at collision points

to exploit physics at the Tevatron. The analysis presented in this dissertation is based on

the data sample collected by CDF during the 2001-2004 (Run II) running period of the

Tevatron.

2.1 The Accelerator Complex

The Accelerator Complex at FNAL (see Figure 2-1) uses multiple stages of

acceleration to achieve proton-antiproton collisions at a center of mass energy -=1.96

TeV. The protons used in the collisions originate from ionized Hydrogen gas molecules.

These H' ions are first accelerated to 750 KeV in the Cockcroft-Walton accelerator. They

are then fed into the Linac, a 150m long series of nine radio-frequency (RF) cavities

which produce an electric field that rapidly changes direction. In this linear accelerator

the H' ions are brought to 400 MeV. Subsequent to this stage, the beam is focused and

made to collide with a thin fixed carbon target which affects the loss of two electrons per

ion. The denuded H' ions are now the protons that will ultimately be collided or used to

make the anti-protons at the Target Station.









The 75.5 m radius Booster is a fast cycling proton synchrotron of conventional

magnets (used to steer and focus the beam) and an RF cavity (used to accelerate the

beam). The accelerated protons leave with kinetic energy of 8 GeV and are then injected



FERMILAB'S ACCELERATOR CHAIN

MAIN INJECTOR

TEVATRON I ECYCLER

ZERO -TARGET HALL
ANTIPROTON
SOURCE
CDF
BOOSTER
-.-.- -LINAC
COCKCROFT-WALTON
PROTON .. -

EUTRINo0. : MESON




Figure 2-1: Overview of the accelerator complex at Fermilab. H- ions are injected into
the linac from the Cockcroft-Walton, to travel to the Booster, then to the Main Ring, and
finally to the Tevatron. Some protons are extracted from the Main Ring and are used to
make anti-protons. The anti-protons are re-injected into the Main Ring and then into the
Tevatron. The final ppi center of mass energy is =1.96 TeV.

into the Main Ring. These protons are then further accelerated to 150 GeV in the Main

Injector, and finally brought to 980 GeV by the Tevatron. The Tevatron was the world's

first superconducting synchrotron. The beam is guided around the closed path by dipole

magnets. As the beam energy is ramped up by RF cavities from 150 GeV to 980 GeV,

the bending magnetic fields and the RF frequency must be carefully synchronized to

ensure beam stability. The transverse motion of the beam is stabilized by quadrupole

magnets that take advantage of magnetic field gradient technology.









Anti-protons are produced by sending 120 GeV protons from the Main Injector to a

nickel target. From the resulting shower of particles, antiprotons of around 8GeV are

selected and sent to the Debuncher and Accumulator Rings where RF and stochastic

cooling systems are used in the momentum stacking process. Once a 'stack' has been

collected the antiprotons are sent back to the Main Injector, accelerated to 150 GeV and

put into the Tevatron, circulating counter to the proton bunches. For every million

protons that hit the target, only about twenty 8 GeV anti-protons will be stacked into the

Accumulator.

The Recycler is placed directly above the Main Injector beamline. This dual

function system serves as a post Accumulator storage ring and as a recycler for the

antiprotons left over at the end of a store'. These recycled anti-protons can be mixed

with those from the Accumulator and then accelerated to 150 GeV in the Main Injector

and then injected into the Tevatron.

Once both beams are at the maximum energy they are focused and brought to

collision at the two interaction points, one of which is at the center of the CDF detector.

The luminous region has a Gaussian dispersion of around 30g1m transverse to the beam

direction, and a length along the beam direction of around 30cm.

The beams typically circulate for 12-18 hours during which time the luminosity

falls approximately an order of magnitude. During this time antiproton are continuously

stacked. When the stack is sufficiently large and the luminosity has significantly

decayed, the beam in the Tevatron is dumped and new bunches are injected.


SA store refers to the period of time when proton-antiproton collisions are taking place. Stores can be
selectively terminated when luminosity has reached a minimum or a new stack of antiprotons is ready.
Alternatively, a store can end with a magnet quench or other problem.









The instantaneous luminosity L is given by equation 2-1

L fNpN (2-1)
L=
A

where is the frequency of bunch crossings, Np and N,, are the number of protons and

antiprotons, respectively, per bunch, and A is the effective area of the crossing beams.

The current status of the luminosity is shown in figure 2-2, and the integrated luminosity

delivered to tape is shown in Fig. 2-3.

Parts of the Fermilab accelerator complex are 20 years old and there have been

some setbacks since the upgrades to take the Tevatron from 1.8 TeV to 1.96 TeV.

However, the initial instantaneous luminosity of stores has been steadily increasing. The

Year 2002 2003 2004 2005
Month 1 4 7 10 1 4 7 101 4 7 1.4

140

120

0 100 ..0 "-

0 0so

S60 I I"



20 r' -



Store Number
Figure 2-2: Run II instantaneous initial luminosity








Year 2002 2003 2004 2005
Month 1 4 7 10 1 4 7 101 4 7 1 4

.&000

g soo



200
31600





Delivered
To tape

1000 1500 2000 2500 3000 3500 4000
Store Number
Figure 2-3: Run II integrated luminosity

projected goal for all of Run II is 4-8 fb'- by the time LHC is ready to begin taking data

(circa 2009).

The total number of events n in a scattering process is proportional to the

luminosity and the cross section a of the process,

n = La 2-2

We can get a rough sense of the reach for new physics and the challenge of enhancing

signal and suppressing background by considering the following examples. At a center-

of-energy of 1.96 TeV, we have:

or(pp anything)= 75mb 2-3

o(ppi -t tt + anything) 6pb 2-4

With about 1fbl' of delivered luminosity we should have seen 6000 top events. However,

not every second of delivered luminosity is observed. Moreover, due to finite capabilities









in data storage not every observed event can be recorded. The task of observing the

events fall on the Detector and the job of selecting events to be recorded is given to the

trigger system.

2.2 The Collider Detector at Fermilab

The Collider Detector at Fermilab (CDF) is a large, multilayered general purpose

detector designed to study a wide range of processes occurring in proton-antiproton

collisions. Figure 2-4 is a schematic drawing of the approximately 5000 ton, 10 m high,

and 27 m long detector. The CDF is cylindrically symmetric about the beam axis and

has a forward-backward symmetry in its tracking, calorimetric, and muon systems.

Figure 2-5 shows an elevated view in which the tracking system is seen to be contained in

a solenoid coil. The calorimetry and muon systems are outside the solenoid. These sub-

systems are described in more detail below.


Figure 2-4: Solid cutaway view of the CDF II detector.















V" S AVj- A W
ax is point-su the p .itive x '-axi point' radi',ll",..twad:fromt
.....* -, (J A-, 4S)



1,. (' '.I ,. ,

---- .ON Jt0 0 .

.:,,,..' /r ..
.. i, .' i I. ---- _-- j.





I, B '. >"








Figure 2-5: Elevation view of the CDF II detector.

2.2.1 The CDF Coordinate System

The geometric center of the detector serves as the nominal interaction point (0,0,0).

Figure 2-6 shows the overall CDF coordinate frame, in both cylindrical and Rectangular

systems. The positive z-axis corresponds to the proton beam direction, the positive y-

axis points vertically upward, and the positive x-axis points radially outward from the

center of the Tevatron ring. In the cylindrical system the azimuthal angle < is measured

about the beam axis from the positive x-axis. The polar angle 0 is defined as the angle

measured from the positive z-axis.









ly




Anti-Protons Protons
J /z (0,0,0) "' x




Figure 2-6: The CDF coordinate system.

The incident proton and anti-proton have no transverse momentum and they have

equal and opposite longitudinal momentum, therefore the total momentum of the

products of the collision would sum to zero in a full 4n solid angle experiment.

However, some space must be left for the beam pipe. Those particles from the collision

that travel at very small angles, two degrees or less (such as hadrons from spectator quark

hadronization), will fly down the beam pipe completely missing the detectors. Such

unmeasured particles will not carry much transverse momentum, but they may carry

significant amounts of longitudinal momentum. For this reason, longitudinal momentum

will not balance in the detector, but the transverse momentum will, to the detectors

accuracy.

For these reasons, rather than using the total energy E and total momentum p, we

generally use the transverse energy E, = Ex sin(O) and the transverse

momentum p, = p x sin(0). In the large energy collisions found at CDF, the E, and pt of

particles in the event are nearly equally. However, by convention we use Et when

referencing energy deposited in the calorimeters, so that it is understood that the angle 0

refers to the geometric center of the detector. Alternatively, Pt usually refers to the

transverse momentum of a particle determined in a tracking chamber so that the angle 0









reflects the true interaction vertex. It is common to use the pseudorapidity in place of the

polar angle 6.

The "natural" kinematic variables for hadron collisions are pseudorapidity,

transverse momentum, and azimuthal angle since the shapes of their distributions are

invariant under a Lorentz boost. Transverse momentum and azimuthal angle are

invariant to Loretnz transformations along the z axis and the pseudorapidity is simply

additive.

The major components of the CDF detector are arranged cylindrically around the

interaction point. Closet to the beamline are the layers of silicon, providing high-

precision tracking and vertexing in the r-( plane. Next is a wire drift chamber that

provides measurements of momentum and spatial parameters of a particles trajectory

(track). The tracking subsystem is embedded inside a superconducting solenoidal magnet

that produces a 1.41 Tesla magnetic field. Energy measurements of jets, electrons,

photons, and hadrons are made by the combined calorimetry systems: central, plug and

forward electromagnetic (EM) and hadronic calorimeters (HAD). Muons are identified

by the presence of a track in the muon chambers matched to a track in the central tracking

chamber. Because of the long lifetime and high penetration of muons, the muon

chambers are placed outside of the hadronic calorimeters, after a steel absorber to

eliminate any electromagnetic and hadronic showers. In front of the backward and

forward calorimeters is a plane of scintillation counters called "Beam-Beam Counters"

(BBC). They provide a minimum bias trigger for the detector and are also used as the

primary luminosity monitor. The layout of these detectors is shown in figure 2-7, which

depicts one quadrant of the cross-section through the detector.












1==0


"' CDF

Detector






Forward
(Not-To-Scale)



rl=2.4


IeTRACTIONPOINT =4.2

Figure 2-7: A quarter of the CDF detector. Only the central and end-plug subsystems are
shown.

2.2.2 Tracking

The CDF uses silicon strip detectors (LOO + SVXII + ISL) and a drift chamber

(COT) for charged-particle track reconstruction and vertex finding. The tracking systems

are inside a superconducting solenoid of radius 1.5m that provides a 1.41 Tesla magnetic

field parallel to the beam axis. The magnetic flux is returned through a steel yoke. The

tracking volume and the endplug calorimeters are shown in figure 2-8. The yoke also

functions as a support to the calorimeters located radially outside the solenoid. The

silicon system and drift chambers were redesigned and completely rebuilt between Run I

and Run II of the Tevatron.










2.0 7 =1.0 o
L 30f



.0=2.






030

/ 0 t1.0 2.0 3.0 m

LAYER 00 SVX II INTERMEDIATE SILICON LAYERS

Figure 2-8: The CDF II tracking volume.

In the silicon tracker, as charged particles move through the 'depletion layer'

created in a biased p-n semiconductor junction, they create electron-hole pairs that drift to

be collected at the surfaces. This induces a signal on metal stripes that have been

deposited on the surface and connected to readout amplifiers. Figure 2-9 shows a

schematic layout of the silicon tracking system.

Layer 00 (LOO) is mounted on the beam pipe, 1.6 cm from the beam axis, and

consists of 8 single sided microstrip silicon detectors. These detectors cover the beam

pipe for about 40 cm in each direction about z = 0 [42]. Outside the L00, the 'Silicon

Vertex Detector' (SVXII) occupies the volume between 2.4 and 10.6 cm from the beam

axis and covers a total length of 96 cm along the z coordinate. The SVXII system

consists of five double sided microstrip silicon layers [40]. Three of these layers provide

track position in the r-O plane from the readout of one side (microstrips parallel to the







beam axis) while the z coordinate is determined by the other side (microstrip
perpendicular to the beam axis). The other two other layers have their microstrips tilted in
such a way as to provide a 3-D track reconstruction with an approximately uniform
efficiency. The Intermediate Silicon Layers (ISL) Detector is placed in the region
between SVXII and the central tracking system [40]. Figure 2-9 shows the position of
the ISL detector. The layers are in the radial range 20 < r < 30 cm and extend to Izl = 65
cm for the inner layer and Iz| = 87.5 cm for the outer layer. The ISL covers the range of
pseudorapidity for TIrl < 2. Figure 2-10 shows an end view of the three components of the
silicon microstrip detector system.

i 'X
ol /
R=29 cm -I

(LI I /=
I /I

Port Cards .




(SVX 11)


(Layer IL00
S- .
-- /



90 cm
Figure 2-9: Schematic layout of the silicon tracking system. The innermost layer,
Layer00 consists of 6 sensors in z.








The Central Outer Tracker (COT) is a large cylindrical drift chamber used to

determine precise position measurements [40]. The tracking at large radii in the central

rapidity region (1i71<1) is done with a large open cell, cylindrical drift chamber using a

readout that can record multiple hits from each sense wire. The active volume of the

COT spans 310 cm in the beam (axial) direction, z; between 43.4 cm and 132.3 cm in

radius, r; and the entire azimuth, 4. The COT provides 96 measurement layers, organized

into alternating axial and +2 stereo superlayers. Sense wires and potential wires are

alternated and arranged in 8 'superlayers' as shown in Figure 2-11, each consisting of 12

layers of sense wires. Within each superlayer are 'cells', bounded by field-shaping

sheets. The cells are angled at 350 to the radial direction to compensate for the Lorentz


Layer 00







isL


SVX II

64 cm


Figure 2-10: End view of the three components of the silicon microstrip detector system.





























Figure 2-11: The COT sense wires and potential wires are alternated and arranged in 8
'superlayers'.

angle of the drifting charged particles. There is a 'spacer' at z = 0 that results in a lower

tracking trigger efficiency at '1 = 0. The chamber is filled with a 50:50 mixture of

Argon/Ethane and a small amount of alcohol. The hit position resolution is

approximately 140ptm and the momentum resolution or(p,) / p = 0.0015(GeV / c)-'. A

reconstructed track provides accurate information in the r-O view for measurement of

transverse momentum, PT, and substantially less accurate information in the r-z view for

the measurement of r.

2.2.3 Calorimeters

As charged particles progress through the calorimeters they interact and develop

characteristic 'showers'. Different size and thickness plastic scintillator and absorber

layers are alternatively stacked forming the electromagnetic calorimeters (allowing for

the energy measurement of photons and electrons) and the hadronic calorimeters









(measuring hadron energies). The primary particle produces a shower of secondary

particles inside the absorber. The shower particles deposit a fraction of their energy in

the sampling material producing a light signal read by photomultipliers (PMTs) through

wavelength shifting (WLS) light guides or optical fibers.

As can be seen in figure 2-7, the CDF calorimeters are physically separated into two

sections: the central region, cylindrical about the beam line and covering |1|1 < 1; and the

forward or 'end plug' regions, covering 1.1 < |Irl < 3.6. The principal components of the

central calorimeter are the central electromagnetic (CEM) [43] and the central hadronic

(CHA) [44] compartments. Both the CEM and CHA are retained from Run I. They are

segmented in 1l and ( with a projective "tower" geometry, shown in action in Fig. 2-12.

In each tower the electromagnetic compartment is backed by the hadronic one, both

readout by different PMTs.

The central calorimeter is azimuthally arranged in 48 physically separated 150 wide

wedges each segmented in rI into ten towers, shown in figure 2-13. Each tower subtends

0.11 x 150 in 4 x rl. The central electromagnetic calorimeter (CEM) is overlapped by a

hadronic section split into two parts, the central hadronic calorimeter (CHA) and the wall

hadronic calorimeter (WHA). The CEM covers 0 < Ji| < 1.1 and uses lead sheets

interspersed with polysterene scintillator as the active medium and employs phototube

readout. The CHA covers 0 < I|ll < 0.9 and the WHA covers 0 < |Ir < 1.3. Both hadronic

calorimeters use steel absorbers interspersed with acrylic scintillator as the active

medium.

Located six radiation lengths deep in the CEM calorimeters, corresponding to the

depth at which showers typically reach their maximum transverse extent is the Central









Electromagnetic Strip Detector (CES). The CES uses proportional strip and wire

counters in a fine-grained array, as shown in Figure 2-14, to provide precise position

(about 2 mm resolution) and shape information for electromagnetic cascades.





















Figure 2-12: Calorimeter tower segmentation in TI-( space.

A further component of the central calorimeters is the central pre-radiator (CPR), a

set of proportional chambers between the CEM and the magnet designed to help separate

electrons and pions.

The plug calorimeters consist of the plug electromagnetic calorimeter (PEM) [45],

newly built for the CDF Run II, and the plug hadronic calorimeter (PHA). Like the

CEM, the PEM consists of a stack of lead and scintillator sheets read out by phototubes.

At 6 times the radiation length in the PEM is the plug shower maximum detector

(PES)[46].







































Figure 2-13: CEM/CES/CHA wedge.


Cathode
Strips


Anode Wires
(ganged in pairs)


Figure 2-14: CES strip and wire.


ZL

x









Finally, the first layer of the PEM is read out separately and referred to as the plug

pre-radiator (PPR). The PPR can help to distinguish between electron/photons and

hadrons by indicating the extent to which the particle shower has already developed at the

face of the calorimeter.

2.3 The CDF Trigger System

The inelastic proton-antiproton cross section at 1- = 1.96 TeV is about 60 mb

(-60x10 2cm2). For a typical instantaneous luminosity of about 1.2x1032 cm2/s we get

-7.6 million inelastic collisions per second at CDF. The CDF readout electronics and

event storage system is not capable of recording events at such a high rate. Moreover,

most of these events do not present a significant interest for the CDF physics program.

The trigger system is used to select an event rate of 75 Hz from the 7.6 MHz (132 ns

crossing) beam crossing rate [40]. The event rate is such that it is necessary to filter

physically interesting events to be written to tape, and this achieved through a three-level

trigger system, designed to be 'deadtimeless'.

The Level-1 trigger is achieved with hardware. Based on preliminary information

from tracking, calorimetry, and muon systems, the output of the 7.6 MHz Synchronous

pipeline with a 5544ns latency at the first level of the trigger is used to limit the rate of

accepted events to <50 kHz. Each next trigger level examines fewer events but in greater

detail. At the next trigger, with more refined information and additional tracking

information from the silicon detector, the -20 ps latency, asynchronous 2 stage pipeline,

reduces the acceptance further to 300 Hz. The Level 2 algorithm uses the information

about high momentum tracks and clustered calorimeter energy. If the accept decision is

made by the trigger, then the information form all subsystems is read out and passed on









to Level 3. At level-2 many triggers are prescaled to reduce the total acceptance rates to

a maximum of about 20 Hz that is the maximum that Level-3 can handle. This means

that a predefined fraction of events that passed the trigger are considered to fail it.

Prescaling is sometimes preferable over making tighter trigger cuts. This method allows

us to record as many rare events as possible while still accepting other data at a

reasonable rate. Some triggers can be dynamically prescaled. A dynamical prescale can

be changed during the course of the run depending on the instantaneous luminosity: it

will be large when the luminosity is high and small when the luminosity is low.

Level-3 consists of the event builder (EVB) and the Level-3 farm. The EVB

assembles event fragments from level-1 and level-2 into complete events, and then the

Level-3 farm runs a version of the full offline reconstruction code. This means that for

example that fully reconstructed 3-dimensional tracks are available to the trigger

decision. The Level-3 output rate is ~ 75 Hz and accepted events are written to tape in

eight separate 'streams', sorted by the Consumer-Server Logger (CSL).














CHAPTER 3
JETS AT CDF

We have studied the "underlying event" in the Run 2 jet trigger data samples using

the direction of the leading calorimeter jet (Midpoint, R = 0.7, fnmege = 0.75) to isolate

regions of rl-0 space that are sensitive to the "underlying event".

Hadronization of the outgoing partons forms the jets we see experimentally. Jet

algorithms are employed to map data onto jets with the idea that theses jets are surrogates

for the underlying energetic partons. In our theoretical picture, the partons produced by

the hard scattering process evolve approximately within a narrow cone based on the

parton showering and hadronization models. We use the Midpoint [47-49] jet algorithm

in which the properties of the constituents of the jet(J) of cone radius R are defined by the

following equations

k e J:(k _-J)2 + (Yk )2 < R2 3-1

ET,k k ETkyk 3-2
0i E ErI' YJ Er
kEJ ET, keJ ETJ

E,,T = ET,k. 3-3
keJ

The MidPoint cone algorithm is based on the so-called "Snowmass Algorithm" which

defines both the stability conditions and the properties of the jets [50].

The basic jet cone idea is that the constituents are nearby each other in simple

geometric fashion. That is, the 3-momenta of the hadrons or partons lie within a cone


defined by a circle in the angular variables (y,(p), where y = Iln[(E + p)/(E- p)] is
2









the true rapidity and (p is the azimuthal angle. A stable jet cone has the property that the

geometric center of the cone coincides with the ET weighted centriod of the particles in

the cone. Jet algorithms involve two distinct steps. The first is to identify the

"constituents" that comprise the stable cone that is the jet. The second involves

constructing the kinematic properties that characterize the jet. However, in practice the

experimental implementation of the cone algorithm is more complicated.

It was imagined that the entire particle/tower list of each event would be searched

for sets of final state particle/towers which satisfy the stability conditions. In practice this

is not possible because of limited computing resources so a number of compromises have

had to be made.

The Midpoint algorithm starts with an ET ordered list of seed towers (Eee >

threshold), and forms "protojets" from every stable cone iterated around a seed tower.

Seed Towers are simply calorimeter towers in which the energy deposition exceeds a

certain predefined limit (usually set to 1 GeV) which is larger than the limit defined to

include a tower in a jet (typically 0.3 GeV). A search for new protojets is carried out

about the Midpoints in (y,(p) between all pairs of protojets with AR < 2xRcon. The

Midpoint algorithm includes an iterative splitting/merging process applied to the PT

ordered list of jets to assign each particle to only one jet. Two jets are merged if the

lower PT jet shares greater than fmerge of its total PT with the higher PT jet. Otherwise the

two jets are split and the individual particles are assigned to the closest jet centriod.














CHAPTER 4
MONTE-CARLO GENERATION AND CORRECTION FACTORS

4.1 Monte-Carlo Generation

In this analysis the data are corrected back to the particle level using PYTHIA Tune

A [22, 23]. The corrected data are then compared with the particle level predictions of

PYTHIA Tune A and HERWIG (i.e. generator level) at 1.96 TeV. PYTHIA Tune A

(5.3.3nt) was generated with the minimum PT(hard) values shown in Table 4-1 and

HERWIG (5.3.3nt) was generated with the minimum PT(hard) values shown in Table 4-2.

Stntuples (5.3.3nt dev242) were created for the QCD group by Anwar Bhatti, Ken

Hatakeyama, and Craig Group.


Table 4-1: PYTHIA Tune A (5.3.3nt) at 1.96 TeV.
PT(hard) minimum Events

0 GeV/c 3,093,106
10 GeV/c 1,039,093
18 GeV/c 4,285,687
40 GeV/c 4,228,873
60 GeV/c 992,087
90 GeV/c 1,497,108
120 GeV/c 2,068,377
150 GeV/c 1,488,786
200 GeV/c 1,042,280
300 GeV/c 1,045,314
400 GeV/c 1,043,634
Total 21,824,345











Table 4-2: HERWIG (5.3.3nt) at 1.96 TeV.
PT(hard) minimum Events

3 GeV/c 1,014,070
10 GeV/c 1,018,974
18 GeV/c 5,001,261
40 GeV/c 5,071,205
60 GeV/c 1,044,202
90 GeV/c 2,057,661
120 GeV/c 2,035,473
150 GeV/c 1,922,568
200 GeV/c 968,906
300 GeV/c 885,867
400 GeV/c 858,936

Total 21,879,123


Smooth curves have been drawn through the QCD Monte-Carlo predictions to aid

in comparing the theory with the data. Fig. 4-1 shows an example of the fits to the

Monte-Carlo results.

4.2 Correcting the Data to the Particle Level

We consider two methods for correcting the data from the detector level to the

particle level. Method 1 is a "one-step" method in which PYTHIA Tune A and

HERWIG are used to calculate the observables in Table 4-3 at the particle level (in bins

of particle jet#l PT "GEN") and at the detector level (in bins of calorimeter jet#l PT

(uncorrected) "CDFSIM"). The detector level data, in bins of calorimeter jet#1 PT









(uncorrected), are corrected by multiplying by a QCD Monte-Carlo correction factor,

GEN/CDFSIM, as described in Table 4-4.

Table 4-3: Observables examined in the "transverse" region (see Fig. 6-2) as they are
defined at the particle level and the detector level. Charged tracks are considered "good"
if they pass the selection criterion given in Table 5-2. The mean charged particle
and the charged fraction PTsum/ETsum are constructed on and event-by-event basis and
then averaged over the events. There is one PTmax per event with PTmax = 0 if there are
no charged particles.
Observable Particle Level Detector level
Number of charged particles Number of "good" charged tracks
dNchg/drld) per unit rj-4 per unit r-(4
(pr > 0.5 GeV/c, hl < 1) (pr > 0.5 GeV/c, h1I < 1)
Scalar pr sum of charged Scalar pr sum of "good" charged tracks
dPTsum/dldd) particles per unit T1-4 per unit 11-4
(pr > 0.5 GeV/c, hi < 1) (pr > 0.5 GeV/c, h < 1)
Average pr of charged particles Average pr of "good" charged tracks
(pr > 0.5 GeV/c, hi < 1) (pr > 0.5 GeV/c, hi < 1)
Maximum pr charged particle
Maximum r charged particle Maximum pr "good" charged tracks
PTmax (pr > 0.5 GeV/c, hI < 1) (p > 0.5 GeV/c, h < 1)
PTmax = 0 for no charged
a r cre PTmax = 0 for no "good" charged track
particle
Scalar ET sum of all particles Scalar ET sum of all calorimeter towers
dET/dTId) per unit 11-4 per unit -(4)
(all pr, hi < 1) (Er > 0.1 GeV, hl < 1)
Scalar pr sum of charged Scalar pr sum of "good" charged tracks
particles (pr > 0.5 GeV/c, hi < 1)
PTsum/ETsum (pr > 0.5 GeV/c, h I < 1) divided by the scalar ET sum of
divided by the scalar Er sum of calorimeter towers
all particles (all Pr, Ir|l < 1) (ET > 0.1 GeV, hi < 1)


Method 2 is a "two-step" method. First PYTHIA Tune A is used to correct the PT

of the leading calorimeter jet. This is done by comparing the matching leading particle

jet with the leading calorimeter jet. Then PYTHIA Tune A is used to calculate the

observables in Table 4-3 at the particle level in bins of particle jet#l PT (GEN) and at the

detector level in bins of calorimeter jet#1 PT (corrected) (CDFSIMcor). The detector

level data in bins of calorimeter jet#l PT (corrected) are corrected by multiplying by the

QCD Monte-Carlo correction factor, GEN/CDFSIMcor. If the QCD Monte-Carlo









described the data perfectly and the detector simulation was exact then method 1 and

method 2 would yield the same result. Differences between the two methods can be used

as a measure of the systematic uncertainty in correcting the data to the particle level.

Table 4-4: Correction factors for Method 1. PYTHIA Tune A and HERWIG are used to
calculate the observables in Table 4-3 at the particle level in bins of particle jet#1 PT
(GEN) and at the detector level in bins of calorimeter jet#l PT (uncorrected). The
detector level data in bins of calorimeter jet#l PT (uncorrected) are corrected by
multiplying by QCD Monte-Carlo factor, GEN/CDFSIM.

Particle Level Detector Level Correction
Observable Observable Response FactorFactor


GEN = Particle CDFSIM = Calorimeter
CDFSIM/GEN GEN/CDFSIM
Jet#l PT Bin Jet#l PT Bin (uncorrected)



Fig. 4-2 and Fig. 4-3 show the particle level predictions from PYTHIA Tune A and

HERWIG for average density of particles, dNalI/dld(, for all particles with hi < 1 in the

"transverse" region as a function of the leading particle jet PT for "leading jet" and

"Back-to-back" events, respectively (see figure 6-3). It is interesting to note that

HERWIG produces more particles in the "transverse" region than PYTHIA Tune A. Fig.

4-2 and Fig. 4-3 also shows the average charged particle PTsum density, dPTsum/dTld4, and

the average charged particle for particles with h i < 1 in the "transverse" region for

"leading jet" events as a function of the leading particle jet PT. It is clear from these

comparisons that HERWIG produces more "soft" particles than PYTHIA Tune A which

will result in different "response" factors (see Table 4-4) at low leading jet PT.

































"TransMAX/MIN" Charged Particle Density: dN/dJd|
1.4
CDF Run 2 Preliminary "trnnMAX_"
1 .1,2 ------- NEPAMG ------- Up- 0 q9-0-0IR

1.0 ------ ------ fit --------
S"Leading Jet"
S. MidPoint R = 0.7 hjet)l <2
S0.6
J "tranaMiN"
0.4
t7 -----------------------I'"~I
0.2
1.96 TeV Charged Particles (|11<1.0, PT>0.5 GeV/c)
0.0 I -I-- -l I
0 50 100 150 200 250 300 350 400 450 500
PT(particle jet#1) (GeV/c)

Figure 4-1: Example of fits to the QCD Monte-Carlo results. Shows the particle level
predictions at 1.96 TeV for the density of charged particles, dNchg/drld), with pr > 0.5
GeV/c and ITll < 1 in the "transMAX" and "transMIN" regions for "leading jet" events
defined in Fig. 6-3 as a function of the leading particle jet PT for PYTHIA Tune A (top)
and HERWIG (bottom).


"TransMAX/MIN" Charged Particle Density: dN/ldrdjl
1.4
CDF Run 2 Preliminary
S1.2 ----- PYTHIATune A ----------


"Leading Jet"
S0.8
. MidPoint R = 0.7 Y(jet)l < 2
0.6

0.4 -------------------------------- ---

0.2
1.96 TeV Charged Particles (|ql<1.0, PT>0.5 GeV/c)
0.0
0 50 100 150 200 250 300 350 400 450 500
PT(particle jet#1) (GeV/c)












"Transverse" Particle Density: dN/dtqdl
5.0
HW Leading Jet"
I'4.0 a- ------------ --- --- ---- -- -------- -- -
4.0 -- -




2PY Tune A
. CDF Ru Preliminary MidPoint R = 0.7 jet) 2--------------
I CDF Run 2 Preliminary MidPoint R = 0.7 q(Jet)I < 2
E in ...


generator level theory
1.96 TeV


All Particles (nhl<1.0, all PT)


0 50 100 150 200 250 300 350
PT(particle jet#1) (GeV/c)


400 450 500


"Transverse" PTsum Density: dPT/dqid7
1.8
S CDF Run 2 Preliminary .
genratorlevel theory --

3 1.2 -
E
"Leading Jet"
0.6

MidPoint R = 0.7 |q(jet) < 2
1.96 TeV Charged Particles (Ihl<1.0, all PT)
0.0
0 50 100 150 200 250 300 350 400 450 500
PT(particle jet#1) (GeV/c)


"Transverse" Average Charged PTI


I 0 50 100 150 200 250 300 350 400 450 500
I PT(particle jet#1) (GeV/c)

Figure 4-2: Particle level predictions from PYTHIA Tune A and HERWIG for average
density of particles dNall/drld) (top), the average charged particle PTsum density,
dPTsum/drldo (middle), and the average charged particle (bottom) for particles with
hi < 1 in the "transverse" region for "leading jet" events defined in Fig. 6-3 as a function
of the leading particle jet PT.













"Transverse" Particle Density: dN/dTd*
5.0
CDF Run 2 Preliminary "Back-to-Back"
generator level theory
4 .0 --------- ---- -- --




2.0
PYTuneA
1.0 ---- ----- MidPoint R = 0.7 tQ( 1.96 TeV All Particles (ql<1 .0, all PT)
0.0 I Ii I i i
0 50 100 150 200 250 300 350 400 450 500
PT(particle jet#1) (GeV/c)


"Transverse" PTsum Density: dPT/dqd4|
1.8
CDF Run 2 Preliminary "Back-to-Back"
generator level theory
1.96 TeV
1.2 ---------------------- ---




0.6 --------------------

PY Tune A MidPoint R = 0.7 Ii(let)l < 2
a PYTuneA
Charged Particles (1ql<1.0, all PT)
0.0 I I I I
0 50 100 150 200 250 300 350 400 450 500
PT(particle jet#1) (GeV/c)


"Transverse" Average Charged PT


CDF Run 2 Preliminary
generator level theory

f.96 TeV


Charged Particles (l 1<1.0, all PT)
MidPoint R = 0.7 I|(Jet)l< 2


"Back-to-Back"

- -- PY Tune A


- a a ~ -


0 50 100 150 200 250 300 350
PT(particle jet#1) (GeV/c)


Figure 4-3: Particle level predictions from PYTHIA Tune A and HERWIG for average
density of particles dNall/drld) (top), the average charged particle PTsum density
dPTsum/dTld) (middle), and the average charged particle (bottom) for particles with

hl < 1 in the "transverse" region for "back-to-back" events defined in Fig. 6-3 as a
function of the leading jet PT.


1.25


1.00
0

0.75-


|0.50


400 450
400 450 500









Figs. 4-4 thru 4-22 show the "response" factors (see Table 4-4) from PYTHIA Tune

A and HERWIG for the observables in Table 4-3 for "leading jet" and "back-to-back"

events as a function of the leading jet PT. HERWIG and PYTHIA Tune A produce

similar "response" factors for leading jet PT greater than 50 GeV/c, but for lower leading

jet PT they are quite different. This will result in large systematic errors on the corrected

observables in Table 4-3 at low leading jet PT.

Fig. 4-23 shows the leading jet PT correction used in method 2 for "leading jet"

events. Figs. 4-24 shows the method 2 "response" factors from PYTHIA Tune A for

some of the observables in Table 4-3 for "leading jet" events as a function of the leading

jet PT. The observable in Table 4-3 do not depend strongly on the leading jet PT and

hence the method 1 and method 2 correction factors are similar. This can be seen in Fig.

4-25 which compares the method 1 response factors versus the leading jet PT

(uncorrected) with the method 2 response factors versus the leading jet PT (corrected)

from PYTHIA Tune A. The method 2 correction factors (1/response factor) are applied

data after correcting the leading jet PT, while the method 1 correction factors are applied

to the data without correcting the leading jet PT.

Method 1 can be easily applied to both the "leading jet" and "back-to-back" events.

In "back-to-back" events, method 1 corrects for calorimeter response for jet#l, jet#2, and

jet#3 in one step. Figures 4-4 through 4-22 show that the response factors for "back-to-

back" events are different from those of the "leading jet" events. The primary source of

the difference is due to the requirement that PT(jet#3) < 15 GeV/c for "back-to-back"

events and the "back-to-back" correction factors are correcting for the calorimeter

response for jet#3. In order to apply method 2 to the "back-to-back" events we would












"TransMAX" Charged Particle Density: dN/dq!d
1.50
.Leading Jet" GEN
=1.25 -- --- - -I CDM I



| 0.75 -- -
CDFSIMIGEN|
S0.50 --- -- ----------- -- -- ----- -- ---- -
0 1.96 TeV MidPoint R = 0.7 I|(jet)l <2
r 0.25 CDF Run 2 Preliminary
PYTHIA Tune A Charged Particles (Iql<1.0, PT>0.5 GeVc)
0.00 i I I -- I i i
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMAX" Charged Particle Density: dN/did|
1.50
1.25 Leading Jet" GEN


1.00

0.75

0.50 .
1.96 e MidPoint R = 0.7 q(Jet)i < 2
S0.25 CDF Run 2 Preliminary ---- -
HERWIG Charged Particles (|i<1.0, PT>0.5 GeV/c)
0.00 I i i I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMAX" Charged Particle Density: CDFSIM/GEN
1.3
CDF Run 2 Preliminary "Leading Jet"
1.2 detector level I generator level -.---- ------ .
z 1.96TeV
1.1 ------ -------------
PY Tune A

S1.0 ------------------- --


0.8 -- -:- -- --- MidPoint R = 0.7 I(jet)l <2 -------
Charged Particles (Iql<1.0, PT>0.5 GeV/c)
0.7 I I I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)


Figure 4-4: Method 1 response factors for the density of charged particles, dNchg/drido,
with pr > 0.5 GeV/c and h|r < 1 in the "transMAX" region for "leading jet" events
defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle level prediction
(GEN) versus the leading particle jet PT and the detector level result (CDFSIM) versus
the leading calorimeter jet PT (uncorrected) with hr(jet#1)I < 2 for PYTHIA Tune A (top)
and HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).






47


have to first correct the PT of jet#l, jet#2, and jet#3. Since the observables in Table 4-3

do not depend strongly on the PT of jet#l, jet#2, and jet#3, it is much easier to use

method 1 for both "leading jet" and "back-to-back" events. We will use the differences

between method 1 and method 2 in "leading jet" events as a measure of the systematic

uncertainty in correcting to the particle level.













"TransMIN" Charged Particle Density: dN/dcdh


1.50

S1.25

1.00

S0.75

0.50

S0.25


0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMIN" Charged Particle Density: dN/dTld


1.50

1.25

1.00

0.75

0.50-

S0.25


CDF Run 2 Preliminary
HERWIG
1.96 TeV


-----MidPoint R = 0.7 et) <------
[-W I Midpoint R=- 0.7 hae)| < 2


I, wnr
CDlSM


0 50 100 150 200 250 300 350 400 450 500
PT(et#1 uncorrected) or PT(particle jet#1) (GeVIc)


"TransMIN" Charged Particle Density: CDFSIMGEN


z


CDF Run 2 Prell
1.2 detector level I gene
S 1.96 TeV


1 1.1

1.0

0.9

0.8

0.7


0 50 100 150 200 250 300 350
PT(jet#1 uncorrected) (GeV/c)


400 450 500


Figure 4-5: Method 1 response factors for the density of charged particles, dNchg/drld,
with pr > 0.5 GeV/c and hr| < 1 in the "transMIN" region for "leading jet" events defined
in Fig. 6-3 as a function of the leading jet PT. Shows the particle level prediction (GEN)
versus the leading particle jet PT and the detector level result (CDFSIM) versus the
leading calorimeter jet PT (uncorrected) with li(jet#l)l < 2 for PYTHIA Tune A (top) and
HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).


"Leading Jet"


ICDFSIMEN


Charged Particles (htkl.0, PT>0.5 0eV/c)


MidPoint R = 0.7 hi(jet) < 2


Charged Particles ( ll<1.0, PT>0.5 GeV/c)


minary "Leading Jet"
ator level ------
MidPoint R = 0.7 Iq(let)I <2



-



Charged Pa--- icle- (--<1-- PT eV/c)
Charged Particles (I1q<1.0, PT>0.5 GevWc)


-r







49



"TransMAX" Charged PTsum Density: dPT/dld|
2.5
"Leading Jet" GEN


c COFSIM


1.5
E CDFSIMIGEN


-- - -
1.96 TeV MidPoint R = 0.7 Iq(|et)| <2
SCDF Run 2 Preliminary
PYTHIA Tune A Charged Particles (|q|<1.0, PTO>.5 GeV/c)
0.0 I I I I i I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMAX" Charged PTsum Density: dPT/diqd
2.5
S"Leading Jet" GEN
2.0
1 L C | CDFSIM

|CDFSIMIGEN
1.0 -- --- -
1.96 TeV


0.0 i I i I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMAX" Charged PTsum Density: CDFSIM/GEN]
1.3
CDF Run 2 Preliminary "Leading Jet"
1.2 detector level generator level ------- -----------
1.96 TeV PY Tune A



|-------[------- --- -- ----- --

0.8 -- ----- -- MidPoint R = 0.7 |I(et)| < 2 -
Charged Particles (hlt<1.0, PT>0.5 GeV/c)
0.7 iI I I I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)

Figure 4-6: Method 1 response factors for the PTsum density of charged particles,
dPTsum/dTId), with pr > 0.5 GeV/c and [rll < 1 in the "transMAX" region for "leading
jet" events defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle level
prediction (GEN) versus the leading particle jet PT and the detector level result
(CDFSIM) versus the leading calorimeter jet PT (uncorrected) with i(jet#1)l < 2 for
PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the detector level
to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e. response factor).












I"TransMIN" Charged PTsum Density: dPT/dlid6|


0 50 100 150 200 250 300 350 400 450
PT(jet#1 uncorrected) or PT(partlcle Jet#1) (GeVlc)


"TransMIN" Charged PTsum Density: dPT/dqd|
1.25
o CDF Run 2 Preliminary Charged Particles (|1i<1.0, PT>0.5 GeV/c)
HERWlG
S1.00- ERW MidPoint R 0.7 lq(let)< 2
"Leading Jet"
0.75
| IV |CDFSIMIGEN
0.50 --

0.25 - -
. 0 ICDFS PM 1.96TeV
0.00 -------I I I I I I


0 50 100 150 200 250 300 350 400 450
PT(jet#1 uncorrected) or PT(partlcle jet#1) (GeV/c)


"TransMIN" Charged PTsum Density: CDFSIMGENI
1.3
CDF Run 2 Preliminary Charged Particles (lq1<1.0, PT>0.5 GeV/c)
1.2 detector level I generator level MidPoint R = 0.7 hlqjet) < 2
S1.96 TeV "Leading Jet"
S1.1


1.0
*- -0.8- --- --------- --- -------------
jO .- --- --

PY Tune A
-A I ---


0 50 100 150 200 250 300 350
PT(et#1 uncorrected) (GeV/c)


400 450 500


Figure 4-7: Method 1 response factors for the PTsum density of charged particles,
dPTsum/dTld), with pr > 0.5 GeV/c and Ill < 1 in the "transMIN" region for "leading jet"
events defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle level
prediction (GEN) versus the leading particle jet PT and the detector level result
(CDFSIM) versus the leading calorimeter jet PT (uncorrected) with r(jet#l)l < 2 for
PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the detector level
to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e. response factor).


CDF Run 2 Preliminary Charged Particles (hIq<1.0, PT>0.5 GeVlc)
PYTHIA Tune A MidPoint R = 0.7 i(jet) < 2
-"Leading Jet"


1.00

0.75

0.50

r 0.25

0.00


500


500







51




"Transverse" Average Charged PT
1.50
|CDFSIM|_
1.25
GEN
1.00 "

0.75 C IM
j "Leading Jet"
0.50
CDF Run 2 Preliminary MidPoint R = 0.7 (let)l < 2
0 .2 5 P Y T H IA Tune A .-... .. .
1.96 TeV Charged Particles (I|<1.0, PT>0.5 GeV/c)
0.00 I i I I i I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(partlcle jet#1) (GeVIc)


"Transverse" Average Charged PTI
1.50--
Leading Jet" CDFSIM
1.25
^125 ------- -- --- -------------------------

1.00

.0O75II
0.75 ------------------ DFMG -

0.50
S1.96 TeV
!7 MidPoint R = 0.7 Il0et) < 2
0.25 CDF Run 2 Preliminary ----
S HERWIG Charged Particles (hll<1.0, PT>0.5 GeV/c)
0.00 I I i I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"Transverse" Average Charged PT: CDFSIM/GEN
1.3
CDF Run 2 Preliminary
1.2 detector level I generator level
1.1


1.0 --- ------

c |PY Tune A "Leading Jet"
0.9-------------- -- MidPoint R = 0.7 Itq(et)l <2
Charged Particles (hl<1.0, PT>0.5 GeV/c)
0.8 I I I I I
0 50 100 150 200 250 300 350 400 450 500
PT(et#1 uncorrected) (GeV/c)

Figure 4-8: Method 1 response factors for the average of charged particles with pr >
0.5 GeV/c and Irl| < 1 in the "transverse" region for "leading jet" events defined in Fig. 6-
3 as a function of the leading jet PT. Shows the particle level prediction (GEN) versus the
leading particle jet PT and the detector level result (CDFSIM) versus the leading
calorimeter jet PT (uncorrected) with I|(jet#1)l < 2 for PYTHIA Tune A (top) and
HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).




































2.0 --- -- ---..-
SCDFSIM

|CDFSIMIGEN|
1.5
a 1.0 > -
g 1.96 TeV
S0.5 MidPoint R = 0.7 l(jet)l < 2
CDF Run 2 Preliminary
HERWIG Charged Particles (|1<1.0, PT>0.5 GeVIc)
0.0 i iI I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeVIc)


"Transverse" Charged PTmax: CDFSIM/GEN
1.3
CDF Run 2 Preliminary "Leading Jet"
12. detector level /generator level

1.1 --------- PYTuneA ---- ----



0.9 -

0.8 MidPoint R = 0.7 Il(jlet)l < 2 -
1.96 TeV
Charged Particles (Ihl<1.0, PT>0.5 GeV/c)
0.7 I I I -I -I -I -I -I --
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)

Figure 4-9: Method 1 response factors for the average maximum pr, PTmax, for charged
particles with pr > 0.5 GeV/c and I|ll < 1 in the "transverse" region for "leading jet"
events defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle level
prediction (GEN) versus the leading particle jet PT and the detector level result
(CDFSIM) versus the leading calorimeter jet PT (uncorrected) with tl(jet#l)l < 2 for
PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the detector level
to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e. response factor).


"Transverse" Charged PTmax
2.5
GEN
"Leading Jet" GE
2.0
1.5 CD-SIM -
CDCDFSIMFSIEN
S1.5

1.0 [A2
1 1.96 TeV MidPoint R = 0.7 |h( et) <2
CDF Run 2 Preliminary
PYTHIA Tune A Charged Particles (|lI<1.0, PT>0.5 GeV/c)
0.0
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(partlcle jet#1) (GeV/c)












"TransMAX" ETsum Density: dET/drildI


0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMAX" ETsum Density: CDFSIM/GEN
1.0
CDF Run 2 Preliminary "Leading Jet"
0.9 detector level generator level PY TuneA -- -
z 1.96 TeV
L 0.8 _- -

0.7



0.5 MidPoint R = 0.7 q(let)l < 2 --
Charged Particles (|1|<1.0, PT>.5 GeV/c)
0.4 I I I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)

Figure 4-10: Method 1 response factors for the ETsum density of all particles, dET/ddldo,
with I|i < 1 in the "transMAX" regions for "leading jet" events defined in Fig. 6-3 as a
function of the leading jet PT. Shows the particle level prediction (GEN) versus the
leading particle jet PT and the detector level result (CDFSIM) versus the leading
calorimeter jet PT (uncorrected) with Ir(jet#l)I < 2 for PYTHIA Tune A (top) and
HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).


5.0

4.0

E 3.0

2.0

1.0


0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


4.0

E 3.0

I-


c 10


Charged Particles (Iln<1.0, PT>0.5 GeVlc)


I"TransMAX" ETsum Density: dET/dnd I


























0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMIN" ETsum Density: dET/dd|
1.50
CDF Run 2 Preliminary
1.25 HEW --- ------ --------

1.00 ---- ----------------------

0.75 --

j0.50 --- -- --------
CDFSIM/GEN
MidPoint R = 0.7 qI(|et) < 2
S 0.25
1.96 TeV Charged Particles (qJ<1.0, PT>0.5 GeV/c)
0.00 I I i i -- I I I i
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jett#) (GeV/c)


"TransMIN" ETsum Density: CDFSIMIGENI
0.9
CDF Run 2 Preliminary "Leading Jet"
0.8 detector level I generator level
z 1.96 TeV


i 0.6 n V -- *- -" - -

m 0.7

0.4 s H MidPoint R = 0.7 th(let)l 2- -
Charged Particles (|II|<1.0, PT>0.5 GeV/c)
0.3 i I II I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)

Figure 4-11: Method 1 response factors for the ETsum density of all particles, dET/drld4,
with f1r < 1 in the "transMIN" regions for "leading jet" events defined in Fig. 6-3 as a
function of the leading jet PT. Shows the particle level prediction (GEN) versus the
leading particle jet PT and the detector level result (CDFSIM) versus the leading
calorimeter jet PT (uncorrected) with Ir(jet#l)l < 2 for PYTHIA Tune A (top) and
HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).


"TransMIN" ETsum Density: dET/dcqd4
1.50
> CDF Run 2 Preliminary
S1.25 ----- PYTH A -------------- --------

1. 1.96TeV

S0.75

0.50
"Leading Jet" CDFSIM CDFSIMWGEN
0.25
MidPoint R = 0.7 In(letl < 2 Towers (hnl0.1 GeV)







55




"Transverse" Charged Fraction: PTsum/ETsum
3.0
SCDF Run 2 Preliminary MidPoint R =0.7 |H(let)| < 2
E 2.5 PYTHIA Tune A Care id-toe l <--l.4, P-.S-.eWe)- -
Is ..a...u Towers (h<1.0, ET>0.1 GeV)


t~~~~~~ ~~~ -. ---9ev------ tdtiet- -- -- -- -
S1.5 "-v ...
SCDFSIMGEN

1.0 --------- ------ -- --

I-k~
0.5-------------------------- --

0.0
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle Jetl) (GeVlc)


"Transverse" Charged Fraction: PTsum/ETsum
3.0-
CDF Run 2 Preliminary MidPoint R 0.7 In0et) 2
., I HERWIG
E 2.5-L - Ct a rg Particle j|
E 2.0
]- \ 1.96 TeV jCDFSIMWGTEN | Towers (hI <1.0, ET>O. GeV))

1.5
"Leading JeM
1.0-- --- -

S0.5 ------------------- -- -----------

0.0 1 I I I I I i i i
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jetl) (GeV/c)


"Transverse" PTsum/ETsum: CDFSIMIGEN
3.5
CDF Run 2 Preliminary "Leading Jet"
3.0 dete level / generator level ----
z

i 2.5- --
2.0

I 1.5 ---- --- -- -- -- -- -
cc PY Tune A MidPoint R = 0.7 I|i(et) <2
1.0 ---1.9- TeV--- Oarged Particl.(|0|<1.0,PT>.5I GeVc -
Towers (|i|<1.0, ET>0.1 GeV)
0.5 I-I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)

Figure 4-12: Method 1 response factors for the charged fraction, PTsum/ETsum, in the
"transverse" region for "leading jet" events defined in Fig. 6-3 as a function of the
leading jet PT, where PTsum includes charged particles with pr > 0.5 GeV/c and Jill < 1
and the ETsum includes all particles with Iill < 1. Shows the particle level prediction
(GEN) versus the leading particle jet PT and the detector level result (CDFSIM) versus
the leading calorimeter jet PT (uncorrected) with I|i(jet#l)| < 2 for PYTHIA Tune A (top)
and HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).












"Transverse" Charged Particle Density: CDFSIM/GEN
1.2
"Leading Jet" CDF Run 2 Preliminary
1.1 -- PYTHIA Tune A
z 1.96 TeV
m TransMAX
1.0 -. --------

- 0. Tran9M
0.89 ---

MidPoint R = 0.7 Ijet)| < 2 Charged Particles (lI|<1.0, PT>0.5 GeVlc)
0.7 III
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)


"Transverse" Charged PTsum Density: CDFSI/GEN
1.2
CDF Run 2 Preliminary
1.1 -PYTHIA Tune A
TranaMAX 1.96 TeV
S1.0




0.8- -
MidPoint R = 0.7 I|(jet)l < 2 Charged Particles (ql<1.0, PT>.5 GeVic)
0.7 -III
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)


"Transverse" ETsum Density: CDFSIM/GENI


Figure 4-13: Shows the ratio of the detector level to the particle level, CDFSIM/GEN,
versus the leading jet PT (method 1 response factors) for PYTHIA Tune A for the
"transMAX", "transMIN", and "transverse" regions for "leading jet" events defined in
Fig. 6-3 as a function of the leading jet PT. Shows the density of charged particles
dNchg/drld4 with pr > 0.5 GeV/c and Ii| < 1 (top), the PTsum density of charged
particles dPTsum/drldo with pr > 0.5 GeV/c and hi < 1 (middle), and ETsum density of
all particles dET/drldo with Jll| < 1 (bottom).


450 500


0 50 100 150 200 250 300 350 400
PT(jet#1 uncorrected) (GeV/c)












"TransMAX" Charged Particle Density: dN/dlqdI
1.50
"Back-to-Back"
1.25- CDFSl M -G-- -

J 1.00 ----------- -- -- -- --
.0o SIM

J 0.75 ---- ------------

g0.50 - -GEN
1.96 TeV MidPoint R = 0.7 (et)I < 2
S0.25 CDF Run 2 Preliminary --------------
PYTHIA Tune A Charged Particles (iql0.5 GeV/c)
0.00 i I I I I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle Jet#1) (GeVlc)


"TransMAX" Charged Particle Density: dN/drid


1.25

1.00

S0.75

0.50

- 0.25


0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMAX" Charged Particle Density: CDFSIMGEN


1.3

1.2

0 1.1

1.0

0.9

0.8

0.7


0 50 100 150 200 250 300 350
PT(jet#1 uncorrected) (GeV/c)


400 450 500


Figure 4-14: Method 1 response factors for the density of charged particles, dNchg/drld),
with pT > 0.5 GeV/c and Irll < 1 in the "transMAX" region for "back-to-back" events
defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle level prediction
(GEN) versus the leading particle jet PT and the detector level result (CDFSIM) versus
the leading calorimeter jet PT (uncorrected) with rl((jet#l)l < 2 for PYTHIA Tune A (top)
and HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).


Charged Particles (h|l<1.0, PT>0.5 GeOVc)


CDF Run 2 Preliminary
- detector level I generator level
1.96 TeV


"Back-to-eack

| PY Tun. A


- ~ ~ ~ --


4- -

- --


M- MidPoint R = 0.7 i(| Charged Particles (h<1.0, PT>0.5 GeVc)












"TransMIN" Charged Particle Density: dN/dqd|
1.50
"Back-to-Back" CDF Run 2 Preliminar
125 --- -- - PYTrIATn-e A
CDFSIMIGEN
1.96 TeV
1.00 ------------------- -------------------

S0.75--
SMidPoint R = 0.7 h(let)j < 2
0.50 -- W ---------------------
CDFSIM GEN Charged Particles (JqI<1.0, PT>0.5 GeVc)
S0.25 ---------- -----

0.00 I I I i I I I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeVlc)


"TransMIN" Charged Particle Density: dN/dWtd4
1.50
"Back-to-Back" CDF Run 2 Preliminary
1.25 CDFSIMGEN HERW
A^ 1.96 TeV
S1.00 ........

S0.75
MidPoint R = 0.7 hq(et)l < 2
S0.50 CDFSIM GEN

t- 0.25 -L- ------- ---
Charged Particles (Il<1.0, PT>0.5 GeV/c)
0.00----- II I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeVlc)


"TransMIN" Charged Particle Density: CDFSIM/GEN
1.3
CDF Run 2 Preliminary "Back-to-ac
1.2 detector level I generator level ---- -------
z 1.96 TeV MidPoint R = 0.7 nq(let) < 2
S1.1----------- PY Tune A -





S0.8- --- --
Charged Particles (|hl<1.0, PT>0.5 GeV/c)
0.7I I II
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)

Figure 4-15: Method 1 response factors for the density of charged particles, dNchg/drldo,
with PT > 0.5 GeV/c and |ri < 1 in the "transMIN" region for "back-to-back" events
defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle level prediction
(GEN) versus the leading particle jet PT and the detector level result (CDFSIM) versus
the leading calorimeter jet PT (uncorrected) with Iri(jet#l)l < 2 for PYTHIA Tune A (top)
and HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).












I"TransMAX" Charged PTsum Density: dPT/dTqdl


0 50 100 150 200 250 300 350 400 450
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


500


"TransMAX" Charged PTsum Density: dPT/dcid4
2.0
S "Back-to-Back" CDF Run 2 Prelminar
HERWIG



I 1.0 7 ------------ --- --
1.0


0.5 EN MidPoint R = 0.7 Ii(|et)| < 2
1.96 TeV Charged Particles (h|l<1.0, PT>O.5 GeVIc)
0.0 I i- ----I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMAX" Charged PTsum Density: CDFSIMGEN


"Back-to-Back" CDF Run 2 Preliminary
------ ----- H detector level generator level




1------- CPYTunge A -------------------


-- -- MidPoint R = 0.7 i(jet)l <2 -- ----
1.96 TeV Charged Particles (|1<1.0, PT>0.5 GeV/c)


0 50 100 150 200 250 300 350
PT(jet#1 uncorrected) (GeV/c)


400 450 500


Figure 4-16: Method 1 response factors for the PTsum density of charged particles,
dPTsum/dild), with pr > 0.5 GeV/c and |il < 1 in the "transMAX" region for "back-to-
back" events defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle
level prediction (GEN) versus the leading particle jet PT and the detector level result
(CDFSIM) versus the leading calorimeter jet PT (uncorrected) with tr(jet#l)l < 2 for
PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the detector level
to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e. response factor).


1.5


1.0


0.5


"Back-to-Back" CDF Run 2 Preliminary
PYTHIA Tune A
- CDFSIMIGEN
|CDFSIM~

----- ------- --- -- ------------


S- - MidPoint R = 0.7 het).< 2 -

1.96 TeV Charged Particles (hIl<1.0, PT>0.5 GeV/c)


1.3

1.2

J 1.1

S 1.0

4 0.9
ac
0.8

0.7












"TransMIN" Charged PTsum Density: dPT/dlqd
1.25
SCDF Run 2 Preliminary Charged Particles (h< .0o, PT>.5 GeV/c)
PYTHIA Tune A MidPoint R = 0.7 W(jet) < 2


0.75
"Back-to-Back"
t0.50 - -

0.25 1.96 TeV
I-
0.05 -----I----- --I----- -c-sl-l-I-- --I- -- -I-- --I- -- -----
0.00 I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMIN" Charged PTsum Density: dPT/dqdtl


E



c
a


1 25
CDF Run 2 Preliminary Charged Particles (hil0.5 GeVIc)
HERWIG
HER1- G MidPoint R = 0.7 qWet)l < 2
1.00 ----

0.75 CDFSIMIGEN- -----------

0.50

0.25 "Back-to-Bac
1.96 TeV
0.00 --- I


50 100 150 200 250 300 350 400 450 5
PT(jet#1 uncorrected) or PT(particle jet#1) (GeVlc)


"TransMIN" Charged PTsum Density: CDFSIM/GENI
1.2
CDF Run 2 Preliminary MidPoint R = 0.7 ihlet) < 2
detector level I generator level "Back-to-Back"
1.1
1.96 TeV PY Tune A
1.0 .


0.--- --- -- ----- --- ------ ------- ---

0.8
Charged Particles (Iql<1.0, PT>0.5 GeVIc)
0.7 I I I I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)

Figure 4-17: Method 1 response factors for the PTsum density of charged particles,
dPTsum/drdd), with pr > 0.5 GeV/c and Irll < 1 in the "transMIN" region for "back-to-
back" events defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle
level prediction (GEN) versus the leading particle jet PT and the detector level result
(CDFSIM) versus the leading calorimeter jet PT (uncorrected) with h(jet#1)| < 2 for
PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the detector level
to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e. response factor).







61




"Transverse" Average Charged PT
1.25
CDFSIMGEN

1.00 --- -.----- -. -- ----------


S0.75 -
| "Back-to-Back"

| 0.50 CDF Run 2 Preliminary- --- MidPoint R = 0.7 (et)l <2 -
PYTHIA Tune A
1.96 TeV Charged Particles (h1<1.0, PT>0.5 GeV/c)
0.25 i I I I I i
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"Transverse" Average Charged PT
1.25
SCDFSIMIGEN CDF Run 2 Preliminary

S1.00 ---------


0.75 GEN

| "Back-to-Back"
S0.50 -----------------------------------------
MidPoint R = 0.7 i(jet) < 2
1.96 TeV Charged Particles (|hl<1.0, PT>0.5 GeV/c)
0.25 i i I-t- I-- -
0 50 100 150 200 250 300 350 400 450 500
PT(et#1 uncorrected) or PT(particle jet#1) (GeV/c)


"Transverse" Average Charged PT: CDFSIMIGEN
1.3
CDF Run 2 Preliminary
1.2 de-ector lel I generator level
SrHW 1.96 TeV

S-------------------------------------

1.0
Y Tune A "Backto-Back"
0.9 MidPoint R = 0.7 Iq(jet)I <2
Charged Particles (q1<1 .0, PT>0.5 GeVic)
0.8 I I I I i
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)

Figure 4-18: Method 1 response factors for the average of charged particles with pT
> 0.5 GeV/c and Ir[l < 1 in the "transverse" region for "back-to-back" events defined in
Fig. 6-3 as a function of the leading jet PT. Shows the particle level prediction (GEN)
versus the leading particle jet PT and the detector level result (CDFSIM) versus the
leading calorimeter jet PT (uncorrected) with Ir(jet#l)l < 2 for PYTHIA Tune A (top) and
HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).







62




"Transverse" Charged PTmaxI
2.0
"Back-to-Back"

1.5 ------------ CDFIMEN- ----------


S1.0
GEN CDFSIM
0 0.5 -1.96 TeV- ---------- MidPoint R = 0.7 iq(jet)| <2 ----
CDF Run 2 Preliminary
PYTHIA Tune A Charged Particles (1ql<1.0, PT>0.5 GeV/c)
0.0 I I II I I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"Transverse" Charged PTmax
2.0
"Back-to-Back"

1.5- --- -- CFSIMGEN --------------------- --

I E
1.0

1.96 TeV
0.5 ------------ MidPoint R = 0.7 (jet)l <2 -
CDF Run 2 Preliminary
HERWIG Charged Particles (Iql<1.0, PT>0.5 GeVlc)
0.0 I I I -
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(partlcle jet#1) (GeVIc)


"Transverse" Charged PTmax: CDFSIM/GEN

CDF Run 2 Preliminary "Back-to-Back"
1 detector -lev el Ienertor level

w -*- --- -

S1.0 PYTuneA -

S0.9- -

0.8 1 V MidPoint R = 0.7 (et) < 2 -
1.96 TeV
Charged Particles (Q1<1.0, PT>0.5 GeVlc)
0.7 I I I I I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)

Figure 4-19: Method 1 response factors for the average maximum pr, PTmax, for charged
particles with pr > 0.5 GeV/c and Il < 1 in the "transverse" region for "back-to-back"
events defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle level
prediction (GEN) versus the leading particle jet PT and the detector level result
(CDFSIM) versus the leading calorimeter jet PT (uncorrected) with [r(jet#1)l < 2 for
PYTHIA Tune A (top) and HERWIG (middle). Also shows the ratio of the detector level
to the particle level, CDFSIM/GEN, versus the leading jet PT (i.e. response factor).













"TransMAX" ETsum Density: dET/dTid4)
4.0
> CDF Run 2 Preliminary MidPoint R = 0.7 |,l(et) < 2
0 PYTHIA Tune A "Back-to-Back"



CDFSVA
S 3.0I COPSI-- -- -- -- -- -


i.o -- e
S2.--- -- ----------




t ICDFSIi;EN Towers (hI<1.0, ET>O.1 GeV)
0.0 I I I I i I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMAX" ETsum Density: dET/drqdd


CDF Run 2 Preliminary
HERWIG


MidPoint R = 0.7 Jl(Jet) < 2
'Back-to-Back"


" 1.96 TeV -EN

S2.0 ------------- ------- --


1.0

[ CDFSIMW EN Towers (hl<1.0, ET>0.1 GeV)
0.0-- I I I II
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeVlc)


"TransMAX" ETsum Density: CDFSIM/GEN


0.9
z
| 0.8-

SO.7-
0
I 0.6


0 50 100 150 200 250 300 350
PT(jet#1 uncorrected) (GeV/c)


400 450 500


Figure 4-20: Method 1 response factors for the ETsum density of all particles, dET/dTld),
with |rll < 1 in the "transMAX" regions for "back-to-back" events defined in Fig. 6-3 as a
function of the leading jet PT. Shows the particle level prediction (GEN) versus the
leading particle jet PT and the detector level result (CDFSIM) versus the leading
calorimeter jet PT (uncorrected) with Il(jet#l)l < 2 for PYTHIA Tune A (top) and
HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).


CDF Run 2 Preliminary "Back-to-Back"
deltecor level i generator level PY Tune A
1.96 TeV


- -- - - --. .



S- MidPoint R = 0.7 Ijet)l <2 -
Towers (|l1<1.0, ET>0.1 GeV)







64




"TransMIN" ETsum Density: dETIdrid|
1.50
CDF Run 2 Preliminary MidPoint R = 0.7 hlet)l < 2
1.25 PYTHIkTune A Back-B
S1.96TeV
1.00 ------------

S0.75 ------------ -----



S0.25
Towers (t11<1.0, ET>0.1 GeV)
0.00 I i i i
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMIN" ETsum Density: dET/dTld4i
1.50
CDF Run 2 Preliminary MidPoint R = 0.7 |lq(et)l < 2
1.25 -- --- -----------------------------
1. "Back-to-Back"

i 1.00 -------------------- --- --------
E 0.75 .- .
,"0.75 ------------------------------------------

0.50 -

S0.25 -------------------- ------
S 1.96 TeV Towers (|j<1.0, ET>0.1 GeV)
0.00 I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"TransMIN" ETsum Density: CDFSIM/GENI
0.9
CDF Run 2 Preliminary "Back-to-Back"
0.8 doctor level generator level I -- l PY Tune A--
z 1.96 TeV -
S0.7 ^ ------------ --- . .
S0. S


0.5 -- ---------------------------------
S0.6 ---L



0.4 MidPoint R = 0.7 (et)l< 2 -------
Towers (Ihl<1.0, ET>0.1 GeV)
0.3 I I I I I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) (GeV/c)

Figure 4-21: Method 1 response factors for the ETsum density of all particles, dET/dTld),
with rll < 1 in the "transMIN" regions for "back-to-back" events defined in Fig. 6-3 as a
function of the leading jet PT. Shows the particle level prediction (GEN) versus the
leading particle jet PT and the detector level result (CDFSIM) versus the leading
calorimeter jet PT (uncorrected) with Il(jet#l)l < 2 for PYTHIA Tune A (top) and
HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).












"Transverse" Charged Fraction: PTsum/ETsum
3.0
CDF Run 2 Preliminary MidPoint R = 0.7 hl(let)l <2
E 2.5 YTHIATuneaA -Gherged Partdcle (it_.5-eVe)- -
S1.96 TeV Towers (hq<1.0, ET>0.1 GeV)
2.0 -

S1.5 ---- --- -- -

| 1.0 .--- ---r D S .. .. .. --- ^ --

L 0.5 -- --
I M "Back-to-Beck"



01.0.--------- ----------------------GN-
0 .0


0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#l) (GeV/c)


"Transverse" Charged Fraction: PTsum/ETsum


CDF Run 2 Preliminary
HERWIG
1 9 -T


CDsl~EN


MidPoint R = 0.7 I(jet) <2
CThrgea Partclis -(hl0Gec)
Towers (thl<1.0, ET>0.1 GeV)


"Back-to-Back"

r


0.0 I---I I I i i I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 uncorrected) or PT(particle jet#1) (GeV/c)


"Transverse" PTsum/ETsum: CDFSIMIGEN


0 50 100 150 200 250 300 350 400
PT(jet#1 uncorrected) (GeVIc)


450 500


Figure 4-22: Method 1 response factors for the charged fraction, PTsum/ETsum, in the
"transverse" region for "back-to-back" events defined in Fig. 6-3 as a function of the
leading jet PT, where PTsum includes charged particles with pr > 0.5 GeV/c and I|ll < 1
and the ETsum includes all particles with ll < 1. Shows the particle level prediction
(GEN) versus the leading particle jet PT and the detector level result (CDFSIM) versus
the leading calorimeter jet PT (uncorrected) with Ir1(jet#l)l < 2 for PYTHIA Tune A (top)
and HERWIG (middle). Also shows the ratio of the detector level to the particle level,
CDFSIM/GEN, versus the leading jet PT (i.e. response factor).


E 2.5

2.0

t. 1.5

j 1.0
t S


3.0

| 2.5

S2.0

I 1.5
(X


CDF Run 2 Preliminary "Back-to-Back
detector level / generator level

- - --- -
-- --- ------- ----


pYU A| ------------------ ---------
MidPoint R 0.7 hq(et)i < 2
1.96 TeV harge -rtleles8qH<1.,PT>0.5 GeVck -
Towers (hil<1.0, ET>O.1 GeV)


CDFSIM












Leading Jet PT Correction: Corrected Uncorrected


0 50 100 150 200 250 300 350
PT(et#1 uncorrected) (GeV/c)


400 450 500


Figure 4-23: Leading jet PT correction used in method 2 for "leading jet" events. Shows
the difference in the observed leading jet PT at the detector level (i.e. in the calorimeter)
compared with the true PT (i.e. corrected) of matched leading particle jets using PYTHIA
Tune A and HERWIG.











"Transverse" Charged Particle Density: dN/drtd4
1.2--


------- 1.96 TeV
WGEN





PYTHIA Tune A Charged Particles (|qi <.0, PT>0.5 GeV/c)
Ir I aI I I
S 50 100 150 200 250 300 350 400 450 5
PT(jet#1 corrected) or PT(particle jet#1) (GeV/c)


1.0

0.8

0.6

S0.4

c 0.2


"Transverse" Charged PTsum Density: dPT/drid*
1.4
S1.2--
1.0
1.0 .---.------ ------------------------



0.6 -- -----------------
0.6

S0.4
I04 -------------- ---------- CDF Run 2 Preliminary
MidPoint R = 0.7 i(Jet)| <2 PYTHIATune A
E 0.2
0 -- -- -- -- --- ------------ -- -- -- --- -- '
Charged Particles (I||<1.0, PT>0.5 GeV/c) 1.96 TeV
0.0 I
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 corrected) or PT(particle jet#1) (GeV/c)


"Transverse" ETsum Density: dET/d'ldi
3.0
> CDF Run 2 PreliminaryEN
S2.5 PYTHIA-Tuner-
I 1.96 TeV

E
S1.5 CDFSIM
.CDFSIM/GEN
1.0 -------------- -----



E 0.5
MidPoint R = 0.7 hjet)l < 2 Towers (JlJ<1.0, ET>0.1 GeV)
0.0 1 + + i ,
0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 corrected) or PT(particle jet#1) (GeV/c)

Figure 4-24: Method 2 response factors from PYTHIA Tune A for "leading jet" events
defined in Fig. 6-3 as a function of the leading jet PT. Shows the particle level prediction
(GEN) versus the leading particle jet PT and the detector level result (CDFSIMcor) versus
the leading calorimeter jet PT (corrected) with I|T(jet#1)l < 2. Also shows the ratio of the
detector level to the particle level, CDFSIMcor/GEN, versus the leading jet PT (i.e.
response factor).













"Transverse" Charged Particle Density: CDFSIMIGENI


1.3

1.2 Method 1
S IPT(uncorrcted)
1.1 -- -

1.0 P 0

0.9

08Method 2
SPT(corrected)


0.7


CDF Run 2 Preliminary
PYTHIA Tune A

_--_---- ---- -t Te- -- _



7] = te
MidPoint R = 0.7 0lUet)| < 2

Charged Particles (i|l<1.0, PT>0.5 GeV/c)


z
mi

CD
0

IL


"Transverse" Charged PTsum Density: CDFSIM/GEN


1.3

1.2

1.1

1.0

C.)


0.8

0.7


0 50 100 150 200 250 300 350 400 450 500
PT(jet#1 corrected) or PT(et#1 uncorrected) (GeV/c)


"Transverse" ETsum Density: CDFSIMIGEN


0 50 100 150 200 250 300 350
PT(jet#1 corrected) or PT(jet#1 uncorrected)


400 450
(GeV/c)


Figure 4-25: Compares the method 1 response factors versus the leading jet PT
(uncorrected) with the method 2 response factors versus the leading jet PT (corrected)
from PYTHIA Tune A.


0 50 100 150 200 250 300 350 400 450
PT(et#1 corrected) or PT(jet#1 uncorrected) (GeV/c)


Charged Particles (|11<1.0, PT>0.5 GeV/c)


1.0

0.9 -
z
W 0.8

0.7

0.6

0.5-

0.4


CDF Run 2 Preliminary
-- PYTHIA Tune A- Method 1 ----
1.96 TeV PT(uncorrected)

~--- --------_


Method 2
---- -- PT(corrected) -- -- -- -------- -


MidPoint R = 0.7 t(jt)I| < 2 Towers (Q|<1.0, ET>0.1 GeV)
I I I I i


0.4-














CHAPTER 5
DATA SELECTION AND SYSTEMATIC ERRORS

5.1 Data Selection
The data used in this analysis arise from the set of Stntuples created for the QCD

group by Anwar Bhatti, Ken Hatakeyama, and Craig Group (see Table 5-1). Events are

required to be on the "goodrun" list (version 7). They are also required to have a missing

ET significance less than 5 GeV"2 and to have a sumET < 1.5 TeV. Except for the Min-

Bias data we require events to have one and only one quality 12 vertex with Izi < 60 cm.

For the Min-Bias data we allow zero or one quality 12 vertices. This only affects the

observables in Table 4-3 for leading jet PT below 10 GeV/c. Above PT(jet#l) = 10 GeV/c

the fraction of events with no quality 12 vertex is negligible.

Table 5-1: Data sets (5.3.3nt) and event selection criterion used in this analysis
(L ~ 380 pb-).
Event Selection Min-Bias JET20 JET50 JET70 JET100
Total Events 20,586,733 30,470,383 9,908,366 4,641,247 5,366,515
"Good" Events (version 7) 18,180,015 19,835,681 6,868,114 3,432,992 4,031,324
MetSig < 5 GeV
MetSig< eV 18,179,280 19,818,879 6,785,357 3,316,514 3,602,989
sumET < 1.5 TeV
1 Q12 ZVtx, z < 60 cm 15,416,180 10,851,963 3,745,616 1,794,739 1,939,382
"Leading Jet" 1(jet#1) < 21 3,712,407 7,679,594 3,200,065 1,648,764 1,884,353
"Back-to-Back"
Pet 1 V/c 2,474 1,462,547 878,014 491,930 602,256
PT(jet#3) < 15 GeV/c
"Back-to-B ack"f'Leading 0.07% 19.04% 27.44% 29.84% 31.96%
Jet"

As in a Run 1 analysis [13] only charged particles in the region pr > 0.5 GeV/c and rll| < 1

where the COT efficiency is high are considered. Our track selection criterion shown in

Table 5-2 is the same as the Run 1 analysis.










Table 5-2: Track Selection criterion.
Track Selection
COT measured tracks
Iz-zol < 2 cm
Idol < 1 cm
Tr > 0.5 GeV/c, hi < 1


In forming the observables in Table 4-3 the five trigger sets shown in Table 5-1 are

pieced together as shown in Table 5-3. The "looser" trigger set is used until it overlaps

the next trigger set and then that trigger set is used until it overlaps the next trigger set etc.

Table 5-3: Range of PT(jet#l) used for each data set.
Trigger Set Calorimeter Jets
Min-Bias PT(jet#l) < 30 GeV
JET20 30 < PT(jet#l) < 70 GeV
JET50 70 < PT(jet#l)< 95 GeV
JET70 95 < PT(jet#l) < 130 GeV
JET100 PT(jet#l) > 130 GeV


5.2 Systematic Uncertainty
The systematic uncertainty in correcting to the particle level is estimated by

combining the two factors shown in Table 5-4. The first factor, o;, comes from correcting

the observables in Table 4-3 to the particle level using method 1 and examining the bin-

by-bin difference between PYTHIA Tune A and HERWIG for each observable. The

second factor, 02, is set large enough to include the differences between method 1 and

method 2 and pile-up (only affects the transverse energy).

Figure 5-1 shows the data at 1.96 TeV corrected to the particle level using method 1

and method 2. The open red squares are the data corrected to the particle level using

method 1 with errors that include both the statistical error and the systematic uncertainty









(see Table 5-4). The black dots are the data corrected to the particle level using method 2

(with no errors). The method 2 points lie within the errors of the method 1 data points.

Table 5-4: The errors on the corrected observables in Table 4-3 include both the statistical
error and the systematic uncertainty (added in quadrature). The systematic uncertainty
consists of ol and 02 (added in quadrature).


Uncertainty Origin
Bin by bin difference between the data
o7 corrected by PYTHIA Tune A and
HERWIG using method 1.
Difference between method 1 and
method 2
02 and pile-up and miscellaneous
(3% for charged particle, 5% for energy)













"Transverse" Charged Particle Density: dN/cdd4#


"Leading Jet"


1.0

S0.8

I 0.6

S0.4

0.2

0.0


200 250 300 350
PT(jet#1) (GeV/c)


0 50 100 150


0 50 100 150 200 250 300 350 400 450
PT(jet#1) (GeV/c)


"Transverse" ETsum Density: dET/dTrdnl


Figure 5-1: Data at 1.96 TeV corrected to the particle level using method 1 and method 2
compared with PYTHIA Tune A and HERWIG at the particle level. Shows the density
of charged particles, dNchg/drld( (top), the PTsum density of charged particles,
dPTsum/drld) (middle), (pr > 0.5 GeV/c and lh < 1), and the ETsum density, dET/dTrdO
(bottom), for particles with Ir|l < 1 in the "transverse" region (average of "transMAX" and
"transMIN") for "leading jet" events defined in Fig. 6-3 as a function of the leading jet
PT.


I I I I


a Data Method 1
Data Method 2
- PYTHIA Tune A
-- HERWIG


MidPoint R = 0.7 q(et#1) < 2

Charged Particles (hl<1.0, PT>0.5 GeV/c)


400 450


"Transverse" Charged PTsum Density: dPT/dqd*


1.6




E
S0.8





0.0


Charged Particles (ht<1.0, PT>0.5 GeV/c)


0 50 100 150 200 250 300 350 400 450
PT(jet#1) (GeV/c)













CHAPTER 6
DISCUSSION OF RESULTS

We study the behavior of the charged particles (PT> 0.5 GeV/c, hl<1) in the

"underlying event" for hard scattering pp collisions at the Tevatron (s =1.96 TeV).

These results are compared to QCD Monte-Carlo models (PYTHIA Tune A and

HERWIG) that simulate pp collisions. The topology of a hard scattering jet event serves

to define a frame of reference. The direction of the leading calorimeter jet, jet#l, is used

to define correlations in the azimuthal angle, A(. The angle A0P = ( (jet#i is the relative

angle between a charged particle and the leading jet direction. Figure 6-1 shows how we

partition il-o space on an event-by-event basis.

In figure 6-2 we define "transverse 1" and "transverse 2" so that we may compare

these regions on an event-by-event basis. This allows us the flexibility to redefine how

the regions are characterized for different analyses. Here we will refer to events in which

there are no restrictions placed on the second highest ET jet, jet#2, as "leading jet" events.

Additionally, we define a subset of these as "back-to-back" events in which the leading

two jets are nearly "back-to-back" (A(12>1500) and with ET (jet#2)/ET(jet#l) > 0.8.

Within this subset, the hard component of the "underlying event" should be suppressed,

thus increasing the sensitivity of the "transverse" region to the "beam-beam remnant" and

multiple parton scattering components.









2z
Jet #1 Region
Direction


"Toward"








Figure 6-1: Illustration of correlations in azimuthal angle A( relative to the direction of
the leading jet (MidPoint, R = 0.7, fnrge = 0.75) in the event, jet#l. The angle A( = -
(jet#l is the relative azimuthal angle between charged particles (or calorimeter towers)
and the direction ofjet#. The "toward" region is defined by < 60 and < while

"Away"the "away" region is > 120 and < The "transverse" region is defined by 60 <
Region
0








|A(I| < 120 and hI < 1. Each of the three regions "toward", "transverse", and "away" and
in +1




Figure 6-1: llustration of correlations in azimuthal angle relative to the direction the




range Pr > 0.5 GeV/c and hi < 1 and calorimeter towers with ET > 0.1 GeV and hI < 1,
but allow the leading jet (MidPoint, R = 0.7, fbee = 0.75) in the event,region jet#. The angle A2.
4jet#l is the relative azimuthal angle between charged particles (or calorimeter towers)



As in figure 6-3, we use the direction of jet#. The "toward" region is defined by < 60 and the two "transverse"
regions, 60" is A 120 and < 1. vent-by-event basis, region defie the "transMAX"by 60

("transMIN") to be the maximum (minimum) of these twohree regions "toward", "transverse", and "away"looking a
multiplicities MAX and MIN refer to the number ofexamin charged particles, but whe
range pr > 0.5 GeV/c and hi < 1 and calorimeter towers with ET > 0.1 GeV and hi < 1,





but allow the leading jet then MAX and MIN refer to the scalar Psum of the charged particles.et# <2.

As in figure 6-4 illustrates the topologyhe direction of jea pt# collision in which a "hard" parton-
regions, 600 JA0I | 1200. On an event-by-event basis, we define the "transMAX"

("transMIN") to be the maximum (minimum) of these two regions. When looking at

multiplicities MAX and MIN refer to the number of charged particles, but when

considering PTsum then MAX and MIN refer to the scalar PTsum of the charged particles.

Figure 6-4 illustrates the topology of a p- collision in which a "hard" parton-

parton scattering has occurred. The contribution from the hardest initial or final-state

radiation should be found in the "transMAX" region. Since both regions should receive

"beam-beam remnant" contributions, the difference between "transMAX" and

"transMIN" should be very sensitive to the "hard scattering" component of the

"underlying event".








Jet #1 Direction


Jet #1 Direction











Jet #2 Direction


Figure 6-2: Illustration of correlations in azimuthal angle A4 relative to the direction of
the leading jet (highest PT jet) in the event, jet#1. The angle A0 = 0 Ojet#1 is the relative
azimuthal angle between charged particles and the direction of jet#l. The "toward"
region is defined by I|A| < 600 and [liI < 1, while the "away" region is IA(| > 1200 and hiJ
< 1. The two "transverse" regions 600 < A0 < 1200 and 600 < -Ao < 1200 are referred to as
"transverse 1" and "transverse 2". Each of the two "transverse" regions have an area in
T1-0 space of ArlAO = 4n/6. The overall "transverse" region defined in Fig. 3 corresponds
to combining the "transverse 1" and "transverse 2" regions. Events in which there are no
restrictions placed on the on the second highest PT jet, jet#2, are referred to as "leading
jet" events (left). Events with at least two jets where the leading two jets are nearly
"back-to-back" (A12 > 1500) with PT(jet#2)/PT(jet#l) > 0.8 and PT(jet#3) < 15 GeV/c are
referred to as "back-to-back" events (right).

Jet #1 Jet #1 Direction


"Towar "Toward"




"Away"

Jet #2 Direction
Fig. 6-3: Illustration of correlations in azimuthal angle A( relative to the direction of the
leading jet (highest PT jet) in the event, jet#l for "leading jet" events (left) and "back-to-
back" events (right) as defined in Fig. 6-2. The angle A0 = 0 Ojet#l is the relative
azimuthal angle between charged particles (or calorimeter towers) and the direction of
jet#1. On an event by event basis, we define "transMAX" ("transMIN") to be the
maximum (minimum) of the two "transverse" regions, 600 < A( < 1200 and 600 < -A< <
1200. "TransMAX" and "transMIN" each have an area in il-( space of ATrIA = 4x/6.
The overall "transverse" region defined in Fig. 3 includes both the "transMAX" and the
"transMIN" region.









Jet #1 Direction


"Toward-Side" Jet



"Toward"


"TransM ransMIN"
J e t # 3 % ** *
'"Away" **

"Away-Side" Jet


Figure 6-4: Illustration of the topology of a proton-antiproton collision in which a "hard"
parton-parton collision has occurred. The "toward" region as defined in Fig. 6-1 contains
the leading "jet", while the "away" region, on the average, contains the "away-side"
"jet". The "transverse" region is perpendicular to the plane of the hard 2-to-2 scattering
and is very sensitive to the "underlying event". For events with large initial or final-state
radiation the "transMAX" region defined in Fig.6-3 would contain the third jet while both
the "transMAX" and "transMIN" regions receive contributions from the beam-beam
remnants (see Fig. 1-1). Thus the "transMIN" region is very sensitive to the beam-beam
remnants, while the "transMAX" minus the "transMIN" is very sensitive to initial and
final-state radiation.


6.1 The MAX/MIN Transverse Regions

As shown in Figure 6-3 we use the direction of the highest PT jet in the region [rl <

2, jet#l, to define the two "transverse" regions, 600 < IA | < 1200 and 600 < -IA I < 120.

On an event-by-event basis, we define "transMAX" and "transMIN" to be the maximum

and minimum of these two regions. "TransMAX" and "transMIN" each have an area in

rl-4 space of A7rlA = 4n/6. When looking at multiplicities MAX and MIN refer to the

number of charged particles. When we consider PTsum, then MAX and MIN refer to the

scalar pT sum of charged particles and when we consider ETsum, then MAX and MIN









refer to the scalar ET sum of particles (or calorimeter towers). The overall "transverse"

region corresponds to the average of the "transMAX" and "transMIN" densities.

As illustrated in Fig. 6-4, one expects that "transMAX" will pick up the hardest

initial or final-state radiation while both "transMAX" and "transMIN" should receive

"beam-beam remnant" contributions. Hence one expects "transMIN" to be more

sensitive to the "beam-beam remnant" component of the "underlying event". This idea,

was first suggested by Bryan Webber, and implemented by in a paper by Jon Pumplin

[7,51-53]. Also, Valaria Tano [54, 55] studied this in her Run 1 analysis of maximum

and minimum transverse cones (R = 0.7).


6.2 "Leading Jet" Events

Figures 6-5 thru 6-13 show the data on the observables in Table 4-3 at 1.96 TeV for

"leading jet" events defined in Fig. 6-3 as a function of the leading jet PT compared with

PYTHIA Tune A and HERWIG. The plots show the uncorrected data (with statistical

errors only) compared with the theory after detector simulation (CDFSIM). The plots

also shows the data corrected to the particle level (with errors that include both the

statistical error and the systematic uncertainty as described in Table 5-4) compared with

the theory at the particle level (i.e. generator level).

Figures 6-5 thru 6-8 reflect a common trend in the data. HERWIG is consistently

below the data and PYTHIA Tune A for leading jet PT less than about 150 GeV. It is

interesting, however, that HERWIG agrees well for PT(jet#l) > 150 GeV for the average

density of charged particles and average charged PTsum density. The "transMIN"

densities are more sensitive to the "beam-beam remnant" and multiple parton interaction







78


components of the "underlying event" and PYHTIA Tune A (with multiple parton

interactions) does a better job describing the data than HERWIG (without multiple parton

interactions).



"TransMAX/MIN" Charged Particle Density: dN/dqd]
1.4
CDF Run 2 Preliminary
Z 1.2 data uncorected ..---- "--- -- -
Sctheory + CDFSIM T" -

S8 PY Tune A
C "Leading Jet"
0.6 W MidPointR 0.71q(e;t#1)2 -
0.4 -- -- -,--- ---- -------- J.96TeV -------
S }^* "tranMIN"
0.2 --- --
SCharged Particles (11<1.0, PT>0.5 GeV/c) I
0.0 -II I I I
0 50 100 150 200 250 300 350 400 450
PT(et#1 uncorrected) (GeV/c)


"TransMAX/MIN" Charged Particle Density: dN/dild*

CDF Run 2 Preliminary .transM" T
1.2 -- oncted top article -
8 1.0
PY Tune A
*0.8 - - -- adding Jet"
o. .HW MidPoint R = 0.7 I|h(et#1) <2
0.6
1.96 TeV
0.4 ------------ -tran--- ------
t 0.2
0 J---*----------f-T --
Charged Particles (III<1.0, PT>0.5 GeV/c)
0.0 I I I II I I
0 50 100 150 200 250 300 350 400 450
PTUet#1) (GeV/c)


Figure 6-5: Data at 1.96 TeV on the density of charged particles, dNchg/drld), with pr >
0.5 GeV/c and hll < 1 in the "transMAX" and "transMIN" regions for "leading jet"
events defined in Fig. 6-3 as a function of the leading jet PT compared with PYTHIA
Tune A and HERWIG. (top) Shows the uncorrected data (with statistical errors only)
compared with the theory after detector simulation (CDFSIM). (bottom) Shows the data
corrected to the particle level (with errors that include both the statistical error and the
systematic uncertainty) compared with the theory at the particle level (i.e. generator
level).














"Transverse" Charged Particle Density: dN/dTjd|
1.0
CDF Run 2 Preliminary "Leading Jet"
Sdata uncorrected
theory + CDFSIM
0.6 ------- --------- -


0.4
S0.4 /-"-----' -W ----- -- -- -- -- -- -- -- -- -- -- -
MidPoint R = 0.7 IlQ(et#1) < 2
2 0.2
1.96 TeV Charged Particles (hiq<1.0, PT>0.5 GeV/c)
0.0 I i I


50 100 150 200 250 300 350 400
PT(et#1 uncorrected) (GeV/c)


450


"Transverse" Charged Particle Density: dN/drjd
1.0
CDF Run 2 Preliminary "Leading Jet"
data corrected to particle level
08 T-------- --------- --- -T -------,----


PY Tune A

0.4-- -
MidPoint R = 0.7 Ilq(et#1)< 2
2 0.2
1.96 TeV Charged Particles (Iq1<1.0, PT>0.5 GeV/c)
0.0 I I I I I I i
0 50 100 150 200 250 300 350 400 450
PT(jet#1) (GeV/c)

Figure 6-6: Data at 1.96 TeV on the density of charged particles, dNchg/dTldq, with pr >
0.5 GeV/c and |l < 1 in the "transverse" region (average of "transMAX" and
"transMIN") for "leading jet" events defined in Fig. 6-3 as a function of the leading jet PT
compared with PYTHIA Tune A and HERWIG. (top) Shows the uncorrected data (with
statistical errors only) compared with the theory after detector simulation (CDFSIM).
(bottom) Shows the data corrected to the particle level (with errors that include both the
statistical error and the systematic uncertainty) compared with the theory at the particle
level (i.e. generator level).







80






"TransMAX/MIN" Charged PTsum Density: dPT/drld
3.0
CDF Run 2 Preliminary "Leading Jet"
S2.5 data unconrected
,, theory + CDFSIM
2.0 ----- L96- -- -

3 1.5 -
MidPoint R= 0.7 I(etl1)< 2
*1.0 --
Charged Particles (tq(<1.0, PT>0.5 GeV/c)


0.0
0.0 I------------I-------I----- ---
0 50 100 150 200 250 300 350 400 450
PT(jet#1 uncorrected) (GeV/c)


"TransMAX/MIN" Charged PTsum Density: dPT/d-nd
3.0
CDF Run 2 Preliminary "Leading Jet"
S data corrected to particle level
1.96 TeV
2. --------- -----------
I10 M C, PYTune A
E

SMidPoint R =0.7 I(Iet1) < 2
1.0 -- ----
Charged Particles (I|<1.0, PT>O.5 GeV/c)
C 0.5
10. MIN"


0 50 100 150 200 250 300 350 400 450
PT(jet#1) (GeV/c)

Figure 6-7: Data at 1.96 TeV on the PTsum density of charged particles, dPTsum/dTld4,
with pT > 0.5 GeV/c and h1 < 1 in the "transMAX" and "transMIN" regions for "leading
jet" events defined in Fig. 6-3 as a function of the leading jet PT compared with PYTHIA
Tune A and HERWIG. (top) Shows the uncorrected data (with statistical errors only)
compared with the theory after detector simulation (CDFSIM). (bottom) Shows the data
corrected to the particle level (with errors that include both the statistical error and the
systematic uncertainty) compared with the theory at the particle level (i.e. generator
level).