.p it“ .I
a tor .3.€.§:xd¢ '0
1y -
1Q.Il1’ ’ O
. .

If

4 A t:
. , . .3
up 2.0-1‘!‘ ‘ . . y .

It:
.U!!I.IXSA
1:. . ‘.. .. _ . v .

3121;...
alliiyila?n.m
'3 pl.

0

.llklullll

fitnvozl us, A“ n: l!
:V‘ll‘ 0". 1|. «.1 0.0
:5; urn-’01}. no

(€115.
. I.’
{'1'-
ul... 1 a. I}: 1.. EN
5.1.Ltl)

‘3‘ ' 'III
.sarfiaitlfiwc. .lftxt

53’1":
fuflhflflfl».fllf$.lv ,v‘ .

Dbl
‘ s. .r .1! .. .1!

I; V f. A\.. Lnuufll . . . L
5.53:» 55.3.57... , .

 

 

This is to certify that the

dissertation entitled

A Study of the Ability of the DO Detector
To Measure the Single Jet Inclusive Cross Section

presented by

Richard Vincent Astur

has been accepted towards fulfillment
of the requirements for

PhD. degreein Ph '

We

Major professor

Date July 13, 1992

 

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

 

 

LIBRARY
Mlchlgan State
Unlverslty

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.

DATE DUE DATE DUE DATE DUE

 

[———————fi

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

fil—jTTT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

msu lo An Affirmative Action/Equal Opportunity Institution
email-9.1

A STUDY OF THE ABILITY OF THE DO DETECTOR TO MEASURE THE SINGLE
JET INCLUSIVE CROSS SECTION

By

Richard Vincent Astur

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astonomy

1992

ABSTRACT

A STUDY OF THE ABILITY OF THE DO DETECTOR TO MEASURE
THE SINGLE JET INCLUSIVE CROSS SECTION

By

Richard Vincent Astur

The DO experiment began accumulating data at the Fermilab Tevatron in
May of 1992. Protons are collided with antiprotons at ~15 =l.8 TeV and an expected
peak luminosity of 5x1030 cm'2 sec‘l. The D0 detector is an all-purpose detector
that will have exceptional jet reconstruction capabilities derived from superior
calorimetry and nearly 41! angular coverage. One of the many physics measurements
that will be made at D0 is the inclusive jet cross section. Comparison of this cross
section with theoretical predictions allows us to test the accuracy of the standard
model of Quantum Chromodynamics (QCD). This comparison is usually in the form
of a measurement of the differential cross section with respect to the transverse
energy of the jet. The extended angular coverage of the DO detector allows
measurements of the differential cross section as a function of jet rapidity as well.
Recently completed calculations of the next-to-leading-order contribution to the
inclusive cross section result in predictions with reduced theoretical errors. In
addition, recent fits to data from deep inelastic scattering and single photon
experiments further restrict the quark and gluon structure functions of the proton
which are necessary in the theoretical predictions of the cross section. It may be that
an experimental measurement of the inclusive cross section would favor some of
these fits over others. We have studied extensive computer simulations of both the
Tevatron and the DO detector in order to determine DO's ability to reconstruct the
inclusive cross section. We present a discussion of this analysis as presently
understood.

To my parents, Oscar Antonio and Maryjane Astur, for all
they have given me.

iii

’ A .

ACKNOWLEDGEMENTS

There are an almost uncountable number of people without whose time and effort
in both large and small ways would have made this work impossible or at least much
more difficult and less enjoyable than it was. In particular I would like to thank the
following people: Barbara Taylor, Stephanie Holland, Teresa Thomas and Dolores Foote
for taking care of all my administrative worries at Michigan State both while I was there
and when I was away; Paul Russo, Kurt Ruthmansdorfer and John Featherly for superb
computer support at DO and FNALDO; Nick Hadley, Boaz Klima, Harrison Prosper, Chip
Stewart and the rest of the D0 software support group for all their work developing,
debugging and testing D0 parton jet and jet reconstruction software; all the work and
contributions of the DO QCD group; Jan Guida and Joan Guida to whom I owe a great
deal of my calorimeter and DAQ knowledge, Alan Jonckheere who answered every dumb
question I ever asked with detailed e-mail instructions; Dan Edmunds and Philippe
Laurens for all their expertise in regards to the Level 1 Calorimeter trigger and simulator
and Jan Hoftun for helping me understand the Level 2 filtering system. I would like to
thank my professors at Michigan State and all the students, physicists and staff who have
worked on the D0 experiment Most of all, I would like to thank my advisor, Harry
Weerts, for his guidance and advice over the last six years (even if I didn't always take it,
I appreciate it just the same).

Richard Astur
May 10, 1992

 

Table of Contents

List of Tables ................................................................................................................... vi
List of Figures ................................................................................................................. vii
Introduction ...................................................................................................................... 1
Theoretical Motivation ..................................................................................................... 5
Desciption of Simulations ................................................................................................ 25
DO Detector and Jets ........................................................................................................ 29
Theoretical Jet Definition. ................................................................................................ 37
D0 Jet Definition .............................................................................................................. 47
Jet Reconstruction Results ............................................................................................... 59
Jet Calibration .................................................................................................................. 66
Jet Triggering at DO. ......................................................................................................... 95
Results .............................................................................................................................. 115
Conclusions ...................................................................................................................... 145
Appendix A-Level 1 Trigger Sensitivity .......................................................................... 147

2-1
2-2

9-2
9-4
9-5
9-3
10-2
AA-l
AA-2
AA-3

List of Tables

Quark Colors ........................................................................................................ 6

Gluon Colors ........................................................................................................ 6

Proposed Level 1 Jet Triggers and Rates ............................................................. 106
Event versus trigger efficiencies .......................................................................... 107
LZJETS timing performance ................................................................................ 109
L2JETS jet reconstruction compared to offline reconstruction ........................... 109
Proposed Level 1 and Level 2 jet triggers and rates ............................................ 110
Parameter Values for Various Parton Distribution Fits ....................................... 135
Jet Et distribution for Herwig and Isajet. ............................................................. 148
Ratio of Level 1 Trigger Tower efficiency with noise to without ...................... 150

Ratio of Trigger Efficiency with Old Smearing Compared to New
Smearing .............................................................................................................. 151

 

 

 

2-3
2-4
2-5
2-6

2-8

2-9

2- 10
2-11
2-12
2-13
2-14

List of Figures

Gluon Couplings ................................................................ 6

Quark Structure of Hadrons .................................................... 7

Hard Scattering of Partons ..................................................... 8

Example of a Leading Order Process ......................................... 9

Example of a Next-To-Leading-Order process .............................. 10
Example of a higher order process ............................................ 10
Typical Proton Parton Distribution Functions ............................... 13
Cross section Dependence on 11.2 for L0 and NLO ......................... 15
NLO Inclusive Jet Cross Section versus ET ................................. 17
Dependence of Theoretical ET Distribution on u2 ........................... 18
NLO Inclusive Jet Cross Section versus Rapidity ........................... 19
Example of Quark Fragmentation ............................................. 23
Central Detector, Central Calorimeter and Level 0 Scintillators ............ 31
DO Calorimeters ................................................................. 33
Calorimeter Readout Cell ....................................................... 35
Theoretical cone definition for jets. ........................................... 39
Cross Sectional Dependence on the Cone Size R ............................ 41
Jet ET Distributions for Various PJET Algorithms .......................... 44
ISAJET Jet Width for Partons and Particle Jets ............................. 49
Typical Two Jet Event as seen by the D0 Detector .......................... 52
Number of Ellis Jets ............................................................ 54

vii

 

6-4

6-5

7-2
7-3
8-1
8-4
8-5
8-2
8-3

8-20

8-7
8-8
8-9
8- 10
8- 12

8-11
8-13

8-14
8-15
8-16
8-17

viii

Number of Ellis Jets - Number of Reconstructed Jets

SPLF=.50 ........................................................................ 55
Number of Ellis Jets - Number of Reconstructed Jets

SPLF=.75 ........................................................................ 56
Reconstructed Jet (D and 11 compared to Generated .......................... 61
Reconstructed Jet E and ET Compared to Generated ....................... 63
Jet Reconstruction Efficiency .................................................. 64
ch! as a function of particle energy and detector 11 .................................... 67
R(E) and R(ET) for single electrons .......................................... 68
R(E) and R(ET) for single pions .............................................. 69
Fractional Energy Carried by Particles within an Average Jet ............. 70
Fractional Energy Canied by Particles with <5% of the Jet's

Energy ............................................................................ 71
Pion Response with and without a Cone ..................................... 73
R(E) versus 11 for Different Cone Sizes ...................................... 74
n bias due to particle showering ............................................... 75
R(E) for Uncalibrated Jets ...................................................... 79
R(E) for Jets Calibrated Using Particles within the Jet ..................... 8O
R(E) for Jets Calibrated Assuming all Particles are Pions .................. 81
R(E) for Jets Calibrated using Slope of the Pion Response

Curve ............................................................................. 82
Example of Particle Tracking Method for Jet Calibration ................... 83
R(E) for Jets Calibrated with Track Cluster Method (leading

particle) ........................ _. .................................................. 85
R(E) for Jets Calibrated with Track Cluster Method (share) ............... 86
R(E) versus Jet Characteristics ................................................ 88
R(E) for jets made with various generators .................................. 89

Predicted Fractional Energy Loss for Various Event Generators .......... 91

 

8- 18
8-19
9-1
9-2

9-3
9-5

9-7
9-8
10-1

10-2
10-3
10-4
10-5
10-6
10-7
10-8

10-9
10-10

10—11
10-17
10-12

ix

R(E) for Uncalibrated Jets Compared with the Predicted Values .......... 92
R(Et) for Uncalibrated Jets Compared with the Predicted Values ......... 93
DO Trigger and Data Acquisition System ..................................... 97
iii-1 fiii‘iiiii??? .“Ie. f‘i‘if’f‘f‘if‘i’? f‘i‘ifTiiif’i. if??? ................ 100
Trigger Efficiency versus Jet ET for one Level 1 nigger setting ........... 101
Ratio of Level 1 Trigger Quantities to the Jet ET ............................ 102
Trigger Efficiency versus Jet ET for Various Level 1 Trigger

Settings ........................................................................... 104
Level 1 Rate and Efficiency versus trigger tower threshold ................ 105
Jet Trigger Rate and Efficiency versus L2JET ET Threshold .............. 111
Ratio of L2JET Jet ET to Reconstructed Value .............................. 112
Correction of Reconstruction Algorithm with Incorrect Splitting

Fraction ........................................................................... 117
Predicted and Real R(E'r)'s for Two Cone Sizes ............................ 120
R(E) With and Without 0.1 GeV Zero Suppression ........................ 122
R(E'r) for both Real and Adjusted Predicted ................................. 123
Ratio of Uncalibrated to Generated Cross Section .......................... 125
Ratio of Predicted Calibrated to Generated Cross Section .................. 126
Ratio of Real Calibrated to Generated Cross Section ....................... 127
Ratio of Predicted Calibrated to Smeared Generated Cross

Section ............................................................................ 129
Ratio of Real Calibrated to Smeared Generated Cross Section ............ 130
Ratio of Unsmeared Predicted Calibrated to Generated Cross

Section ............................................................................ 132
Ratio of Unsmeared Real Calibrated to Generated Cross Section ......... 133
Sensitivity of Reconstruction to a 2 percent Calibration Error ............. 134

Jet ET Cross Section at n=0. for Various Structure Functions ............ 137

 

 

 

X

10-13 Jet ET Cross Section “11:2. for Various Structure Functions ............ 138
10-14 let ‘1 Cross Section at 51:10. for Various StruCture Functions ........... 139
10-15 Jet 11 Cross Section at ET=60. for Various Structure Functions ........... 140
1:: Cross Section Dependence on Parton Distribution-LO vs NLO ----------- 142

P.D.F. Differences Compared with Reconstruction ........................ 143

Chapter 1: Introduction

Hadrons, like the proton, are believed to be composed of more elementary
particles called partons. Partons have been grouped into two categories: charged
fermions called quarks and the neutral bosons known as gluons. Evidence for the
existence of partons came initially from jets seen at electron-positron colliders while the
parton structure of the proton was inferred more directly from Deep Inelastic Scattering
(DIS) of neutrinos and electrons from protons. Collisions at greater energies were
studied at proton-proton and then proton-antiproton collidersl. Currently, the Tevatron
at the Fermi National Accelerator Laboratory in Batavia, Illinois collides protons with
antiprotons at a center-of-mass energy of 1.8 TeV, the highest in the world. In all
cases, the scattering and liberation of a parton were evidenced by sprays of particles at
wide angles to the beam line after a collision. These sprays of particles are referred to
as jets and are widely accepted as being representative of a scattered parton of
approximately the same direction and energy.

At the Fennilab Tevatron, jet production is one important way to experimentally
test Quantum Chromodynamics (QCD), the theory that describes the interactions of
quarks and gluons. The simplest experimental jet measurement one could make would
be the cross section for pi» jet + X. Here X denotes any other product of the
interaction. This is known as the single jet inclusive cross section for proton-antiproton
interactions. This can be compared to the QCD predictions for pi» parton-i- X in those
kinematic regions where QCD is able to make such predictions.

QCD predictions can currently only be calculated for those collisions in which
there is a 'large' momentum transfer between the colliding hadrons. In these cases, a
parton is exchanged which is sufficiently energetic to resolve the partons within the

1

 

 

 

2
hadron. 'Large' is determined by the relation of the momentum transfer, Q, to a QCD
parameter, A. which must be measured. In the kinematic region where Q2>>A2, the

proton-antiproton interaction is expected to act like independent elastic scattering
between individual partons because the strong coupling constant, as, asymptotically

approaches zero as Q is increased without bound. For small as, calculations can be
performed perturbatively in (15. These calculations quickly become complicated and
time consuming as the order in as is increased, however. For this reason, many
measurements of the inclusive cross section have been compared only to the leading
order (L0) 052 predictions. Recent experiments2 have had the benefit of predictions
for next-to-leading—order (NLO) (153 jet production at proton-antiproton colliders3.

Theoretical errors in the prediction are greatly reduced in the NLO calculation.4
However, there is still a 15-20% uncertainty which results from imperfect knowledge
of the momentum distributions of the quarks and gluons within the proton. Nominally
the proton consists of 2 valence up quarks and a valence down quark. But there is also
a large gluon presence as well as a lesser occurrence of other quark flavors. Further,
none of the parton types carries a fixed fraction of the proton's momentum but rather
have some distribution as a function of that fraction. These are described by the proton
parton distribution function (p.d.f.) for each parton. Being the largest source of
experimental errors, it may be possible that comparison of predictions for various sets
of parton distribution functions to a precision experimental measurement could prefer
some sets over othersS. Further errors in using QCD theory to predict the jet cross
section are associated with the definition of a jet and the assumption that the scattered
parton kinematics can be inferred from measurements made on the jet. We will discuss
jet definitions in detail in later chapters.

The DO detector6 is an all-purpose detector that is especially suited to jet
detection and reconstruction. It consists of a central detector which identifies charged
tracks and the location of the collision, a hermetic calorimeter for containing and
measuring the energy of all particles that are produced (except neutrinos and muons)
and a muon system that detects and reconstructs muons. Neutrinos are detected
indirectly through the measurement of transverse momentum imbalances in the detector.
D0 has begun taking data in the spring of 1992 at the Fermilab Tevatron where protons
and antiprotons collide with a center of mass energy of 1.8 TeV and an expected peak
luminosity of 5 x 1030 cm‘zseC'l. Various elements of the DO detector have been
subjected to the Fermilab fixed energy particle beam (D0 Test beam) for calibration and
study". The detector has also undergone numerous commissioning runs using cosmic
ray muons to test both detector and data acquisition perfonnanoe.8 Additionally, the

 

 

 

3
performance of the DO detector at the Ferrnilab Tevatron has been simulated
extensively. To simulate proton-antiproton collisions, event generators such as
ISAJET9, HERWIG10 and PYTI-IIA11 were used. These programs vary in how they
simulate QCD above leading order and how they fragment the resulting partons into
final state particles. The response of the D0 detector to these particles is simulated by
combining the GEANT12 physics package with details of DO geometry to form a
program named DOGEANT. The GEANT portion simulates various physics processes
that can cause leptons and hadrons in the detector to scatter, shower and deposit
energy.

In the succeeding chapters we will discuss DO's ability to measure the single jet
inclusive cross section based on these simulations. We will start with a detailed
description of the simulated data that was analyzed as well as further theoretical
motivation behind the jet cross section. The theoretical and DO experimental definitions
of jets will be discussed. A brief overview of the D0 detector and its role specifically in
reconstructing and detecting jets will be presented. Predictions for jet reconstruction
and detection will be discussed as well as methods for correcting biases in this
reconstruction. Finally, we interpret the results in terms of the predicted accuracy of
reconstructing the single jet inclusive cross section at D0 and make conclusions based
on the entire analysis.

 

1368 numerous papers by the CDF, UA1 and UA2 collaborations.

2CDF Collaboration, Jet Results from CDF published in the Proceedings XXVth
Reconstres de Moriond, (1991)

3S. D. Ellis, Z. Kunszt and D. E. Soper, Phys. Rev. Lett. 64 2121 (1990)
41bid Ellis. (1990)
5A. D. Martin, R. G. Roberts and w. J. Stirling, Preprint RAL-90-084 (1990).

6D0 Collaboration, An Experiment at DO to Study Antiproton-Proton Colllisions at 2
TeV: Design Report, Print-840306 (Ferrnilab) (1983)

7See for example M. Abolins et al., Nucl. Instr. Meth. A280 36 (1989) and H.
Aihara, Performance of the DO End Calorimeter Electronic Module, LBL- 29784,
October 1990. and N. Amos, Proceedings of the First International Conference on
Calorimetry in High Energy Physics (ed. D. Anderson, M. Derrick, H. E. Fisk, A.
Para, C. Sazama), 84 (1990)

81. Kotcher, Ph.D. thesis, New York University

9 ISAJET Event generator written by F. E. Paige and S. D. Protopopescu, Brookhaven
National Laboratory

10G. Marchesini and B. Webber, Nucl. Phys, 3310 461, (1988)

11Event generator written by H-U Bengtsson, Department of Physics, University of
Lund, Lund, Sweden

12R. Brun et aL, GEANT3 Users Guide, CERN DD/EE/84

Chapter 2: Theoretical Motivation

As our interest in measuring the inclusive jet cross section is motivated by a
desire to test the predictions of standard QCD theory, we will first discuss the relation
between the twol. QCD is the theory that describes the strong force, which is credited
with holding both nucleons and atomic nuclei together. In analogy with Quantum
Electrodynamics (QED), QCD predicts a strong 'charge', a strong coupling constant
(or s), and exchange particles that mediate the strong force. The only particles that
interact strongly are quarks and gluons. Since nucleons, like the proton, are believed to
be composed of such particles, quarks and gluons are sometimes generically referred to
as partons. Similarly, antinucleons are composed of antiquarks and gluons. Another
way of describing QCD is then, the theory of the interactions of quarks and gluons.

Strong Charge

The strong 'charge' is called color. Quarks (antiquarks) each come in three strongly
charged varieties: red, blue and green ( antired, antiblue and antigreen). Further, there are
5 experimentally detected 'flavors' of quarks and a predicted sixth flavor known as the top
quark. Table 2-1 lists the quark flavors and their color charge as well as their electric
charge. Gluons, unlike the analogous photons in QED, also carry strong charge. The
eight colored varieties of the gluon are listed in table 2-2.

 

 

 

Quark har e olor Charge Types
UP +573 r, b or g
Down -1/3 r, b or g
Strange -1/3 t, b or g
Charm +2/3 r, b or g
Bottom -1/3 r, b or g
Top‘ +2/3 r, b or g

 

 

 

 

 

* Not yet detected experimentale
Table 2-1: Quark colors

 

Gluon Charge Color Charge Types
Gluon Neutral 113: ii, bg', bF,’ gr',’

(rF- brim/3. st:
or (rr-+ bF- ZEEZNE .

 

 

 

 

 

 

Table 2-2: Gluon colors

The charge of the gluon allows its emission or absorption by a quark to cause the quark
to change color. For example, a blue quark that absorbs a gli'gluon would become a
green quark of the same flavor. The charge of the gluon leads to more interesting
differences between QCD and QED. The charge of the gluon allows it to interact with
itself as well as quarks as shown in figure 2-3.

 

Figure 2-3: Gluon couplings. In addition to coupling with quarks, the gluon is
able to couple with other gluons in several ways.

 

These extra gluon interactions lead to a strong coupling constant which decreases with
increasing energy of the mediating gluon as shown in equation 2-1. Strong coupling at
low energies means that quarks are constantly exchanging gluons with neighboring
quarks resulting in the tight bonding of quarks into colorless configurations of either 3
quarks (or antiquarks) or a quark-antiquark pair. The former is known as a baryon and
the latter is known as a meson. Figure 2-4 shows the simple quark structure of both.
Not shown is the exchanged gluons and quark-antiquark pairs which can be formed
momentarily by the gluons.

<9 <9
@. ®

Figure 2-4: Quark structure of Hadrons. All hadrons come in two types. Baryons
contain three quarks each with distinct color (antibaryons contain three antiquarks with
distinct anticolor.) Mesons contain a quark and an antiquark of the same color.

Strong Coupling Constant and Perturbative QCD

The strong interactions between quarks and gluons at low energy make attempts
at calculations nearly impossible. However, at the collider, where protons and
antiprotons are collided at high energies, large momentum transfers between partons
(mediated by energetic gluons), have decreasingly small couplings. Thus the scattered
parton behaves more and more like a free particle with increasing gluon energy. This is
known as the asymptotic freedom of the partons. The strong coupling constant has the
form: 3

a = 1271' (21)

‘ (33-2f)1n(Q2/Az)

 

Here Q is the 4-momentum magnitude of the exchanged gluon. f is the number

of quark flavors assumed to contribute. Equation 2.1 is valid only for large Q/A,
where interactions can be calculated perturbatively in terms of the as. Figure 2-5

 

 

shows a high energy interaction between a proton and an antiproton in which a quark
from each scatter elastically while the remaining 'spectator' partons continue on their
way. Each coupling with the gluon

O r r 9
O >———+ Q

 

 

 

 

Figure 2-5. Hard scattering of partons during a proton antiproton collision. The
remaining partons continue along the bearnline. Two jets are formed from the
scattered partons and two jets, from the remains of the baryons, continue along the
beamline.

contributes a x] as to the amplitude and the lowest order calculation that could be made

would involve two partons scattering to two partons in the final state. Figure 2-6

shows an example of such 2—» 2 interactions. The cross section for such a calculation
would be proportional to 0152 which we refer to as leading order (L0). The next-to-

leading-order (NLO) calculation would involve, additionally, terms of 0153. Some of
these terms involve the emission of an energetic gluon away from a parent parton as
shown in figure 2-7. There can also be the splitting of a gluon into a quark-antiquark
pair. Figure 2-8 shows an example of an even higher order process. Thus perturbative
QCD theory predicts the cross section for two partons to scatter into some final state
and inceasingly complex final states are described by increasingly higher order as
terms.

 

 

Figure 2-6: Example of a leading order 0152 process.

 

10

\
I \
I \
I \
or a or \«'
\ 4‘1
\ I
\ I
I

l I t l t

Figure 2-8: Example of a higher order (154 process.

Patton-Patton Scattering Cross Sections
Given the wide variety and complexity of partonic final states, the simplest
class to consider is the inclusive final state which contains at least one parton.
Note that this prediction must involve some quantity like the center of mass energy of
the two initial parton system. First, we look at all the possible ways two colliding

11

partons 0f 59991539 type (a,b) can form a partonic final state. This simplest
configuration has two final state partons. To this contribution we add the contribution
for 3,4 and higher final state parton multiplcities. We must sum over the types and

colors of the final state partons and average over the initial state colors. Note that
although the 2—) 2 contribution has contributions to all orders of as, it is the only

term that has 0152 terms. On the other hand, predictions calculated only to order
0152 predict only 2-r 2 interactions. The inclusive parton production for a specified

2 parton subprocess (a,b) is the sum of all types of 2 parton processes (those with
2 parton final states, those with 3 parton final states etc...).:

6(ab -) parton + X) = 2Cab20'(ab —-> cd) + 3C”, 2 0(ab —-) cde)+...
c,d

c,d.e

1 l
CT=qu=Cfi=-3_2-=-9-
(2.2)
_ _1
%'a-a
l 1
c =_=_
7‘ 3x8 24

Here X denotes "anything else in the final state" and the C's are the color-averaging
factors for the various parton pairs. c,d and e are summed over all types and colors of
partons. We must also average over the initial spin states and sum over the final spin
states.

Parton distribution functions

Since we can't experimentally isolate interactions that involved a particular
parton pair (a,b), we must sum over all possible pairs. To do this, we need some
knowledge of the partonic structure of the proton as some partons occur with larger
frequency than others. Additionally, the partonic cross sections shown in equation 2.2
have an intrinsic dependence on the invariant mass, 3 , of the subprocess. However,
the partons do not carry a fixed fraction of the proton's momentum. Thus 3 can
vary from low values up to the s of the proton-antiproton system which is (1.8
TeV/)2. We need to know this 3 distribution.

Parton distribution functions are probability distributions that describe the
frequency that a parton occurs in a hadron with a certain fractional energy of the
hadron. X; denotes the fraction of the hadron's total energy carried by parton a.
The parton distribution function is denoted fa/A(Xa) and is the probability density

 

12

parton a in hadron A with a momentum fraction Xa. For the case of protons it is more
common and convenient to write:

fq/p(Xq) - q(x) for quarks and
fg/p(Xg) - g(x) for gluons.

The valence quark composition of the proton and the requirement that the partons
together carry all of the proton's momentum, give the following relations:

Juvm dx = 2; Id,(x)dx =1

(2.3)
Ix [goo + it th)+€i(x> 1 ]=1
M

Such functions must be measured. The quark distribution functions are measured from
deep inelastic scattering of electrons and neutrinos on protons. Since these collisions
involve electroweak interactions, the gluons cannot contribute. The gluon distribution
functions can be determined, for example, from single photon experiments in which a
gluon and a photon are produced in the final state.

Many sets of these parton distribution functions have been made using various
fits to data from various experiments with various assumptions. Uncertainty in the
p.d.f.'s tend to be the largest source of uncertainty in the cross section measurement.
Figure 2-9 shows the up quark and gluon parton distribution function for two of these
fits. Note that the up quark distribution peaks at ~10-15% of the proton's momentum.
Both fits indicate that gluons dominate the soft portion of the distribution while the up
quark dominates the region where a parton carries a large fraction of the proton's
momentum.

l3

 

 

Examples of Typicol Proton Porton Distribution Functions

 

y.
p—
p.
in
P
f
073- ‘t
P
i
“i
"e
.3.

0.6

  
      

0.5
0.4
0.3

0.2

.\ \
MT-B xg(x) —> \‘x (— HMRSB x

0.1 \\
- \
‘.\
\ \
e‘.\~‘

.\
O L111.llllllllllllJJle+1.T.P

0.1 0.2 0.3 0.4 0.§ 0.6 0.7 0.8 0.9

IIUTIUIITIITrI'IrUI'IIUI

 

 

Figure 2-9! Plotted is 00:) weighted by x for both the gluon and the up
quark content of the Proton for two different fits: HMRS set 3 and
Morphin-Tung set 3

 

 

 

14

Total Inclusive Jet Cross Section
Thus we must use the p.d.fs in summing over the parton subprocesses to end
up with a formula for the total inclusive cross section for parton scattering. We assume
that a scattered parton will manifest itself as a jet:

C(AB —) jet + X) = andexade fa/p(xa) fry/50(1))
a.b (2.4)
x6(ab —> parton + X)

a and b are summed over the 8 gluons and the three colored varieties of each flavor of
quark. As already mentioned, the parton subprocesses cannot be calculated exactly. If
we truncate our approximation at some order of as, we introduce an error that is
manifested in an arbitrary QCD energy scale uz. Theoretically, the cross section is
independent of this parameter when calculated to all orders, but a dependence does
appear when the calculation is done to some finite order and uncertainty in how to
choose this scale then contributes to uncertainty in the calculation. Figure 2-10 shows
the p2 dependence of both the L0 and NLO total inclusive cross section
calculations. The NLO cross section is much less sensitive to the choice of [1.2.
All of our NLO and LO cross section calculations come from the calculations of
Ellis, Kunszt and Soper combined with any one of a variety of parton distribution
function sets.2

 

 

15

 

 

d’a/dP,dy (nborns/Gev)

p. Scole Dependence of Cross Section for L0 and NLO

 

 

 

 

80 La.
70 l
50 ; LO
so '—
40 '— --
30 :§.-.u-§"....:--'....:.--..-1---...2”'...o.o-:-o-;-_:--f-— "a ...... ‘u.
: NLO —._':_ .............................. ‘ ..........
20 '— ___—-
C
10 l
C
I. I I I I I I I I I I I I I I I I I I I I I I I I I L I I I I I I I I I I I I
0.25 0.5 0.75 1 1.25 1.5 1.75 2
[Jr/Er

Figure 2-10: L0 and NLO Cross Section with P,=5o. y=0.
and cone size R=.7

 

 

16

Differential Jet Cross Section

Although the total cross section is predicted by the theory, it is not the
most useful quantity for comparing theory to experiment. One reason is that
measurement of a scalar number is very sensitive to normalization errors.
Additionally, it is experimentally difficult to measure jets over all phase space,
especially for low jet energies and jets that are directed along the beamline.
Therefore, predictions are usually made for the differential cross section with
respect to some variable. The most popular choices are the transverse momentum
(PT) and the rapidity (y) of the jet. Rapidity will be defined later but it is strongly
related to the angular direction of the jet with respect to the beamline. Both
quanities are Lorentz invariant with respect to a momentum boost along the
beamline which occurs whenever the x of the colliding partons are not equal. The
shape of these differential distributions is a more sensitive quantity to compare
with experimental measurements. Figure 2-11 shows the resulting differential
cross section for jet production using three different p.d.f. fits. The distributions
show a dramatic fall as a function as PT as well as sensitivity to the choice of p.d.f.
set. (which can changes portions of the spectrum by as much as 20%) The
impressive decrease in sensitivity to the choice of u2 when using NLO as opposed
to L0 is shown in figure 2-12. Other experiments have already seen close
.agreement to the NLO prediction for this distribution3. D0 will also be able to
measure the rapidity distribution; an Ellis prediction for the rapidity distribution is
shown in figure 2-13.

l7

 

 

0. (nbarns/Gev)

d’a/dP,dy ly

Ellis NLO Inclusive Jet Cross Section vs PT for y=O

 

 

 

 

 

 

10‘:—

10’;—

1oz;—

10“:L .1....i..l.L....1....1....1
20 40 60 80 100 12p?

Figure 2-1 1: Shown are the next to leading order cross section spectrums
from the Ellis program using various sets of proton distribution functions.
Solid,Dash and Dotted line correspond to HMRS—B, MRS-BO and MRS-8135

 

 

18

 

 

L0 d'a/dP,dy ly=0. (nbarns/Gev)

Inclusive Jet Cross Section vs PT for y=0

 

 

    

 

 

 

 

 

 

 

:- ? .-
cu
4 4
10 Q 10
.. in .
- E :
I B L
- c:
.i g i
' 3
3 ll .—
10 ____ 2: 10 :
: >~ I
I- q .-
: o '
U I-
.. \ b
- «o
'0 2
2 10 .-
10 r 3 :
: Z I
Z I
10 E—
10 L- :
: r
~ 1-
. 1 E'
1 .3- E
" \‘x _‘
'rrrlrrLJLrerV‘I 101Lrlrrrrlr r
40 80 120 40 80 120
b) P:

a P
Figure 2-122 p.’ dependenc)e of 0) Lb and b) NLO cross section. In
both cases the top curve (p’=P,’) and the Bottom curve
(p'=P,’/16.) surround the curve calculated with
fiz=Prz/4-

 

 

19

 

 

40 GeV (nbarns/GeV)

d’a/dP,dy 1?,

Jet Cross Section for 40 GeV PT Jets

 

N
O

100

80

60

4O

20

 

 

_fI I I l I I I I I I I I I I I I I I I I I I I I I I I

I I I I I l I I I I I I I I I I I I I I l I I I I I I I I I I AM,
0.5 1 1.5 2 2.5 3 3.5 4
Jety

Figure 2-132NLO y cross secton for 40 GeV PT Jets

 

 

 

20

The fall of the PT spectrum

We can see qualitatively why the PT cross section falls so quickly by looking at
the parton subprocess gg—P gg which is the dominant subprocess for jets emitted
transverse to the beam line. The cross section is related to the square of the matrix
element; for this parton subprocess it is the following:
g2 + E2 A2 A 2 A2 + A 2
M2(g. g, —> gcgd -—-(47ra,) [ £12 + S {2“ +t g2“ + 3 (2.5)
where s = (Pa +P,) ; t = -(P, -P,)2 :6 = -(P. -Pd>2

 

Assuming a massless gluon and evaluating the expressions in the center of mass

frame:
§2=(2E) Eza-=(P3+P§-2P .CZ;P) 1‘12=(Pf+P§—2P,-Pd)2

Using (l-cosOw) x (la-case“) = (l-costc) = sine:c and IP,| = |Pc| z E(2.6)

A

t2 = 7::§2(1-c030,c)2 ; fi2 = -‘li-§2(1+0059ae)2

A2"2 "4 A4 ‘2 A2
4 -l—-§‘sin‘6 S
16 ”

l(1+ c0320”) + TL“ - cosGE)‘ + 1:604. cosOx)‘

 

IVO

=-(4rra,2)

 

J>|

isin 6,c
16

aria-case”): ~i-211-(1-1-c039m)2 + 3 )

 

2 4
=-9-(47ra,)’ lO+4cos.9f +2cos 9£+-2-(1+cos§c) +3
4 sm 9.; 4

We insert this M2 into a familiar formula for the differential cross section and
recognize that the first term dominates for smaller angles:

_1_ _f___(9) 2
M": 64 P,‘ ( '7)

1
dt dP’cosB,lc 1632'

21

Thus the parton subprocess by itself predicts a cross section that falls quickly as
a function of Pr. Normally, the PT distribution is calculated with the angle between
the outgoing quark and the incident direction fixed. In that case the distribution is
dependent on P. But the angle is fixed in the laboratory frame and not the center of
mass frame of the partons. We will try to estimate the PT dependence when we require
the outgoing parton to be completely transverse in the laboratory frame. By
constraining the angle, the Pr dependence is essentially a dependence on P and P2 is

proportional to s.

1
16s2

d6’(pp -) jet+ x)
de

 

 

z deadxbg(xa)g(xb) |M2|

and

§= ((x.\/s+ x,,\/-s-)2 -(x,\/s - x,~/§)2) = 4xaxbs
Experimental fits show that:

1 o
300 .. ;(1- x)

Thus the integrand is proportional to:

6 o 1
<1-x.>(1-x.) —
Since the angle is relatively fixed, the only way to increase Pr is to increase the

x values and thus this term falls faster than l/P6. Thus after the integral is done, we
might expect the differential distribution to fall like Pr to some power. Fits to the

calculated spectrum show that:

Although the fall of the ET spectrum provides a more sensitive test of the QCD
predictions than a softer spectrum, it does make the measurement of the spectrum more

difficult. There is always some systematic error in the measurement of the jet Pt at the
experimental level. For a given M, the consequential bias in the cross section might

be expected to be:

22

do dP .
7 = 41/?“ if we assume 0' cc P,” (2.8)

I

Thus our fractional error in measuring the cross section is magnified N times by
our fractional error in measuring the jet PT

Even if the jet measurement was made without bias, such that the PT was
measured correctly on the average, there is always an effect due to the finite Pr
resolution combined With the steeply falling cross section. Finite resolution means that
jets that belong in one Pt bin will sometimes be mismeasured enough to be deposited in
a higher or lower bin. To some extent, neighboring bins compensate the losses of each
other, but if the spectrum falls fast enough, each bin receives many more entries from
the more populated bins than it gives to the less populated bins. Hence the distribution
becomes 'smeared' and thus the measured spectrum must be unsmeared at some point

Fragmentation of quarks into jets

Our attempt to measure the inclusive jet cross section depends on our ability to
infer the energy and direction of the original parton with the jet of fragmented particles
which we see in the detector. This process cannot be calculated perturbatively at
present; instead a fragmentation scheme is used by the generator to simulate jets in the
detector. Our estimate of how well we can determine the attributes of the parton jet
from the particle jet may depend on which scheme is used.

One type of fragmentation scheme is an independent fragmentation scheme‘ in
which the scattered parton is fragmented in a manner independent of the other present
partons. This method was first presented by Feynman and Field‘. Other methods do
consider the other partons in the proton. For example, string fragmentation methods
describe the partons as being connected by strings which may break and form quark-
antiquark pairs5. Figure 2-14 depicts a very simple model of how the breakup of a
proton and subsequent fragmentation of the quarks might look in its center of mass
frame. In b) the valence quarks begin to separate and as they do, the color field lines
are become collimated between the quarks rind the rest of the system. In c) the quarks
move further apart and the potential energy of the field grows almost linearly with the
separation until d) it becomes energetically favorable for quark-antiquark pairs to be
created. These pairs can form colorless mesons in e) and move off as a jets of particles

inf).

 

 

 

 

 

 

 

0)

24

 

1v. Barger and R. Phillips, Collider Physics, Addison-Wesley, Redwood City, CA
(1987) .

2Calculations obtained via a software routine which would make the calculations using
one of many sets of parton distribution functions supplied by Morhin-Tung (J.
Morphin, W-K. Tung), HMRS (P. N. Hariman, A. D. Martin, R. G. Roberts, W. J.
Stirling), and MRS ( A. D. Martin, R. G. Roberts, W. J. Stirling)

3CDF Collaboration, Inclusive Jet Cross-Section in Anti-P P Collsions at sqrt(S)=1.8
TeV, FERMILAB-Pub-9l-231 (1991) (submitted to Phys. Rev. Lett.)

4R. D. Field and R. P. Feynman, A Parametrization of Quark Jets, Nucl. Phys.
8239, 349 (1984)

5B. Andersson et. al., Parton Fragmentation and String Dynamics, Phys. Rep. 97,
147 (1983)

Chapter 3 : Description of Computer Simulations Used

All work presented here has been the results of extensive computer simulations
and analysis of the results of such simulations. We will describe the various
simulations used and, where possible, point out some of their limitations. The
simulations fell into two categories, the first of which is Event Generation in which the
collision of a proton with an antiproton at the expected center of mass energy of 1.8
TeV is simulated. The second category is known as Detector Simulation. Here the
output from the Event Generation was combined with detector geometry and selected
physics processes to simulate the response of the detector. The results were written in a
format similar to that produced by the D0 Data Acquisition System. Finally,
reconstruction and analysis routines were run on the output of the first two. For the
most part, this software is identical to what will be used on real data.

Event Generation
Although various event generators have been used for comparison's sake, the ISAJET
event generator was used primarily. ISAJET simulates proton-antiproton interactions
at \Is_=l.8 TeV. We will briefly summarize the features of the program. First, a
parton hard scattering is generated using a parameterized perturbative QCD cross
section. All quarks are assumed to be massless except the top and bottom quarks.
This is always a 2—9 2 process. The user can set kinematic limits on the energy and
angular direction of the partons in the final state as well as the types of partons that
are in the initial state. Such limits only apply to the two partons that result from the
initial 2-+ 2 process. To approximate higher order QCD, radiative corrections in
which either the initial or final state partons may emit gluons are made. Each quark
or gluon has a chance to emit a gluon. This probability is proportional to a splitting
function multiplied by as. The same probability exists for a gluon to split into a

25

26

quark-antiquark pair. The procedure is reapplied to the daughter quarks and gluons.
In this way, ISAJET approximates higher order processes by producing events with 3
and more final state partons. The process is terminated once the parton falls below 6
GeV in energy. At this point, the partons are fragmented into particles using a Field-
Feynman fragmentation schemel. Particles with a lifetime of less than 10'12 are
decayed immediately. This finishes the simulation of the hard scattering. The beam
jets, which represent the remains of the fragmented proton and antiproton, are added
by simulating an interaction in which no hard scattering took place. This event is
superimposed on the hard scattering event. This process conserves transverse
momentum, but not energy. Thus the event energy is rescaled at the end. The vertex
of the event is selected with a Gaussian generator which is centered around the
nominal interaction point with a width of 30 cm. This is expected to simulate the real
distribution of collision points from the Tevatron. At the end of the event generation
phase we are left with two lists of 4 vectors; one for final state partons and one for
the final state particles. Note that meant simulation does not include events in
which there was more than one proton-antiproton collision and it does not include the
possibility of simultaneous cosmic rays. An associated piece of software that often
ran after event generation was a jet finder named PJETSZ. PJBTS tried to identify jets
from the generator's list of final state partons or particles. Such jets are referred to as
'generated' jets and will be discussed further in a later chapter.

Detector Simulation

Detector Simulation is the most complicated and time consuming portion of the
simulation process. It combines detailed knowledge of the geometry and makeup of the
DO detector with simulated physics processes to determine the response to high energy
particles streaming outward from the vertex point. The detector is represented by
nested volumes within volumes. Each volume is meant to approximate the size and
material makeup of a real detector piece. If this were done precisely, the resulting
geometry would require large amounts of computer time to process. Therefore
approximations had to be made. Since jet reconstruction was dependent almost entirely
on the calorimeter simulations, we will limit our discussion to that portion of the
detector simulation. The three large calorimeters which consist of alternating layers of
uranium, readout boards and gaps filled with liquid argon were too intricate to be
included. (See chapter 4) Therefore, they were replaced by a 'mixture' material whose
density approximated that of the real structure. Still maintained after this
'simplification' is the gap between the central and endcap calorimeters, the walls of the

 

27

cryostats which contain the calorimeters and the phi cracks which are between the
modules of the central calorimeter. The GEANT physics program was used to simulate
particles in the detector. Physics processes such as Compton scattering, pair
production, photo electric effect and photo fission as well as multiple scattering,
ionization, delta ray production, bremsstrahlung, nuclear and hadronic interactions were
simulated. Detector response is calculated in terms of energy loss in 'active' portions of
the calorimeters. Output data banks which are similar to those produced by the real
data acquisition system were made. Since each particle that moves through the
calorimeter loses only a small fraction of its energy in any physics process, the
simulation is slowed considerably if the processes are allowed to continue indefinitely
for any particle. Normally an energy cutoff is set which requires that a particle deposit
all of its energy once it falls below this cut off. This is especially important in the
predicted transverse shape of electromagnetic showers in the detector. The real
calorimeter channels all have 'noise' distributions which come from the electronics and
real argon ionization from decays in the uranium plates. Noise means that an empty
calorimeter cell outputs a finite signal that often follows some Gaussian-like
distribution with irregular tails. The detector simulation had no noise simulation in it
A simulation of the detector’s trigger system was available but it was not used to select
events for these studies and will only be discussed in the chapter on jet triggering.

Event Reconstruction

Finally, offline reconstruction and analysis routines were run. These routines
are the sarrre as those that will be used on real data and were evolved into their present
form through this simulation process. Although a vertex reconstruction routine was
available, most of the studies done used the vertex supplied by the event generator.
Therefore, additional errors in reconstructed jet quantities due to vertex
mismeasurement are not included in those studies. An offline jet reconstruction routine
named CAJETS3 was used to reconstruct jets. Results of this routine will be referred to
as ”Reconstructed jets.

28

 

 

lIBID. Field and Feynman.

213. Klima and c. Stewart, PJET-Parton Jets in the Monte Carlo. DO Note 905, D0
Experiment at Fermilab, Batavia, IL, December 1989.

3N. J. Hadley, Cone Algorithm for Jet Finding. D0 Note 904, D0 Experiment at
Fermilab, Batavia, IL, November 1989.

Chapter 4: D0 Detector and Jets

Jets are characterized by a Spray of energetic, high ET particles in a localized
area of space. This definition is vague, but the truth is that jets are not well defined
objects. We will see that even at the parton level, what constitutes a jet is ambiguous.
For now, the above definition is enough to make apparent the challenges of
reconstructing jets. We have seen that the theory can make predictions about 1) The
transverse energy of the jet and 2) The rapidity of the jet. Therefore, our detector
should be able to l) reconstruct the energy of the jet 2) reconstruct the vertex of the
event and 3) identify the direction in space of the jet. The last two together allow the
polar angle, 9, of the jet axis with respect to the nominal beamline to be reconstructed
We will describe the various components of the D0 detector, paying special attention
to those components that aid in accomplishing any one of these three objectives. We
will also mention to what degree they were simulated for our studies.

Level 0 Scintillatorsl

There are 2 sets of scintillators, one on each side of the nominal interaction
region, offset about 130 cm, which comprise the Level 0. Each set covers an angular
cone of about 10 degrees around the beamline. (covering 11 from 2.2 to 4.1)
Whenever the proton fragments, particles are thrown transverse to the beamline.
These scintillators are intended to detect such particles and hence flag those

interactions in which breakup of the proton or antiproton occurs. The Level 0 was not

V simulated for this analysis. The Level 0 scintillators are labeled in figure 41. The
primary role of the Level 0 is that of a trigger element and it will be discussed further
in the chapter on jet triggering.

29

 

30 WE

Central Detector2 '
The Central Detector (CD), fills a barrel shaped region that surrounds the

beam pipe and extends radially out to 84 cm and out to 2:130 cm on both sides of the
nominal interaction point. Primarily, the CD consists of three concentric regions
flanked by two identical sections of a fourth type as shown in figure 4-1. Most of
these regions contain drift chamber cells. Drift chambers are detectors that measure i
the trajectory of charged particles. A charged particle ionizes the drift chamber gas t
and these ions -'drift' under the influence of an applied electric field. Position and drift
time measurements can be used to reconstruct 'hit' positions along this path which in
turn are fitted to produce the trajectory of the path itself. Assuming that the number
of such ionizations are proportional to the energy deposited by the particle allows the
determination of its (1de (energy loss per unit length). The dE/dx of an electron
differs from that of a photon which converts into a electron-positron pair allowing
discrimination between the two. Unlike some detectors, the DO central detector lacks
a central magnetic field, this means that the momentum and sign of the charged
particles cannot be determined.

Vertex Chamber: The vertex chamber is closest to the beam-pipe and
reconstructs tracks around the interaction point. Its job is to measure the interaction
point. This is crucial in determining the Pr of the jet.

Tramitional Radiation Detector (TRD): The purpose of the TRD is to
discriminate electrons from charged pions by measuring the transitional radiation
produced when a charged particle crosses a dielectric interface.

Central Drift Chamber: (CDC): The CDC reconstructs trajectories of
charged particles from the interaction region.

In addition, there are two drift chambers (one forward and one backward of
the other central detector elements) that fill the entire radial region from the outside of
the beam pipe to the outer radius of the other central detector elements. These are the
Forward Drift Chambers (FDC).

Although simulations of these detector elements exist, jet reconstruction for
the most part is only concerned with the location of the vertex. In most of the studies
described in the following chapters, the vertex was taken from the event generator
instead of from the reconstruction. Thus the added uncertainty in jet Pr derived from
mismeasurement of the vertex is not included in those analysis. However, the vertex
reconstruction was used in the chapter on Jet Reconstruction and in the high statistics
sample with which we reconstructed the jet cross section in the Results chapter.

 

 

31

    
    

 

 

(beam line)
(beam line)

 

 

 

level 0 sc'nt.
level 0 scint.

\

 

 

Figure 41: Central Detector, Central Calorimeter and Level 0 Scintillators are
shown in this slice view of the central portion of the detector. The arrow marks
the beam line.

D0 Calorimeters3
The Central Detector is unable to provide either momentum or energy
measurements of the particles that pass through it. In fact, it does not see neutral
particles at all. It is the job of the D0 calorimeters to contain and measure the energy
of all the particles produced in the collision except for muons. They must also
provide spatial resolution to allow determination of transverse energy and the
separation of jets from each other. Thus the calorimeter is the most important

32

detector element for jet reconstruction. DO has three calorimeters: a central
calorimeter and two endcap calorimeters, one on each side of the central calorimeter,

To measure as much of the event as possible and to identify broad jets, the
calorimeters must be both hermetic and containing. Figure 4-2 shows a side view of
the calorimeters. The calorimeters are symmetric in 11) and provide coverage down to
a pseudorapidity of 4.1. This corresponds to 2 degrees from the beam line. Hence the
calorimeters cover nearly 41! in solid angle. The calorimeters should provide
containment for hadrons as well as for electrons and photons. The central calorimeter
electromagnetic section (labeled CCEM in figure 42) contain 20 radiation lengths of
material. In the end calorimeters, there is an electromagnetic section (ECEM) located
just inside the End Cap Inner Hadronic (ECIH) which provides similar
electromagnetic containment For hadrons, each calorimeter contains several sections
of hadronic calorimetery. The central calorimeter has a uranium fine hadronic
(CCFH) section followed by a coarse hadronic (CCCH) section which is made of
copper plates. The endcap has two sections (ECIH and ECMH) outside of the ECEM,
which have both a fine uranium section and a coarse stainless steel section) and an
outer ring of stainless steel modules referred to as the outer hadronic (ECOH) section.
The central detector provides 7 interaction lengths of material while the end
calorimeters provide up to 9 interaction lengths.

 

33

Calorimeter and Detector Viewed from the side (E-w)

CC CH

EC

Figure 4-2: The three calorimeters of the D0 detector.

Spatial resolution is also important to allow one to distinguish among nearby
jets and to measure the transverse energy of the jet . The calorimeters are divided into
various read out channels that segment the calorimeter azimuthally in tit, in
pseudorapdity and longitudinally outward from the nominal interaction point. Thus
the readout channels are divided into projective 'towers' that occupy .lx.l in d)-
pseudorapidity space. Pseudorapidity will be defined later but is related to the polar
angle that the tower makes with respect to the beam line. These towers become
physically smaller in the forward and backward regions of the detector as shown in
figure 9-2. The calorimeter is divided into 64 o sections, 74 pseudorapidity bins and
about 14 longitudinal layers in each tower for an approximate total of sixty-six
thousand readout channels. The central calorimeter is separated into many phi
modules each of which span the length of the central calorimeter. Although the
CCEM and CCFH modules are staggered so that their phi edges do not align, there
are cracks in between modules. This is also true of the ECMH and ECOH rings. The

 

 

4__l

34

ECEM and ECIH are one piece modules and hence do n0t have cracks in either it or
n. The only pseudorapidity cracks are between the calorimeters. Special detectors
(see the next section) are installed in these regions to measure energy deposited in this
region. There is transverse segmentation for both the electromagnetic as well as the
hadronic sections. The electromagnetic sections have four sections and the third one
(which is expected to contain from 50% to 80% of the energy of an electromagnetic
shower) is twice as finely segmented (.05 x .05 in 1141) space) as the rest of the
detector. The hadronic section has three layers of uranium calorimetry and a final
layer of copper calorimetry in the central calorimeter and four uranium layers and a
couple stainless steel sections in the endcap calorimeters.

Each readout channel is divided up into several readout cells whose signal is
summed. For the most part, each readout cell looks like every other readout cell in
the three calorimeters. Each cell consists of a liquid argon filled gap sandwiched by
an absorber plate (usually uranium) and a signal board. Each calorimeter is contained
by a cryostat which holds and preserves the liquid argon. The dense absorber plates
cause the breakup and showering of particles that pass through. Although most of the
particle's energy is deposited in the absorber, some of it is lost in the liquid argon gap
in the form of ionized argon atoms. The fraction of energy deposited here is expected
to be a fixed fraction of the overall energy deposited. An electric potential between
the absorber plate and the resistive surface of the signal board moves the liberated
electrons across the gap and induces an electric current which can be determined by
measuring the voltage difference across a capacitor This signal is amplified, baseline
subtracted and digitized. Uranium-liquid argon calorimeters have been found to have
a response that is more linear with energy and less sensitive to particle type than other
designs.4

 

35

1 G l 0

  
   

Copper

Resistive Coat

Uranium Plate

Liquid Argon

/

 

Figure 4-3: Sample Calorimeter Readout Cell

Inter-Cryostat and Massless Gap Detectors

As mentioned above, energy deposited within the calorimeter rs determined
by measuring the charge within an argon gap and using this amount of charge as an
indicator of how much energy was deposited in the entire uranium-argon cell. But
when particles move from one cryostat to the other they first pass through liquid
argon between the modules and the cryostat walls that cannot be read out and then
pass through the space in between the cryostats as well The situation is made worse
by the thick steel endplates of the modules which can cause the particles to start
showering and deposit energy if they were not already. Special detector elements
were constructed to detect such energy. The massless gap detectors are alternating
sets of high voltage and grounded signal boards which were joined to the calorimeters
module end plates inside the cryostat. In this way, particles showering on their way
out of the calorimeter would deposit some amount of energy in the argon between
these gaps and this could be read out. The space between the cryostats was filled with
scintillators that made up the inter-cryostat detector (1CD). The 1CD covers the MH
ring and a portion of the OH as well. Rings of massless gaps were placed on the
central calorimeter fine hadronic end plates as well as the endcap calorimeter middle
hadronic and outer hadronic modules. Both these detectors were simulated and the

36

results used for reconstructing jets. Large portions of jet energy can be deposited in
these detectors if the jet points in these directions,

Muon Chambers5
Three layers of muon chambers (one before the iron and two afterwards) make

up the Wide-angle-muon-system which provides 211 11) coverage in the central region.
Furthermore, special magnet iron and chambers provide extended coverage down to
small angles (Small-angle-muon-system:SAMUS). Particle and heavy quark decay
within the jet may produce muons which may not be contained by the calorimeter.
Hence it is necessary to add such muons back into the jet. Currently this is not done
in our present jet reconstruction.

 

1F. Nang and R. Partridge, Level 0 Detector Layout, DO Note 998, D0 Experiment at
Fermilab, Batavia, IL August 1990.

2A. Clark et al, The Central Tracking Detectors for DO, CONF-8806235-8-mc
(microfiche), (1988)

3Numerous references on the D0 Calorimeter exist. See reference 5

4P. Franzini, Nucl. Instrum. Meth., A263, 78 (1988)

5D0 Collaboration, An Experiment at DO to Study Antiproton-Proton Colllisions at 2
TeV: Design Report, Print-840306 (Fermilab) (1983)

Chapter 5: Theoretical Jet Definition

Jets have traditionally been defined by the experimentalists as leading order
perturbation theory predicts two final state partons which are well separated due to
transverse momentum balancing. There is little ambiguity at this level; each quark is
expected to manifest itself as a jet. In next-to-leading-order theory, the definition of a
jet is not as well defined. We are concerned with the theoretical definitions of jets for
a couple of reasons. First of all, a theoretical jet definition allows the calculation of
theoretical distributions to which we can compare experimental results. Also, as we
must simulate hard scattering events to test our reconstruction procedures, we need to
identify the 'true' or 'theoretical' jets for comparison with our experimentally
reconstructed jets. Finally, the theoretical jet definition will necessarily motivate our
experimental jet definition and jet reconstruction algorithms.

We will discuss two theoretical jet definition types below. The first describes a
definition that was used to calculate the single jet cross section to next to leading
order in perturbation theory by Ellis, Kunszt and Soper. The second definition was
used to identify theoretical jets from event generators, such as ISAJET, which
approximate all orders of peturbation dreary. The first definition must guide our
experimental reconstruction of jets as it is our best guess at what is 'true' in real data.
We will describe that definition in great detail. But the second definition is necessary
for determining reconstruction biases and efficiencies. In this paper, the terms
"theoretical jet" or "parton jet" or "particle jet" will always refer to one of these
definitions and therefore does not necessarily refer to the 'spray of particles’ which is
the signature of an experimental jet

37

 

38

NLO Jet Definition According to Ellis et al.1
Perturbation theory simply predicts the final state partons 0f the event since the
fragmentation process through which partons turn into a jet of hadrons is
nonpeturbative At lowest order QCD, there is simple parton elastic scattering and
hence the final state consists of two final state partons which are well separated in
space due to transverse momentum balancing. Since, it is experimentally easier to

detect jets which are emitted at wide angles from the hadron beam line, the cross
section is often described in terms of the transverse momentum (Pt) and the rapidity

(y) of the parton. Pt is simply defined as P- sine, where theta is defined as the angle

between the final state parton and the incoming partons. The rapidity is defined
formally as :

=%ln(E+Pc036) (5.1)

E - PcosO

This is preferable as both quantities are Lorentz invariant. Hence the predicted
quantity is: do/dPTdy.

However, NLO diagrams allow 2 or 3 parton final states. The third parton
could be a gluon which can be emitted at small angles to one of the other partons and
with small energies as well. Alternatively, it could be a gluon which splits into a
quark-antiquark pair. Divergences as the energy of the third parton or the angle
between it and the parent parton become small prevent the calculations of finite cross
sections for a 'two parton' final state or a 'three parton' final state although the sum of
the two is finite. These divergences can be removed by introducing an arbitrary
parameter to distinguish the two states unambiguously. The common technique is to
choose as this parameter a distance R in y-ttt space:

R = ‘j(Ay2 + Adz) (5.2)
and define a 'partonic jet' as the sum of all partons within a cone of radius R. Figure
5-1 shows an example of this.

 

 

 

 

39

 

Figure S-l: A cone definition of a jet allows unambiguous classification of
jets from next-to-leading-order processes.

Thus for NLO QCD, the theory predicts do / dPtdy(R). This is the differential cross

section for producing a partonic jet (using the cone definition of a jet with radius R)
with transverse momentum Pt with rapidity y.

The next to leading order calculations of Ellis, Kunszt and Soper have been
recently published. In addition, we have made use of a program written by them to
predict inclusive jet cross sections. We will refer to results from this program as
"Ellis results". As we intend to compare to their predictions, it is important to
understand their definitions:

a) Each parton has a rapidity (y), azimuth direction ((9) and a transverse
momentum PT

b) A cone algorithm is used to 'merge' a pair of partons if they meet the
following criteria:

 

\l((yt -yt)2 +(¢t -¢t)2) SR; i=1.2 (5.3)

where i=1,2 refer to the partons under consideration and

1 1
Pr = EFF; yt =— zy-Pr- : ¢t=— 24%- (5.4)
J i=1,2 ‘ PT] i=1.2l ‘ PTJ i=1,2l ‘

It then follows that two partons jets are merged into one jet if:

4O

 

”1 + PTz
max(PT1,PT2)

 

(in. -,,)2 +(¢1 — ¢2)2) s

x R (5.5)

If this case is true, the parton jets P1 and P2 are not included in the cross
section, but only the merged jet which has transverse energy of Pt] and a position of

0] and y J.

Since the NLO predictions depend on the definition of the cone via the cone
size R, the theory can be further tested by making measurements that depend on this
dependence. Traditionally, the energy distribution within a jet was described only by
fragmentation schemes; but the NLO predicts the widening of the previously pencil
thin parton jets through gluon radiation and gluon splitting. Additionally, the
dependence of the cross section itself has an explicit R dependence as opposed to L0
theory. The NLO cross section is expected to vary as A + BlnR + CR2. Figure 5-3
shows the predicted cross section dependence for jets with PT=40. GeV at y=0., for
both L0 and NLO. The L0 curve is completely flat, as expected, while the NLO
curve rises as the cone size is increased and thus making it 'easier' for 40 GeV to be
contained in a cone.

 

41

 

 

d’N/dP,dy1y1<.5 (tr/5 Gev )

PJET Distribution for Signal Events

 

 

 

 

 

103:
i'
2
10 _—
10 LI I L L I I I I I I I I L I I I L I 4 LL I I I LJ I I I I I L I I
50 50 7O 80 90 100 110 120

El
PJET [T

Figure 5-22 Inclusive Jet Distributions for PJET S in various modes.
Solidi Parton PJETS. Dash: Particle PJETS Dot: Modified Particle PJETS

 

 

42

Event Generator Jet Finder : PJETS

As our event generators simulate jets physics to all orders of as, we need a
theoretical definition for these as well. A software package was developed to provide
this for the various event generators used in D0; it is called PJETS. This algorithm
determines jets from either a) a list of the event's final state partons or b) a list of the
events final state particles. We thus refer to them as parton jets or particle jets. The
algorithm requires a cone size (R) to be specified. The algorithm proceeds as follows:
The list is Pt ordered Then the list is scanned from top to bottom. Each unused
parton/particle on the list becomes the center of a jet. The rest of the list is then
searched and any particles/partons within the given cone size is added into the jet. A
new energy weighted jet center is found and the process can be repeated until the
center is stable. But usually, the algorithm only does one repetition. The next
particle/parton on the list (that has not been associated with a jet) is then used as a jet
center and the process continues until all particles/partons have been considered. No
jet merging or splitting is done. Figure 5-2 shows various (unnormalized) transverse
energy distributions for the various PJET algorithms when a cone size of R=.7 is
used. This sample was generated from ISAJET under the condition that one of the
two initial generated partons had a rapidity value between y=-.5 and y=.5. Two of the
curves correspond to the PJET algorithms described above. Note they do NOT fall on
top of each other. The spectrum found when using the final state partons is
systematically higher than the spectrum found when the final state particles are used.
This might be explained if the fragmentation process caused partonic energy to leave
the cone in the form of particles. More likely, fragmentation of the partons may
widen the jet enough to make it seem like two jets instead of just one. In any case, the
PJET defmition is not completely compatible with the Ellis definition. This can be
seen by examining the simple example of two equal energy partons separated by a
distance of .8. The PJET parton algorithm described above will always see two
parton jets if the cone size is R=.7. But the. Ellis definition would merge these two
jets into one according to equation 5.5. Of course, PJETS was not meant to match the
Ellis definition, but as a comparator for the reconstructed jet finder. The reasoning
becomes circular when we then realize that we want the offline reconstruction to
match the Ellis definition and the PJET definition to match the reconstruction
definition.

We attempt to standardize our jet definitions by introducing and using a
Modified PJET definition which takes normal parton or particle PJETS and applies the

 

43

Ellis merging criteria (equation 5.5) to form merged jets when the criteria is satisfied.
Ftrjgure 5—2 shows that the new modified particle PJET distribution in addition to the
o ers.

 

 

 

d’o/dP,dy (nbarns/Gev)

120

100

80

60

4o

20

Cone Dependence of L0 and NLO Cross Section

 

 

 

 

o o o o o o o o o o a

Leading Order 1'
a
a
it
Next to Leading Order *
a
a
a
a

a
L I I I I I I I I_ I I I I I I I I l I I I I I I I I I I
0 0.2 0.4 0.6 0.8 1

Cone Size R

Figure 5-32 Cross section versus cone size for transverse jets with
P,=40 GeV. and y=0.

 

 

 

46

 

1S. D. Ellis, Z. Kunszt and DB. Soper, Physical Review D40 2188 (1989)

 

Chapter 6: D0 Jet Definition

Since the scattered partons undergo fragmentation into a spray of particles and
each particle than showers while in the calorimeter, a cone algorithm (or a similar
energy clustering algorithm) is always necessary at the experimental level, even if it
were known that only 2 partons were in the final state. This is because the partons
fragment into particles before detection is possible. Figure 6-1 shows a histogram
that relates the width of a parton jet versus the same jet after the partons have
fragmented. This width is defined as a summation over all the partons or particles
associated with the jet:

 

Jetwidth = \[nitdth + 183.21»: (6.1)
where 17%,, = El—z E,|n,. - El and a similar definition holds for 11).

let

This was obtained by looking at ISAJET parton jets and then tracing all the final state
particles that had fragmented from any one of the partons in the jet. It can be seen
that although the parton jet is always within a cone of R=.4, the fragmented jet can
throw particles at wide angles from the original parton direction. Historically, the
cone size is chosen to separate the energy that belonged to the parton from energy that
was contributed by the two beam jets. This'type of contamination is known as the
'underlying event'. Now that the NLO theoretical predictions include a cone size as
well, it becomes important for the experimentalist not only to apply a cone to the jet,
but to understand how much of the cone dependence is due to the underlying parton
cone dependence and how much is due to the fragmentation of the partons and the
showering of single particles in the detector. The process is further complicated by
the assumption that the fragmented particles that make up the jet come only from the

47

48

underlying parton. This cannot be true strictly as color conservation would require
that the jet have color which it clearly cannot. Thus the identification of 'jet' energy
with parton jet energy is flawed at some level. Fragmentation is not the only
difficulty when using a cone algorithm. Since D0 uses its calorimeters for jet
measurement, each particle will shower in the calorimeter and spread its deposited
energy over some area. Measurements at the DO test beam1 indicates that the shower
spread of one 50 GeV pion is such that the shower is 95% contained by a circular
region whose radius is 24 cm (the module being struck by the beam was the 1H). In
the central region, this area is contained by a cone of size R=.2. However, in the
forward region, the cone size needed jumps to R=.7 due to the decreasing separation
of rapidity lines for the region near the beamline. Hence, even a thin jet (or a single
particle) will look broader in the calorimeter.

49

 

 

ISAJET Jet Width for Particle and Parton Jets

 

 

 

 

 

 

 

 

5 2
.0
$1.75
3 1.5
£1.25 .5 . .
as. 1 s... :‘F;
0. 75 31.3}, . '.'_', .
0-5 ..
0.25 sis-53’
o .L.IIIILLIIIIIIIILLII
0 0.25 0.5 0.75 1
Partonic Jet Width
3
a; 10
C
0
3
U'
E
2
10
10
I4LLIIIIIIILIIIIIIV
0 0.5 1 1.5 2

Particle Jet Width

Frequency

 

4
10

10

10

10

 

IIIIILIkIIIII

0.5 0.75 1
Partonic Jet Width

IIIII

0 0.25

Figure 6-1 I A scatter plot of Jet Width comparing partonic jet width to
the resulting jet width calculated from the particle remains of the partons
after fragmentation. The fragmented jets become much broader.

 

 

50

Still, the experimental jet definition is intended to mirror theoretical
definitions in most respects. Some changes are required, however. Since the D0
calorimeter measures energy instead of momentum, transverse energy (ET) replaces
Pr in the algorithm. Further, the rapidity cannot be measured since that would
require both momentum and energy knowledge. We make the small mass assumption
that reduces rapidity to pseudo-rapidity which is defined simply in terms of 9.

E + Pcosd
“(ml and E = P

 

We refer to this quantity as pseudo-rapidity:

n = —ln(tan-g-) (6.2)

Thus lines of constant angle from the beam line are lines of constant pseudorapidity.
But these lines grow closer and closer together as the angle becomes close to 0 or 180
degrees.

Jets are reconstructed most accurately during offline analysis. The framework
for jet reconstruction at D0 has long been in place and been tested extensively on a
wide variety of both simulated QCD and rare physics events as well as simulated
special events such as single pions and single electrons. Two algorithms are currently
available. The first is a fixed cone algorithm which we will describe in more detail.
The second is a nearest neighbor algorithm ’in which jets are formed by clustering
cells following some prescription. Similar'algorithms have been used by many other
experiments. However, theorists are able to do calculations using only a fixed cone
algorithm and so that is the one we concentrate on for now. We first give a
description of the D0 jet reconstruction algorithm and then discuss how well it mirrors
the Ellis definition.

 

51

The steps of the algorithm are as followsl;

l)First the algorithm considers all the towers in the calorimeters. A tower is
defined as one 1141) tower with all of its layers summed. Figure 6-2 shows an event as
viewed in n—tb space broken up by readout towers. The towers are ordered by Et.
There are 64 (I) towers and 74 n towers. This diagram shows two forward jets.

2) Preclusters are formed by sorting through the towers in order of Et. Only
towers above some threshold (usually 2 GeV) are initially considered. The algorithm
then looks at the nearest neighbors of these seed towers and joins them if they are
above some smaller threshold (usually 1 GeV). Thus the calorimeter is divided up
into preclusters and the rest of the lower Et towers. The average 11 and it) of each
cluster is calculated.

3) Each precluster is used as the center of a cone. All cells within a cone in
n-tb space defined by the radius R = (“Ayz + A432) are joined into the jet. A new n-tl)

 

average is calculated from the ET weighted x and y positions of the cluster and the
procedure is repeated until the center of the cone is equal to the averaged n-tl) of the

jet to within some precision.
E, = 21E,i defined for y and 2 as well.

all cells

E E 9
:= -1 _y = -1 z =— —L
a, tan [Ex] 6, cos [JEi+E§+E§] n, ln(tan(2))

4) The total ET of the jet is defined as the sum of the ET's of each cell.
ET = XETi
all cells
5) The list of jets is inspected for cases in which two jets share common cells.

In this case the amount of energy shared is compared to the jet with the smaller ET. If

 

the ratio of these numbers is above some splitting fraction (usually .5) the jets are
merged. Otherwise, the energy is split evenly between the two jets.3

6) Additional quantifies for each jet are calculated. The electromagnetic
fraction of the reconstructed jet is equal to the ratio of the jets energy which was
found in any electromagnetic section of a calorimeter divided by the total energy.
The second moments of the ET weighted n and the d) distributions are calculated. The
reconstructed jet width is defined simply as the sum of these two when added in
quadrature.

52

Comparison to Ellis jet definition

We will test our jet reconstruction abilities in the simulations by comparing
the distribution of reconstructed jets to the distribution of simulated PJETS. This is
because we are interested in recreating the input distribution and not necessarily the
calculated distribution of the theorists as approximated in the NLO distribution.
However, it is still important to verify that our reconstruction respects the Ellis
definition as well. The reconstruction algorithm mirrors most of the Ellis definition
with the exception of the merging criteria. Merging of jets is enforced in the
reconstruction in two ways. The first is by changing the jet center until it matches the
ET weighted center. Thus if the jet center starts in the direction of one of two closely
spaced jets, the center will move in between the two and perhaps merge them both
within the cone. The second, more explicit enforcement of jet merging is the splitting
fraction which causes the merge of jets if they share too much energy. Although
there are prescriptions for jet merging in the reconstruction algorithm as well as the
Ellis algorithm, it is not clear that they are consistent with each other.

The following simple study was done to gauge the compatibility of the
reconstruction and Ellis jet definitions with respect to jet merging. Since the Ellis
merging criteria only applies to two partons at a time, we used ISAJET events in
which we could find only two partons which were within R=l.l of each other. The
Ellis definition can then be applied to determine whether it is one jet or two. We
further require that if the cone size is changed to .3, that the partons satisfy the Ellis
definition of 2 jets. By then comparing the number of reconstructed jets in each case,
we can see how the experimental definition compares to the theoretical one. The only
other requirements were that the PJET was within .5 of y=0., that the ET was in the
range from 75. to 140. GeV and that the smaller ET parton have an E1 above 15.
GeV. Figure 6-3 shows the distribution of the Number of Ellis jets for various cone
sizes. For larger cone sizes there is a spike at N=1, but our selection of events forces
this distribution to become a spike at N=2 by the time the cone size is .3. Figure 6-4
shows the corresponding distributions for dN= Number of Ellis Jets - Number of
Reconstructed Jets for a Splitting fraction of SPLF= .5. This distribution is usually at
O (agreement) with shoulders at dN = l and -1. Thus the disagreement goes both
ways: sometimes the reconstruction sees an extra jet and sometimes it sees one less
than the Ellis algorithm. But there is agreement from 70% to 100% depending on
which cone size is used. This is encouraging considering we have chosen parton
configurations where the disagreement should be at its worst. Figure 6-5 shows the

 

53

distributions for SPLF= .75. Surprisingly, the curves are basically identical to the
SPLF=.5 set; this implies the agreement between the reconstruction algorithm and the

Ellis definition may be due to the recursive procedure for determining the jet axis and
not to the value of SPLF.

 

54

 

Transverse Energy (Et)

Typcial 2 Jet event as seen by the DO Detector

 

’

 

 

Figure 6-21 Lego plot of the transverse energy of an event as a function

of‘nandw

 

 

 

55

 

 

Cone Radius = .3

Cone Radius = .7

100

80

60

40

-20

90
80
70
60
50
40
30
20
1 0

 

 

IIIIIIIIIIIIII'IIII'IIIIIII

I

 

 

1

 

I

 

 

 

 

 

 

 

 

 

 

-2 2
Number of jets
l I 1 i
-2 2

Number of jets

.5

Cone Radius =-

Cone Radius =- .9

60
50
40
30
20

10

100

80

60

40

20

0

Number of Ellis jets for various cone sizes

 

IIII‘IIIIIIIIIII[_IIII'IIIIITIII'I

 

 

 

l I

 

 

 

 

1 I

 

 

 

 

 

 

 

 

-2 0 2
Number of jets
E
E
C l r . l L
-2 O 2

Number of jets

Figure 6-32 Variation in number of jets as cone size changes

 

 

56

 

 

Number of Ellis jets - Number of Reco jets (Split Fraction=.5)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

n. 8° : tr! :
11 70 E— 11 :3 E—
m : m ..
'- 3 =
’3 60 E- '13 60 F.
O : O :
a 50 :- “ so =
u : u :-
C :_ C =
3 4° 3 40 =-
20 E" 20 —
10 E- 10 E- .
O=.+.LLI. 05.1.1.11m
-2 0 2 -2 0 2
Number of jets Number of jets
n. a!
11 90 11100 :—
3 3° 2 =
a; 70 '13 80 E-
l: 60 a: 5
s 50 § 5° 3'
0 4o 0 :
4 —
30 0 E
20 20 2.
10 I'— E
o r I r I 1 I o " r I I A I L
-2 0 2 —2 O 2
Number of jets Number of jets

Figure 6—42 Number of jets found with Ellis algorithm - Number of jets
found with Reconstruction algorithm when splitting fraction = .50

 

 

57

 

 

Number of Ellis jets - Number of Reco jets (Split Fraction=.75)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

n. r; “I! :
11 7o 5- 11 8° _':_'
: in L.
s 6° 3- s :2
o? so — t2
2 to 5 2 5° 5‘
s 8 40 =-
30 E- 30 E.
2° 1" 20 -
10 E- 10 E— N
0 = t L l 1 . t . 0 5. 1 . 1 . I r .
-2 O 2 -2 0 2
Number of jets Number of jets
l\ 0’ .
ll. 90 “.100 :-
tg 80 g :
8 7° '13 3° .-
2: 6° i. at
5 33 a 2
4o '—
30 '5
2° 20 "-
10 —-J‘ E
O r 12 r (I) —!—a 5 r 0 5' I |2=== (1) L E L
Number of jets Number of jets

Figure 6-52 Number of jets found with Ellis algorithm - Number of jets
found with Reconstruction algorithm when splitting fraction = .75

 

 

58

 

1S. J. Durston, Private communication.

2N. J. Hadley, Cone Algorithm for Jet Finding, DO Note 904, D0 Experiment at
Fermilab, Batavia, IL November 1989.

3N. J. Hadley, Splitting and Merging in Cajets., Internal memo. February 1991.

Chapter 7: Jet Reconstruction Results

As mentioned at the beginning, we have used extensive computer simulations
to determine the extent of DO's ability to reconstruct jets. Primarily we have used the
ISAJET event generator to generate the final state partons and the hadrons produced
by the fragmentation. To this extent we are biased to the ISAJET generation. To
determine our jet reconstruction efficiency as well as the quality of the reconstructed
jet characteristics, we must make comparisons between the generated jets and the
reconstructed jets. In this chapter, a generated jet refers to a particle PJET; that is, a
jet formed from the event generator's list of final state particles. We use the particle
PJET instead of the parton PJET in order to isolate reconstruction biases and
problems without the complications of fragmentation. A reconstructed jet refers to a
jet found by the DO reconstruction algorithm. In both generated and reconstructed
algorithms, the cone size was R=.7 and the reconstruction jet splitting parameter was
.5 (jets that shared more than 50% of the least energetic jet are merged).
Additionally, reconstructed jets that had been split or merged were considered only
in the efficiency studies. We determine the reconstruction efficiency by searching for
a reconstructed jet match for each generated jet. The requirement for a match was
simply that a reconstructed jet was located within a distance of .7 in n—tl) space of the
generated jet. If more than one jet satisfied this requirement, then the distance
requirement was changed to .5. If more than one still satisfied, the reconstructed jet
nearest in energy was taken. The matching between generated and reconstructed jets
is 1-1. We will see below that these matching requirements are not overly strict.

We will determine the quality of our reconstructed jet characteristics by
comparing a generated jet to its reconstructed match. We define two quantities for
such comparison which will be used here and in the following chapters:

59

60

‘i’ .
R(ty) = Reconstructed (7 l)

Generated

A? = \PGenerated _ \PReconstmcted . (72)

where ‘I’ can refer to any jet quantity (e.g. energy (E), transverse energy (131‘), phi
direction ((1)) etc).

Figure 7-1 shows a histogram of the quantity Acp, This distribution peaks at
zero and has a width of .03 which corresponds to 1/3 the size of a readout tower.
Also shown is a plot of this quantity versus n and a mild bias is apparent for large I].
Figure 7-1 shows the same plots for An. The width of the distribution is about the
same as in phi, but now there is a larger r] bias which results in an l'lreconstructed that
is prejudiced away from the beam line. This is attributed partly to the finite shower
size of particles within the jet‘, the decreasing size of the readout towers as 11
increases and partly to the asymmetric size of the cone in the forward region. This
will be discussed in the calibration section. Even still, the magnitude of the bias is at
worse one-fifth of a readout tower. The small widths of these distributions verifies
that the matching requirements used were generous. The generated jets in these
histograms had a ET of approximately 40 GeV.

61

 

 

Reconstructed Jet 77 and go

 

5. 45000
5 40000
3 35000
1: 30000
25000
20000
15000
10000
5000

e

0
-0.4 -0.2

 

    
   

O

1
cm
W

 

0.2

910.!
054316”
40:91:42

ML.

 

<14

Generated ¢ - Reconstructed ¢

 

IIIl'lIIllIIIIIIIIIIIIUIIIUUUIUI

 

0 1
-0.4 -0.2

 

 

  

0
Generated 17 - Reconstructed 17

I

 

0.2

cm unfit.“

SIIJ

  
   

 

(£4

< Generated 1) - Reconstructed 1) > < Generated 4' — Reconstructed it >

 

0.04
0.03
0.02
0.01
0
-0.01
-0.02
-0.03

IIIIIIIIIIIIIIIIIIU

 

-0.04

IIIIIIIIIUIIIUTIITTI

 

 

 

0.04
0.03
0.02
0.01

-0.01
-0.02
-0.03

 

IIIIIIIIIIIIIUIIIIIIIIIIIIIIIIIIIIIIII

 

 

-0.04

—2 0 2 4
Generated 11

Figure 7-12 st and n reconstruction biases f‘ar Jets with ET
between 35 and 55 Gev. A clear 17 dependant bias is shown in the 17

reconstruction.

 

 

62

Figure 7 -2 shows the distribution of R(E) and R(ET). This is a complicated
plot which will be discussed further in the calibration chapterz. One evident feature is
the over-estimation of ET compared to E. This is partly due to the n bias described
above. The R(E)pcurve shows a systematic jet energy loss of approximately 20%.
The generated jets in this histogram all had at least 40 GeV in transverse energy.

Note that generated jets with the same ET have larger energies for larger
pseudorapidities than at n-O where they are the same.

The predicted mismeasurements are due to detector systematics which we can
try to correct and we will discuss that in the next section. Another question that must
be addressed when talking about jet reconstruction, is that of reconstruction
efficiency. We define jet efficiency as the percentage of generated jets for which we
found a reconstructed match. Finding a match can be difficult when jets are nearby.
Figure 7-3 shows histograms of b0th generated jets and those generated jets for which
a reconstructed match was found. The generated jets were selected from the region in
which the reconstruction begins to be inefficient. The curves are nearly identical
above ET=16 GeV which implies complete efficiency. Jets below this energy are
more difficult to reconstruct because they tend to be jets that are associated with
nearby jets, or broad jets whose most energetic tower may not exceed the 2 GeV
threshold required to initiate a reconstructed jet

63

 

 

0.96

0.92

0.88

0.84

0.8

0.76

Reconstructed Jet Energy and Transverse Energy

 

I I I r

Frjj I I I I I I I

I I I

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

 

l I I I I l I I I I I

 

 

"lllllllllllllllLllLLAIIIIIIIIILllllllll

 

-—-l— —+—
DOT=R(Et)
—"——'—-—"—3‘—. ..... 3 ...... _h—
SOLID=R(E)

 

 

 

-4

-3 -2 - 1 0 1 2 3 4
Generated 17

Figure 7-22The calibration ratio R for both-Energy and Transverse Energy
as a function of generated 77 for Jets with E, between 35 and 55 Gev

 

 

64

 

 

Jet Reconstruction Efficiency

 

1200

 

 

 

 

 

1 000

800

 

 

 

 

600

 

 

400

OOOOOOOOOOO

 

 

iiiiiiiii

200

 

 

o 1 1 1 "i 1 l 1 1 L J 1 1 1 l 1 1 1 l—T—l—T—l 1
O 4 8 12 16 20 24

.. Generated Et
Figure 7-32 Shown is a histogram of PJETS as superimposed on a histogram
of those PJETS that had a reconstructed jet match. The curves match at
16 gev.

TWIIITIIIITIIIIIIIIIIIIIIIIIIIII—

 

 

 

 

 

 

 

 

 

65

 

lN. Amos, P. Draper, S. J. Durston, Eta Dependent Efiects Due to Shower Size. DO
Note 1162, DO Experiment at Fermilab, Batavia, IL, July 1991.

23. J. Durston, Energy Calibration and Systematics, D0 Note 1202. DO Experiment at
Fermilab, Batavia, IL. September, 1991.

Chapter 8: Jet Calibration

The need for ET calibration is obvious from the previous section which shows
that the reconstruction underestimates the ET of the average jet by about 16-20%.
There is also a reconstructed n bias, but only for the very forward regions. We will
first detail some of the causes of these mismeasurements. Then we will suggest
various 'jet calibration' schemes for correcting the reconstructed ET. Since there are
always differences between the behavior of a computer simulation and the real
detector, we will discuss especially calibration methods that use as little simulation
specific knowledge as possible. Such a scheme would be ideal for jet calibration in
the first few months of D0 datataking.

Causes of reconstruction ET mismeasurement in the
reconstruction

1) WWW Particles may deposit energy
in the azimuthal cracks between the modules, the area between cryostats or other
uninstrumented regions where there is no 'live' calorimetry to measure the energy
deposit. Also, particles that are produced too far forward may miss the calorimeter
altogether or deposit energy in the central detector. Although not included in our
calorimeter simulation, the real calorimeters have many other dead areas such as
notches in the signal boards and absorber plates and spacers which keep the cell
spacing regular.

2) eaLThe calorimeter does not respond to electrons and photons in the same
way as it responds to pions and other hadrons. This effect is often referred to as the
e/n ratio. This number is determined by injecting pions and electrons of the same
energy separately into a region of the calorimeter and measuring the response. This

66

67

was done in the D0 Testbearn using Fermilab's fixed target beam. The e/rt is the ratio
of the electron response to the pion response. This is done for several different
energies and an e/n curve can then be produced. Figure 8-1 shows such a curve as
determined from monoenergetic electrons and pions that are evaluated by the detector
simulation. Typically the e/n ratio is greater than 1. This implies that the detector
has a greater response to electrons than to pions. Since it is very difficult to identify
the type of particles captured in the detector, such curves are more useful when one
assumes that photons will respond as electrons do, and that hadrons respond
approximately the way pions do. e/n is important when measuring jets as jets can be
either be very hadronic or very electromagnetic; on the average 33% of the jets
energy enters the calorimeter as photons. Note that knowing the e/n is not direCtly
applicable for calibration unless you can determine whether the energy in each cell
was deposited by a electron/photon or a pion/hadron.

eln for single particles

     
  
 
   
      

 

 

 

 

 

135 _ Itrlrrrrlrrrrlrr
E —0—Eta=.3
l3 :-\ —°-Eta=.6
: -e-Eta=l.6
_g "25 E'\ --*--Eta=2.l
.3- 1'2 :70 ”+Eta=2.7
3. :
“5 1.15 :—
5 -
o :
1.1 :-
1.05 3.
I:41]llllLlllllLlLllllllll-1111
O 10 20 3O 4O 50 60

Particle Energy

Figure 8-1: e/rt as a function of particle energy and detector 11

3) mm The calorimeter responds differently to identical particles at
different energies.1 This is particularly a problem since jets are made of a variety of
particles at various energies. Consider figure 8-2 which plots the fraction of total jet
energy carried as a function of the fractional jet energy of the particles that carry it. It

68

is easier to interpret figure 8-2 if an example is given. The value of the first bin is .35.
The first bin has a width of .05 and holds values from 0.0 to 0.05. The interpretation
is that, on the average, 35% of a jets energy is carried by particles that have less than
5% of the total jet energy. This information is taken from the ISAJET event simulator
and hence may be biased to the fragmentation scheme it uses. The first two bins
contain almost 56% of the total jet energy hence we say: on the average, 50% of the
jets energy is canied by particles with less than 10% of the t0tal jet energy. Figure 8-
3 shows the distribution of the first bin. We can see that some jets have as much as
80% of their energy carried by particles with less than 5% of the total jet energy. This
idea is extremely important in jet calibration as one naively might try to treat a 200
GeV jet like a 200 GeV particle. Instead, figure 8-2 implies that it is more accurately
described by many 5 GeV particles and a few energetic ones. If the calorimeter
response is exactly linear, then the energy distribution of the particles within a jet
does not matter. Figures 8-4 and 8-5 show the fractional responses R(E), R(ET) for
simulated single electrons and pions injected into the calorimeter at various angular
regions but scattered over all 0. It is important to understand how this was done. As
single particle events were used and there was no noise in the simulation, all of the
energy deposit was due to the electron or pion. Thus all the energy was added up and
attributed to the single particle. The figures show consistently better response for
higher energies. In order to calibrate, we would ideally like to determine R(ET), for
example and multiply l/R(ET) by Etreconstructed to determine the 'real' jet transverse

energy. A non-linear curve implies that one must first group the energy that was
deposited by each particle and then correct using the appropriate R(E) value.

R(E) For Single Electrons

)for sl lee

    

0 95 0.95

0.9 0.9

“(H
R(fl)

-o—Eta- 3
+Eta-6

08$ +Eta-l .S

+Eta-2.1
+Eta-26

 

0,6
0 I 0 20 30 40 SO 60 0 l 0 20 30 40 SO 60
Homer Frergy Flertrcr- Frergy

0.8

Figure 8—4: R(E) and R(ET) for single electrons as a function of electron
energy and detector psuedorapidity.

 

69

R(E) For Single Plans

R(Et) for single p1

      

1 105
095 1
09 095
; 065 a mg 5 09
‘ 08 +Eta-6 I
—o—Eta-1s 085 *5‘3'3
075 . -e-Eta-2.1 oe +Eta'6
' +Eta-26 —o—Era-1 s
07 075 +Eta-21
+Eta-26
065 07
0 10 20 30 40 so so 0 10 20 30 40 so so

Dur‘r Margy Our Frorgy

Figure 8-5: R(E) and R(Et) for single pions at various energy and
psuedorapidity

70

 

 

Jets with Energy from 200 to 300 Gev

 

I

Carried

 

.0
(.1
UI

9y

0.3

.0
N
on

Fraction of Jet Ener

 

 

0.2

0.15

 

 

0.1

 

 

 

0.05

 

 

 

IIII'IIIITTIIIIIIIIIIIIIIIIIT'IIFI

 

 

 

o 1 1 1 1 l 1 1 1 L —I‘=[_1—l1 [—1l—l-l 1 L l 1 1 1 1 I 1
0.4 0.6 0.8 1

Particle Energy F ractian

 

o
.o
N

Particle E(f) dist

Figure 8-2 shows (for example) that, an the average, 35% of a Jets
Energy is comprised of particles that each carry less than 5% of the
total jet energy.

 

 

71

 

 

Jets with Energy from 200 to 300 Gev

 

N
O

 

.“
on
1

Frequency

 

 

 

 

 

,5- T

 

12.5 '-

 

10-

7.5 1-

 

 

 

 

2.5 -

1- I
o l L 1 1 1 L L l l L I 1 l L L l

O 0.2 0.4 0.6 0.8 1
' Energy Fraction carriedaby particles with <5% of Total Jet Energy
1n

 

 

 

 

 

l l l

 

Figure 8-3 shows (for example) that particles with <57. of the Jet
Energy often comprise >402 and sometimes as much as 80% of the total.

 

 

72

4) W As discussed in the section on the theoretical
definition of a jet, the cone algorithm is used to define the energy of a jet. This cone
is meant to be applied to the final state partons of the event. Since the calculation
does not include the fragmentation of the partons, the loss of energy due to particles
leaving the cone is not included. Experimentalists have traditionally attempted to
correct both for this effeCt and the compensating effect of particles entering the cone
from other jets or from the beam jets. We refer to these type of effects as "Out of
cone" gains or losses. Nominally, we have removed this effect in our studies of jet
reconstruction by comparing the reconstructed jet to a generated jet which is formed
from the final state particles instead of the final state partons. However, particles
within the cone start to shower and the size of the shower can be wide. Thus particles
near the edge of the cone may deposit energy outside of the cone. Our reconstruction
algorithm compensates to some degree by clustering groups of energy and using the
center of such clusters to decide whether inclusion into the jet cone is necessary. If
there were an effect due to energy spilling out of the cone, (see figure 8-7), it might
show up first in the forward regions where the lines of constant rapidity grow close
together. Figures 8-4 and 8-5 show no such effect for single particles because they
were made using all the energy in the event and no cone was applied. As discussed in
chapter 6, the cone size needed to contain 95% of a 50 GeV pion seen at the D0 test
beam would be R=.2 in the central region but would be R=.7 in the forward region.
The simulated single particles show this type of behavior as well. Figure 8-20 shows
the difference in response for 50 GeV and 2 GeV pions in the case where all the
energy in the detector is used versus the case where only the energy within a cone of
R=.7 is used. The former is from the curves in figure 8-5. We see that 50 GeV pions
have nearly all of the detectable energy contained in a cone of R=.7 except in the very
forward regions where 1-2% of the energy is lost outside the cone. The 2 GeV curve
shows a 3% loss even in the central region and this becomes 11% in the very forward
region. We expect the same effect for jets and indeed, figure 7—2 shows a strong drop
in response for n>3.0. We might expect that jet response would be dependent on the
cone size used. Figure 8-6 shows the average R(E) versus 11 for 50 GeV ET jets with
various cane sizes. (The generated jet cane size and the reconstructed jet cone size
are kept the same.) One can see that for a cone size of .9, the R(E) curve behaves
better in the forward region as the single particle curves might predict. But smaller
cone sizes drop in response by as much as 15% compared to the central region even
when they are far from the beam pipe.

 

73

It seems clear that out of cone losses will be very important in jet
reconstruction in the forward regions and with small cone sizes.

 

   
   
 

—°— 2 Gev no cone
—0 - 2 Gev R=.7

- 0 - ‘50 GeV no cone
"*“SO Gev R=.7

 

 

R(E)

11111111111111141111111111111]llll

 

0.65 ll "04"”: llllLuiiiliill
0 0.5 1 1.5 2 2,5

Detector eta

 

(A

Figure 8-20: The response of pions is shown both with a cone of R-.7 and
with no cone (all energy found is used).

74

 

 

R(E)

0.96

0.92

0.88

0.84

0.8

0.76

0.72

R(E) versus 77 for different cone sizes

 

IIIIIIIITITITII

-.-fl-o-

3......1----l‘ """ 1 .......... , ........
1:... ..'..:..-—i—_“_ ' ' “l T '
................. ‘ f '
R=.5 I

.......

 

 

 

 

 

llLlLlllllllllllllllllllllllLlllllLL4

 

-J -2 -1 0 1 2 3 4
Generated ..’7 of jet

Figure 8- 6. Dependence of R(E) with cone size. The dependence is minimal
in the central region but large in the forward regions

 

 

 

 

75

Note

There iS also a bias away from the beam line for 11 reconstruction in the
forward regions as discussed in chapter 7. This may also be due to the finite width of
the particle showers. Indeed, this effect has been seen with single pions in the Monte
Carloz. We can understand this as follows: if a particle, moving along a line of
constant angle from the beam line, showers symmetrically in a circular region around
its original direction, more of the area is contained above that angle than below. See
figure28-7.

 
 
  

Particle Shower

 

0

Figure 8-7: A particle showers while moving along a line of constant angle with
respect to the beam line. If it does so symmetrically, more energy will be
deposited away from the beam line than towards it.

5) Zero suppression.

Noise in the calorimeter results in energy being seen in nearly all
channels even though only a few may actually have had energy deposited by particles.
This causes the readout and transfer of large amounts of uninteresting information to
the data storage media. To combat this, channels can be forced to zero when they are
below some threshold and zero energy channels are not included in the data that is
transferred. This is referred to as zero suppression. There was no noise in the
calorimeter simulations and no zero suppression used in the jet calibration studies.
However, there was a .10 GeV per readout cell zero suppression that was applied to

 

76

the high statistics event sample which we used to reconstruct the inclusive jet cross
section, thus a correction was made and this is discussed in the Results chapter.

Calibration Methods

Calibration of the D0 detector is an enormously large and complicated task
and we will not discuss the general problem here. Even the subtopic of a relative jet
calibration, is complex enough that all the factors involved and schemes envisioned
cannot be included here. We will discuss two approaches and three techniques in
particular. The third technique is used to reconstruct the inclusive jet cross section in
a later chapter.

There are two general approaches to calibrating jets at D0. The first uses the
results of the D0 test beam, which involved the injection of monoenergetic pions and
electrons into sample D0 modules which had been arranged in a manner similar to
that in the real detector. Thus, in addition to directly measuring the response of D0
detector elements to single particles, the dependence of this response on geometry
was also measured. Three separate runs injected particles into configurations of
modules that modeled a) the middle of the central calorimeter, b) the endcap regions
and c) the crack region between the central and end calorimeters. The drawbacks are
that the system is still not exactly that of the D0 detector and there is no way to
directly measure jet response as jets could not be produced at the test beam facility.

The second type of calibration scheme involves use of the detector itself using
real data. This scheme proposes the calibration of the electromagnetic portion of the
calorimeter using the decay of particles with known masses such as the n0 or the JP? .
After the electromagnetic section is calibrated, one can then look for events in which
one jet is electromagnetic and the other decays hadronically. The hadronic section is
thus calibrated using these events by requiring ET balancing. This technique is
expected to only be useful in the central areas of the calorimeter. Once this is done,
one could then use 2 jet events in which one jet is central and the other forward to
calibrate the rest of the detector. 3 The basic drawback is that these methods require a
few months of running before they can be applied and the calibration determined.
Needless to say, jet calibration will be an ongoing, evolving process that will use
elements of both types. In both cases, the computer simulations will be used to make
predictions that can be verified directly. But the simulations will be tuned and
retuned to agree with what is measured.

 

77

We will confine ourself to methods that can be used at the start of data taking
and that make maximum use of test beam results. Thus we assume that we will have
access to curves similar to 8-4 and 8-5. We further assume that results that we obtain
using the simulation results of 8-4 and 8-5 which are then applied to the simulation,
might be equally as good if we took the test beam results and applied them to the real
detector.

To verify that energy loss is derived from the causes we expect, we use a
technique that we will exploit time and time again. Reconstructed jets are compared
with the generated jets which are calculated using the PJET particle method and
identical cone sizes. Thus the problem of comparing the generated to reconstructed
energy is basically a calibration issue. The jet energy is just the sum of the particles
within the jet. We can obtain this from the generator:

50m... = 25, (8.1)

all particles in jet

We look at each of the particles that made up the generated jet, and for each
one, we can associate a response from the single pion and single electron response
curves in figures 8-4 and 8-5. The jet response is then the sum of these terms. We
assume that the particles respond according to the curves and add them all up. Thus
we end up with a prediction for the reconstructed jet energy. Thus we can predict
R(E) for jets:

R(E),"med = E—L— 2[EiR(Ei, ni,idi)] (8.2)

Geneated all particles in jet

Where id equals 'electron' if the particle is an electron or a photon and id = 'pion'
otherwise. This tells us which curve to use. We can then calibrate the reconstructed
jets using this predicted value of R(E). If jet energy loss is truly due completely to the
response of single particles, this method should calibrate fairly well. Figures 8-8
describe the percentage energy loss before we calibrate. An average energy loss of
about 15-20% is shown. Figures 8-9 shows the same quantity after calibration. The
calibration removes the energy loss to within 2% except for n>2. which suffers from
out of cone showering effects which we have not yet tried to correct. Although this
method seems to move the response to 1, it is not useful for real calibration as D0 can
not determine the momentum and energy type of every particle that entered the
detector. Even if the energy information could be extracted, the id would remain
unknown. Some experiments operate under the assumption that jets behave as if they
were composed entirely of pions. Figures 8-10 show the results of the calibration

78

when only the pion curves are used. This results in an over-calibration of
approximately 3-4%. This is because the calorimeter responds worse to pions than
electrons and hence we overcompensate if we assume the jet is entirely composed of
pions. Jets are 33% electromagnetic on the average.

Before we discuss complicated calibration schemes , we should at least verify
that the simple does not work. The most naive method of calibration would be to
assume that a jet of a particular energy acts like a single pion of the same energy and
hence responds as shown in figure 8-5. Figure 8-12 show the disappointing results.
Simply treating the jet like an energetic particle improves matters only 4% leaving a
10% loss. We therefore try harder. The following three methods were tried. All of
them try to correct the jet based on some estimate of type and energy of the particles
that make up the jet.

 

79

 

 

R(E) for Uncalibrated Jets generated in 160-240 Et Bin
1

 

 

R(E)

 

 

 

 

 

 

 

 

- Q _
- m ..
r ..
0.96 - 0.96 -
0.92 - 0.92 -
0.88 - + 0.88 .. +
Z+++++++++ 1L 1 3 ere-*4—
0.84 — + 0.84 — +
0.8 1— 0.8 -
0.76 — 0.76
ll 1 l l l l l l l l l 1 l I l I I; l l l l l l l
100 200 300 400 -4 —2 0 2 4
Generated Jet Energy Generated Jet 11

Figure 8-82R(E) distributions for uncalibrated jets. Typically only 85%
of the generated energy is seen by the reconstruction.

 

 

80

 

 

c—b
c—l
N

R(E)

1.08

1 .04

0.96

0.92

0.88

R(E) for Single Particle Calibrated Jets (160—240 Et Bin)

 

+ ++ +
+++ ++ ‘1
1 ++

rIIIIlIIIIIIIIF'IIII'IIIjIIIII

 

 

llllllllllllllLll

1 00 200 300 400
Generated Jet Energy

 

€1.12
c:

1.08

1 .04

0.96

0.92

0.88

 

 

[IIIrlITII'IIIIIIIII'IIII'IIII

 

 

+

1 1 1

 

 

l
.1.

2 4
Generated Jet 71

Figure 8-91R(E) after calibration using kriowledge of the energy and type
of the particles that make up each jet.

 

 

 

81

 

 

R(E) for Single Particle Calibrated Jets (160-240 Et Bin)

 

 

R(E)

 

 

 

 

 

 

1 12 €1.12 -
1- (r -
- r
1.08 - 1.08 -
r h-
1. l' —+—
1.04 - + 1.04 — —1—
. + + .
- +++ +++ + l - —1— -1—
l '— 1 r—
- 1 . 1—
. - +
L p
. l.
0.96 — 0.96 L-
. L
0.92 - 0.92 -
0'88 T1 1 LL 1 1 1 1 l 1 1 1 1 I 1 1 1 1 0'88 -[ L l 1 l 1 JL 1
100 200 300 400 -4 -2 O 2 4
Generated Jet Energy Generated Jet 11

Figure 8-102R(E) after calibration using knowledge of the energy but
with the assumption that all particles behave as pions.

 

 

82

 

 

R(E) for Simple Slope Calibrated Jets (160-240 Et Bin)

 

 

 

Q Q
1: : a:
1 .08 - 1 .08
1-
1 .04 - 1.04
1 - 1
0.96 - 0.96
0.92 - - 0.92
3 +++ ++Jr 1+ "
0.88 _ 0.88
’- l l l l L l L L l 1 l I l 1 l l l l

 

 

 

1 00 200 300 400
enerated Jet Energy

 

IIIIIIjTIIlIIIIlfiIrI'IIITTIT

 

:14

+

+ —1—

l

-+——1—

 

 

 

 

—4

-2

l L l l L
0 2 4

Generated Jet 11

Figure 8-12IR(E§ after calibration using the slope of the pion response
curve. This method still leaves a 10% jet energy loss.

 

 

 

 

 

83

Method 1: Particle Tracking

One method that was developed entailed using the tracking chambers to
identify the energies of particles within the jet. Clusters of energy were matched with
central detector tracks. If the energy cluster could not be matched it was shared with
adjacent clusters if possible, if it was isolated, it was assumed to be a neutral particle
and a 'pseudo' track was created and pointed towards that cluster. See figure 8-11.
The solid lines represent charged tracks while the dashed lines represent 'pseudo
tracks'.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 8-11: Example of how the Particle Tracking Method for Jet Calibration is
done. The tracker supplies trajectories of charged tracks that are associated with
clusters of energy in the calorimeter. If a cluster has no track match, it is assumed
to come from a neutral particle and a 'pseudo' track is created.

The charged tracks were provided by the event generator in this analysis instead of
the central detector. A further decision had to be made in the case that more than one
track pointed to the same energy cluster. In one case the energy was shared among
tracks which indicated particles with equal energies. In the other case the energy was
assumed to belong to only one particle. In both cases, it was assumed that 1/3 of the

84

jet was electromagnetic by using as the response: two thirds of the pion response
added to one third of the electron response for each energy and pseudo-rapidity point
used. Figures 8-13 and 8-14 show the results of these calibrations. Central jets are
calibrated to within 4% although the forward jets will still exhibit losses due to out of
cone showering. The two differ by only 2% at most and give us a way to calibrate on
an event by event basis. Unfortunately, it requires full track reconstruction and
assumes that energy deposits by single particles are reasonably localized. The
addition of noise will further complicate matters. It is also not clear whether the
method is actually identifying particles within the jet or is simply breaking down the

jet in some random way and hence allowing a calibration that moves in the correct
direction. This method was not developed further.

 

85

 

 

—.
-.
N

R(E)

1.08

1.04

0.96

0.92

0.88

Figure 8-132R(E§

R(E) for Track Cluster Calibrated Jets (160-240 Et Bin)

 

IIIIIrIlIrIfilerII

+ ++

l+~l+ +++++
+

 

TIrTrIIIIIfI

 

 

T

llllLlLllll_LLLllll

 

@112
C!

1.08

1.04

0.96

0.92

0.88

1 00 200 300 400

enerated Jet Energy . . .
after cal1brat1on us1ng the track1ng method assummg

 

 

 

 

 

 

L

1.

p

F —1—-—’—

L- I + —1—

I I

L

r

—| l l L l l I I

-4 -2 o 2 4

Generated Jet 17

one particle contains all the energy of the cluster.

 

 

 

86

 

 

 

 

_a
N

R(E)

1.08

1.04

0.96

0.92

0.88

R(E) for Track Cluster Calibrated Jets (160—240 Et Bin)

 

 

 

 

 

 

 

 

 

 

e sz _-

1- Q! t-

1- 1.

_ 1.08 -

- 1.04 -

1— 1 .—

i- + -

3+ 111$ + 1+ in 3 1
+ + - |+

L + - _l.

- 0.92 -

_111l111111111l1111 0'88 L-|1 1 LL 1 L 1
100 200 300 400 —4 -2 0 2 4

enerated Jet Energy -‘ Generated Jet 17

Figure 8-14IR(E§ after calibration using the tracking method assuming
particles share equally the energy of the cluster.

 

 

87

Method 2: Calibration as a function of Jet Characteristic

Another method is to base calibration on some jet quantity that is
characteristic of the type of particles within the jet For example, electromagnetic
particles respond better than hadronic particles, thus a calibration number could be
assigned on the basis of electromagnetic fraction. Also, jets that are very broad tend
to be contain softer particles, so jet width could also be a quantity to use for
calibration. Figure 8-15 relates the calibration ratio (R(E)) versus the electromagnetic
fraction and the jet width of both the reconstructed jet and‘the generated jet.

Let us first consider the electromagnetic fraction plot. It is produced by first
looking at each generated-reconstructed jet match. This allows us to determine the
R(E) for this pair. We can then determine the electromagnetic fraction of the
generated jet by looking at the particles that make up the jet and taking that fraction of
the jet's energy that is carried by photons or electrons. This is the electromagnetic
fraction of the generated jet. The solid line is for these points and shows that jets that
have energetic photons/electrons have a distinctively better energy response (by
almost 12%) than for totally hadronic jets. The electromagnetic fraction for
reconstructed jets is defined similarly but is based on which sections of the
calorimeter the jet deposits energy. The dotted curve displays the average value of
R(E) for reconstructed jets versus energy fraction. This curve varies only by about
5%. The difference between the curves comes from the fact that the amount of
energy deposited in the electromagnetic sections of the calorimeters is not a good
indicator of whether the particles were electromagnetic in nature. Hadrons frequently
deposit large amounts of energy in the electromagnetic section just as photons and
electrons deposit small fractions in the hadronic layers.

The second plot made in a similar way, but this time versus the width of the
generated and reconstructed jet. Jet width in the case of the generated jetis defined
by equation 6.1 while the reconstructed jet width is the second moment of ET
distribution of the jet in 1H) space. We see‘that thin jets (small jet widths) respond
better than broad jets. Additionally, the reconstructed jet width seems to be
comparable with that of the generated in the sense that generated jets of a particular
jet width have a similar response to reconstructed jets of the same width. Jet width
may be an important quantity to consider in calibrating jets. This method was not
developed further however.

88

 

 

1

R(E)

0.96

0.92

0.88

0.84

0.8

0.76

R(E) versus Jet Characteristics for Central 40 Gev Et Jets

 

 

 

 

 

 

 

 

1—

P

1—- ‘0‘
" -l-
He: +

1 +1 .-

E « +
++ 5
i +£-

": ++ .

1+ +1-

-: +

+

ELL 1 1 1 l 1 L 1 L1 1 1 1 1 l l 1 LL
0 0.25 0.5 0.75 1

Generated Jet Et Em Fraction

R(E)

1

0.8

0.6

0.4

0.2

0

 

 

 

 

 

F
11"

L. +‘

1- ~4-

1-. +

+

"t ++

: +<|-....

r

’1 1 l l l l l 1 1 l I l l l I l 1 1 l
O 0.25 0.5 0.75 1

Generated Jet RMS Width

Figure 8—152R(E) versus Jet Em fraction and Jet Width. The solid lines
are for the generated jet and the dotted is for the reconstructed.

 

 

89

Method 3: Assumed Fragmentation of Jet

If we assume that we can understand the behavior of single particles in the
detector from the test beam results, we only need to understand how particles are
distributed in a jet to be able to predict its response. This was discussed above and
seems to be true for jets with n<2. when a cone of at least R=.7 is used. To do this,
one must use a generator like ISAJET or HERWIG to model the particle structure of
the jet. This may leave the calibration sensitive to which model is used. We can
proceed if either we believe that one particular model is reasonably accurate in
predicting the particle structure of a jet or if we believe that the predictions are
relatively insensitive to which model is used. We can combine the two statements if
we test the jet response predictions on several models including one which seems to
compare favorably to measurements of jet fragmentation. HERWIG is such a
generator.4 Figure 8-17 shows the distribution of the predicted response R(E) for
various event generators for 50 GeV Et jets generated at n = 0. Note that width of the
distribution is only 2%. This is considerably smaller than the width of the R(E)
determined from the simulation which is about 10%. Presumably this is because the
width is dominated by energy resolution and perhaps out of cone fluctuations.

 

—6— Predicted ISAJET
—a— Pred. HERWIG
+ Pred Pythla

1": —-x— ISAJET

; —9— HERWIG

:fl—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a,
t“ 0.9: q
8 . 1 \
O 1. -1
Ln 1- .1
E 0.85 _ ~ . j
an f
0.75 ' 1 . ‘
-l O l 2 3 4

letn

Figure 8-16: R(E) for 50 GeV ET jets at various detector '11. Curves are both
predicted and measured for various simulations. Error bars are shown only for
predicted values

 

We»

90

Note also, that the different fragmentations agree to within 2%. Figure 8—16 shows
this predicted R(E) for jets at fixed ET at various rapidity pointS- Each data point
consists of at least 500 points leading to error bars well within 1%. The simulated
values of R(E) have also been plotted. Note that all the points agree within 3%. We
conclude that although we do not know which fragmentation model to use, it may be
that the fragmentation does not matter to the 3% level. This is certainly a function of
the non-linearity of our detector but given a set of non-linear response curves (as we
have assumed here) we can predict this difference. Figure 8- 18 shows both predicted
R(E) and the Monte Carlo R(E) from a sample of generated jets with ET between 40
and 60 GeV. The agreement starts at about 2% and slowly gets worse until an n of
2.5 where the calculated response turns over and drops quickly. Figure 8-19 shows
similar results for R(ET) done in a similar way. As mentioned above, this is the
region where the finite shower width of the jet starts to spread out of the cone. The
out of cone issue will be addressed partially later.

Summarizing, this method calibrates jets in the central calorimeter at the 4%
level using only knowledge of the behavior of single particle pions and electrons at 6
different energies and at 5 different pseudorapidity positions in the calorimeter. Since
such measurements have been made with real pions and electrons and real modules at
the D0 test beam, this calibration method could be very useful as a starting jet
calibration upon collider start up and the beginning of data taking at D0 this year.
This technique is being currently implemented.

 

 

91

 

 

Frequency

Frequency

70
60
50
40
30

N
O

10

100

80

60

40

20

0

Predicted Fractional Energy Loss ( 1—R(E) )

 

 

 

IE 5.3!. m

 

 

 

 

 

1 l L L I 1 L L 1 1

b
D
b

1 LL 1 i l 1 0

 

 

o IIII'IIIIFIII'IIIIIIIII'IIIIIIIIIII

03
O
o IIIIIIIIIIIIIIIIIIIITITITIII]IIII'IIII

0.1 0.2
Fractional Energy Loss - HERWIG

0.1 0.2
Fractional Energy Loss - ISAJET

 

 

[E W

 

1 1 L L L4 L I L

 

 

oIIII'IIII'IIII'IIII'IIII

0.1 0.2
Fractional Energy Loss - PYTHIA - -

Figure 8-172Predicted fractional jet ener y loss for various generators
for 50 Gev Et jets at 17:0.0 This is 1—R(E?.

 

 

92

 

 

R(E)

0.96

0.92

0.88

0.84

.0
or

0.76

Figure 8—181Predicted and reconstructed R(E) for 50 GeV jets.

R(E) for 50 Gev Et jets from the ISAJET 40-80 Et bin

 

Predicted +++

.......

 

_—

 

 

 

 

LllllllLLlL'LLJlll1111111111111111Llllll

0.5 1 1.5 2 2.5 3 3.5 4
Generated Jet 17

 

oIIIITI

The discrepency in the forward regions implies additional
sources of energy loss (e.g. out of cone showering).

 

 

 

 

 

93

 

 

R(Et)

!|IfirIIlIIIITIIITTIjII

0.96

0.92

0.88

0.84

0.8

0.76

Figure 8-192Predicted and reconstructed R(Et) for 50 GeV jet
The discrepency in the forward regions implies additional
sources of energy loss (e.g. out of cone showering).

R(E) for 50 Gev E, jets from the ISAJET 40-80 Et bin

 

Predicted

 

no.
can'oae
U

+
++ + ._

—

 

 

 

++ Reconstructed
:4 ............. + ... I ... + +
llLllllLllLLlll111111111141111111111111
O 0.5 1 1.5 2 2.5 .3 3.5 4

Generated Jet 11

 

 

94

 

18.]. Durston, Presented at the DO McPhysics II Conference D0 Note 1202 (1991)
Energy Calibration and Systematics

_ 2N. Amos, P. Draper and S. J. Durston, Eta-Dependent Efiects Due to Shower Size,
D0 Note 1162. D0 Experiment at Fermilab, Batavia, IL. July, 1991.

3Current proposal by G. Blazey, G. Forden et al.

4CDF Collaboration, Measurement of QCD Jet Broadening in p-pbar Collisions at
1.8 TeV, FERMILAB-PUB-91/23-E (submitted to Phys. Rev. D. 1991)

 

 

 

Chapter 9: Triggering on Jets at D0

Protons and antiprotons circulate around the collider in 6 bunches each. At
current design specifications, bunches cross at the DO interaction point once every
3.5x10'6 seconds. The cross section for an inelastic (the protpn or antiproton
breakup) collision is about 50 millibams. At the expected startup luminosity of
5x1030 cm'zseC'l, this implies a crossing rate of about 250,000 events per second
with an average of at least one inelastic collision per crossing and a significant
occurance of multiple interactions in a crossing. The rate at which events can be
written to tape is expected to be on the order of l per second. The job of choosing 1
event out of 250,000 belongs to the D0 Trigger system. We will overview the trigger
system and then refocus on their roles in jet selection.

The D0 trigger system primarily consists of 2 levels. The first level is a
hardware trigger that consists of an electronic framework which accepts input from
any one of four hardware trigger subsystems:

Level 0: The Level 0 trigger consists of two sets of scintillators on either side

of the interaction point. This purpose of these scintillators is to detect a

charged particles from an interaction, supply the location of the interaction

and determine if more than one interaction took place.

TRD: The TRD trigger system can trigger on the presence of charged,

relativistic particles (electrons!) that move throughout the transitional

radiation detector.

Level 1 calorimeter trigger: This trigger constructs quick sums of

calorimeter cells and constructs quantities that can be used for triggering

purposes.

95

96

Muon trigger: The Muon Trigger is able to detect events in which hits in the
muon system are aligned in such a way that they might point to the nominal
interaction point.

There are 256 trigger terms that represent various settings of these 4 trigger
subsystems and the Level 1 trigger framework allows the definition of 32 triggers
which are made up of any combination of these terms. If any of these 32 trigger
conditions are satisfied, than the event is given to the second level (Level 2) of the
trigger system for the final decision on whether the event will be accepted or not. The
rate into this second level should be reduced to at least 200 hz by this time. Figure 9-
1 is a diagram of the D0 trigger system. Upon a Level 1 trigger, the framework
causes the readout and digitizing of a set of detector ADC crates which were
associated with that specific trigger. Special processors sequence this data and
transfer it along one of 8 data cables. The event is sent to one of 50 microvax 4000
model 60's. Each one is approximately a 16 (VuP) MiP machine. Before processing
occurs, the event is built in a format that is identical to that which is used in offline
analysis. At this level, the event can be reconstructed using FORTRAN routinesl
which are similar in function to those used offline. A complicated set of parameter
sets for each routine decides whether the event is to be written to tape. These routines
give answers to yes/no type questions such as "Were there 3 jets found with at least
20 GeV in ET?" or "Was an electron found?". A Level 2 trigger requirement is often
referred to as a script and consists of a series of calls to these routines. It requires a
'yes' to all the questions asked in order to 'pass' the script. A total of 128 such scripts
may exist. We will review the trigger system in more detail, this time concentrating
on jet triggering.

 

 

 

Eaum>m cowuwmwzaa< «use can gawauue an “HIm ahsuwm

 

 

 

 

my}

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:u...m>m zoEw500< <20 m5
oz< $00.5. muEziofio
mzh .5 25830 x005

 

 

 

 

 

 

, , on... g
a... In“...
H53 5:... 5:383.

 

 

v w_ _mo:
ggo~§uggtgm§
Epic
6&on
«89%
LL 93 BE
EEBUB
gun»? .538... 985... as -
< mug E:
g“
as: _gmuaa ,
7 . 8389: 2:8 55..
Q was 98 #3.. 9.8 3.3 as
’85 g E 18.8
i
rates... .33.”. an
mpg aura 28555.3 598‘
music

 

 

 

 

 

 

 

 

 

 

u mucus:

_ _1 h? 1T «2an
mmuozgoum 8.8338 9:
ukwfis _sao :3 _1 523$

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- . g N
g E p- .

 

‘ su>us , . -
1 BE 1395 _ Shoes
as. as .8.... as a... . 855... 8. 8% ma: _oEN as:

 

 

 

 

 

 

«3th _ «29:3

20::

 

 

 

428..

 

 

 

 

1 L

 

 

Ill

98

Level 02
The Level 0 scintillators are primarily responsible for flagging crossings in which the
two colliding baryons both fragmented although at the expected peak luminosity, this
is the rule rather than the exception. Still, the luminosity changes during the run and
the probability of inelastic collisions will change as it does. The Level 0 is to be used
in coincidence with a beam crossing signal. In some cases only one of the baryons
fragments or else it interacts with some of the nuclei in the evacuated beam tube; the
Level 0 is designed to discriminate against such events. As described above, this
trigger consists of 2 sets of scintillators located 130 cm away from the nominal
interaction point on each side. Each set is composed of different scintillators at
different transverse distances from the beam line. Since the scintillators do not reach
all the way to the beam line, beam crossings that do not result in the breakup of the
oncoming baryon do not trigger. The Level 0 trigger is set up to be sensitive to the
breakup of one of the baryons. As charged particles from the interaction move
through each scintillator set, the time of the hits are compared and a time difference
between scintillator sets is used to determine whether both scintillators were indeed
hit and whether the time difference is consistent with an interaction point within some
distance of the nominal interaction point. A slower analysis of these hits can mark the
presence of additional interactions in the event. It is planned to use these features to
obtain 'higher quality' jet events by triggering on events which have only 1 interaction
and the vertex is very close to nominal for high rate jet physics events. The Level 0
was not simulated in any of the analysis presented here. The lack of a Level 0
simulation means that we knew our luminosity exactly. Additionally, the simulation
did not incorporate multiple interaction events or events where there were soft
collisions between the protons.
Level 1 Calorimeter Trigger

We are particularly interested in events where there was a hard scattering (not
just breakup of the proton and antiproton) between colliding partons. We further
restrict our attention to those cases in which the scattering partons had significant
transverse energy. This is necessary both because our detector only covers
pseudorapidity down to 4. and because scattered partons that moved along the beam
line would be hard to distinguish from the beam jets. It is the job of the Level 1
Calorimeter trigger to distinguish those events which contain jets or other objects with

large amounts of ET. We will discuss the features that are directly applicable to jets
and how they allow us to select jets of a particular ET range while rejecting those of a

 

99

smaller ET range. Appendix C discusses the stability of our results with respect to
fragmentation scheme, calorimeter resolution and noise. We expect that although the
relative results of our simulations will predict what is seen at the collider, the overall

rate scale may differ by as much as an order of magnitude.
Traditionally, hadron colliders have used triggers based on the total 131‘ of the

event to select high ET jet events. This capability exists at DO as well; indeed, DO's
extended pseudo-rapidity coverage provides it with a better than average measure of
the event ET. However, the total ET is not a good indicator of the ET of the jets
involved and our high event rate requires the use of a more specific trigger. As the
definition of jets is vague, triggering on jets is not trivial. Jets can be narrow like a
single particle, or can be broad and cover large portions of the detector. Ideally, one
would like to sum up adjoining energetic cells in hardware and hence identify the jet.
This is difficult to implement in hardware and DO has adopted a simpler approach.
The Level 1 Calorimeter trigger does a fast sum of the electromagnetic and fine
hadronic layers in each (i) and n readout tower of the calorimeter. The coarse
hadronic, massless gaps and inter-cryostat detector are excluded in this sum.
Additionally, each 2x2 group of these sums (.2x.2 in n-d) space) is combined into a
larger 'trigger tower'. There is an electromagnetic trigger tower and a total
(electromagnetic + hadronic) tower. Each sum is weighted by a number that
corresponds to the sine of the theta location of that tower using a vertex dependent
lookup table which groups the vertex into bins of 30 cm. Figure 9-2 shows the
segmentation of 11 space as seen by the Level 1 Calorimeter trigger. As each trigger
tower is .2x.2 in size, 40 trigger towers cover the region from n--4. to n-4. while 32
trigger towers cover the entire azimuth range for a total of 1280 trigger towers.

 

 

100

Trigger Towers
5 6 7

 

Figure 9-2: The n segmentation of the detector at the trigger tower level.

The Level 1 trigger uses these sums to construct such quantities as total ET,
total Ex, total By and the corresponding vector quantities as well. These quantities
can be used to make triggering decisions. However, the most important trigger for
jets is the ability of the Level 1 calorimeter to make a comparison of each of the 1280
trigger towers to a threshold. The system can be programmed to recognize when
some number of these trigger towers is above that threshold. We refer to this
threshold as the Level 1 jet ET threshold and the number requirement as the Level 1
jet count. Note that the word 'jet' here is misleading as the Level 1 has no ability at all
to identify a jet, but can only identify trigger towers whose total ET is above the Level
1 jet ET threshold. '

But jets seldom deposit all their energy into one trigger tower. Computer
simulations have shown that jets deposit on average US of their energy into the most
energetic trigger tower3. The distribution is not a delta function however; some jets
can deposit all their energy into one trigger tower while others can deposit less than
10% in the most energetic tower'.. Figure 9—3 shows the ratio of the energy contained
in the jets most energetic trigger tower to the total energy of the jet itself. This
distribution is broad. Nevertheless, it is apparent that a trigger that asks for 10 GeV in

 

101

one tower will not trigger on anything less than 10 GeV jets. However, it is not true
that it will trigger on all 10 GeV jets. The requirement that a certain amount of the
jet's energy be localized in one trigger tower is a severe one.4 Figure 9-4 shows that
simply requiring 7 GeV in a trigger tower precludes full trigger efficiency until 40
GeV or so. Another approach that can be tried is to require more than one tower
above threshold. Instead of requiring 1 tower with more than 10 GeV, one could
require 4 towers with 2.5 GeV each. In each case 10 GeV is asked for, but the latter
case is much more efficient for 10 GeV jets. But since the Level 1 has no idea
whether those trigger towers are adjacent or not, the latter requirement tends to accept
a higher rate of lower ET events. We will see that the background rate from lower ET

jet events can be very high.

 

Erriciency I

 

 

 

Require I Trigger Tower Above 7 Gev

‘2 l l l l l l

 

 

l - -

0.8 r- 4

0.6 - _

Errlclency

0.4 - ~

02-- -

 

 

O l L l l l l

0 2O 4O 60 80 100 120140
JetEt

 

Figure 9-4: Trigger Efficiency versus Jet ET for one particular Level 1 trigger
setting. At least one trigger tower whose total ET is above 7 GeV is required.

 

102

 

 

Frequency

Ratio of Jet Trigger quanity to Jet Et for 50 Gev Et Jets

 

W W
lg mate

U
N
O

280

240

200

 

160

 

120

80

 

40

IIIIIIIIIlTiII'I'll'jllITlWIIIIIITIIIIW'I

 

 

 

o l l l l l I I l 1 l l l l l l
O 0.25 0.5 0.75 1
0) Maximum Trigger Tower Et/Jet Et

 

 

@250 To: mm
c I 7'

 

200

 

160

120

 

80

40

I‘IjTTTIUIIIIIIIFITIITIII'lUrTlTIrT

 

 

l llllllllllllll

O 0.25 0.5 0.75 1
b) Maximum Super Tower Et/Jet Et

i-
p-

 

0

Figure 9-32Ratio of Jet Trigger Ouanity to'Jet Et. Trigger towers seem
to contain about 39% of the Jet Et while Super Towers contain 64%.

 

 

 

103

As the jet ET spectrum falls as ET to the ~-6th power, a trigger which was
efficient for 30 GeV jets would rarely see an event which had a 80 GeV jet present.
We plan to obtain samples of different portions of the spectrum by defining triggers
that target separate jet ET ranges and prescaling them so that we receive
approximately the same number of events from each. Figure 9-5 shows the triggering
efficiency as a function of jet ET for various trigger settings: 1 trigger tower > 3 GeV,
1 trigger tower >7 GeV and 2 towers >7 GeV. We can see that they become fully
efficient for 25, 45 and 80 GeV respectively. We require full efficiency to eliminate a
bias in the types of jets we receive in our events.

Thus we are left with the guideline that to select jets with a particular ET, we
need to set the trigger threshold at some small fraction of the jet's ET to be efficient.
Unfortunately, this allows the trigger to be flooded with events whose leading jet is
less than the target ET, Consider as an example: The QCD jet ET spectrum falls
almost as ET‘6. We wish to trigger on 40 GeV jets and decide that since a 40 GeV jet
averages 1/3 of its energy in one trigger tower, we will ask for l trigger tower with
ET greater than 10 GeV as our trigger. Thus we might get 90% of that signal
according to figure 9-3. But a 20 GeV jet will deposit 10 GeV about 20% of the time
according to the same plot. Since the cross section is falling like ET'5 we expect the
signal to noise ratio for 20 GeV jets alone to be :

signal = 90% x a(E'l‘=40)
noise = 20% x a(ET=20)
a signal/noise = 4.5/(26) (assuming sigma ~ET‘6)
= 4.5/64 = .07

 

 

 

104

 

 

Efficiency for 1 trigger tower 3 Gev

Efficiency for 2 trigger towers 7 Gev

Jet Triggering Efficiency for Level 1

 

9.0.0.0
Olflmlo—e

 

9.0
#U'

I I I I I I I I I l I I I I I

25 50 75
Jet Et

 

0.8
0.6
0.4

0.2

TUI'IIIIITIIIIIIITIIIIIIII

 

 

I I I I I I I I I I I I I I I

 

25 50 75

Jet Et

 

9
on —a

.0
OI

.0
N

IIIIIIIIIIUIIU'IIIIIIIII'I

 

 

O

I I I I I I I I I I I I I I

25 50 75
Jet Et

 

Efficiency for 1 trigger tower 7 Gev
o
45

Figure 9—52The efficiency for triggering on jets under various Level 1

triggering conditions is shown.

 

 

 

 

 

 

105

Thus most of the background will come from lower ET jets that are narrower
than the ones we are triggering upon. This is the leading cause of 'jet noise' in the
trigger. But the amount of background is anticipated to be larger than implied above.
This is because we are forced to lower the trigger threshold even further due to trigger
and calorimeter imperfections. First of all, the trigger only sees energy deposited in
the electromagnetic and the fine hadronic sections. The coarse hadronic in all three
calorimeters is left out. as is the massless gap and inter-cryostat detector. This means
that jets which deposit large amounts of energy in these regions will be discriminated
against. To correct for this, the threshold must be lowered. Further, the vertex
correction used by Level 1 is coarse and thus this leads to some ET smearing. Even if
we could measure a jet energies exactly, smearing in the calculated ET would result in
pulling some jets below our cuts. On top of this, there is finite calorimeter resolution
already. The level 1 calorimeter trigger simulation included additional noise which is
expected to be present due to electronics and the decay of the uranium. All of these
factors drive the selection of the trigger tower threshold downward. At the same time,
the resulting event rate increases dramatically as shown in figure 9-6.

— -Efficency for 40 Gev Jets

 

Level 1 Output Rate

 

lOOO '-

Level I Output Rate
0
O
I
srar A69 07 J0] Kauaaujg

 

 

 

 

O 5 10 IS ' 20 25

Trigger Tower Threshold

Figure 9-6: As the trigger tower threshold increases the event rate falls but the
efficiency drops.

We have seen that in order to be efficient for events with a desired jet ET, we

must lower the trigger tower threshold with the resulting rate contamination by lower
ET jets. Table 9—1 shows a proposed set of L1 trigger settings, the jet transverse

 

 

 

106

energies they are designed to select and the resulting signal to noise ratios. These
trigger settings are fully efficient for jets at or above the target ET. Note the low
signal to noise ratio from the large fraction of lower ET jet events which are able to
satisfy these triggers due to the rapidly falling jet ET spectrum.

 

 

Target Jet ET L1 Trigger Signal Rate Total Rate signal/noise
l tower >3 120 15900 .008

40 1 tower >7 14.8 600 .025

90 2 towers >7 .36 70 .005

110 3 towers >7 .027 13 .002

155 4 towers >7 .003 3.4 .0009

 

 

 

 

 

 

 

Table 9-1: Proposed Ll triggers and rates. Note that the signal rate is a small
fraction of the total rate allowed by the trigger. The triggers are fully efficient for
jets above the target ET.

 

We would like to complete our discussion of jet triggering with Level 1 by
discussing two miscellaneous topics. The first has to do with jet efficiencies and the
second has to do with the possibility of triggering on very low ET jets.

Although we have found trigger configurations that are fully efficient on the
average, there might be certain types of jets for which we are very inefficient. One
example would be jets that are pointed towards the region where the massless gap and
Inter-Cryostat Detector are located; neither is included in the trigger ET sums. If this
happens 1% of the time, a complete inefficiency there might show up as 99%
efficiency overall. However, studies have shown that the triggers tend to be very flat
as a function of rapidity. This comes from our definition of trigger efficiency. We
define our trigger efficiency for a target jet as the number of events in which the
target jet was present and the trigger was satisfied divided by the number of events in
which the target jet was present. Note that we do not require that the target jet cause
the trigger directly. Thus we have been talking about em trigger efficiencies rather
than jet trigger efficiencies. Since other jets are always present in the event, the event
can still trigger even though the target jet was not involved. Table 9-2 shows both
types of efficiencies for various target jet ET and various level 1 trigger settings.

 

107

 

 

 

 

 

 

 

 

 

# Tower 2_5 5_10 10_15 20_25 40_45 80__85
cut

1 3GeV .19 .34 .70 .98 1.0 1.0
.006 .05 .32 .78 .97 .97
l 5 .03 .02 0.2 .76 .99 1.0
0. .006 0.1 l .64 .96 .97
l 7 .002 .06 .48 .97 l.
.0004 .03 .42 .94 .97
l 9 .02 .28 .92 l.
.01 .25 .89 .97
1 ll . .004 .14 .79 .99
.0005 .07 .55 .92

 

 

 

 

 

 

 

 

 

Table 9-2: Event versus trigger efficiencies for various jet ET bins. We show both
the efficiency for a trigger in an event which contains a jet of that ET bin (first
row) and the efficiency for a jet of that ET bin to directly cause the trigger.

Using Super Towers in Level 15

The Ferrnilab Tevatron will allow us to see jets as energetic as 400 GeV in
ET. We want to obtain a distribution on as wide a range as possible. Although
triggering on high ET jets is not normally difficult, triggering on low ET jets can be.
Noise and electronic behavior may forbid the use of trigger thresholds below or even
at the 3 GeV threshold we have suggested for 25 GeV jets. A modification to the
trigger may solve this problem: Since Level 1 calculates the total ET of the event, it
sums up the detector in large pieces. The results of these pieces are stored and might
be available for use in the trigger for the collider run. At one level of the summation,
the pieces cover an area equal to 1.6 by .8 in n-d) space. Since most cone sizes are
less than .8, such 'super towers' are guaranteed to contain more than 25-50% of any
jet. Thus instead of asking for 3 GeV in a trigger tower to get 25 GeV jets, one might
ask for 12.5 GeV in one of these super towers. The result is a similar efficiency for
the jets of interest with a reduction of rate. Figure 9-3 shows the Super Tower ET
distribution for 40 GeV jets. While normal trigger towers contain only 38% of the jet
energy, Super Towers contain almost 64%. Studies have shown that for 10 GeV jets,
super towers would result in twice the signal to noise as the single tower threshold at
3 GeV. However, the 3 GeV threshold should be more sensitive to noise and

108

unforeseen problems in the system, so the real benefit of super towers would be
realized in the case that low single tower thresholds like 3 GeV cannot be used.

Jet finding in Level 2 : L2JETS6

Up to this point in the trigger, there has been no facility to identify the entire
ET of the jet. In Level 2, however, software routines can be called which can
reconstruct the entire event. In particular, a routine named LZJETS is used to
reconstruct jets in the calorimeter. Offline routines exist which do an excellent job of
finding jets in the calorimeter; but they cannot be used in the Level 2 system as they
require large amounts of time and memory. We will give a brief description of
L2JETS, some results concerning its performance as both a trigger and a jet finder
and finally the reduction in rate we obtain by using LZJETS in addition to Level 1 jet
triggers already discussed.

The basic features of L2JETS is as follows:

1) LZJETS uses locations of the trigger towers above threshold from Level 1
as jet candidates. This means that jet efficiency is determined completely at
the level 1 level since LZIETS cannot find jets that did not cause triggers.

2) LZJETS applies a cone algorithm to form jets as is done with reconstructed
jets in the offline. The size of the cone is a parameter that is trigger
dependent. The jets are reconstructed with the following quantities calculated:
the n-tb of the jet axis, the total ET, the electromagnetic fraction and its width.
All of these quantities are thus available for triggering purposes. Only one
iteration is done to calculate these quantities. This is different than the offline
reconstruction which reapplies the cone algorithm until the calculated jet
center becomes stable.

3) The trigger tower ET's calculated by Level 1 are available in a special data
bank. Thus LZJETS can use these ET values to do its clustering. The
advantage of this is that it saves large amounts of unpacking time. The
disadvantages is that coarse hadronic and inter-cryostat information is left out.
Altemately, LZJETS can use the digitized calorimeter information. The
former mode is referred to as NO_CL2 while the latter is named CL2 mode
(named after the unpacking package that it uses.) The CL2 package is similar
to the offline unpacking, but it ignores the massless gap and inter-cryostat
detectors and is much faster.

4) No jet merging or splitting is done in LZJETS.

 

 

 

109

LZJETS is intended to provide accurate jet reconstruction while minimizing
processing time and memory. L21 ETS stores results based on prior calls so that a jet
is only reconstructed once unless the reconstruction is intended to be different
(different cone sizes for example). The program also stores its PASS/FAIL results
and will use them instead of recalculating if needed. Reconstruction results as well as
a list of parameter cuts used are stored for comparison with offline, debugging and for
use by analysis packages. The time required to reconstruct a jet is a reasonable
fraction of the total Level 2 time budget of 250 msec. The timing result for NO_CL2
compared to CL2 ,as shown in table 94, shows that the time requirements are
dominated by unpacking and that the logic is fast.

 

 

 

 

 

mode/cone=size time/jet (msec) width (msec)
CL2 cone = .5 27 +/- 1.5 9.0

CL2 cone = .7 46 +/- 2.2 14.0
NOCL2 cone = .7 5. +/- .3 1.3

 

 

 

Table 9-4 : LZJETS Timing Performance

The reconstruction quality of LZJETS is favorable compared to the full
offline. The average and standard distributions of the difference between
reconstructed n, (I) and electromagnetic fraction of the jet are as shown in table 9-5.

 

 

 

 

 

 

 

 

Offline Reco - LZJETS Mean of quantity Standard Deviation
n reconstructed .003 +/- .004 .17
0 reconstructed .001 +/- .001 .05
Em fraction -.022 +1- .001 ‘ .05

 

 

 

Table 9-5: LZJETS jet reconstruction compared to reconstruction offline

A 2% bias is evident towards lower electromagnetic fraction, but this is not
anticipated to be a problem. Also the resolution is larger than the offline
reconstructed resolution but is still sufficient to serve most trigger requirements. The

 

 

110

distribution of LZJETS Jet ET to the offline reconstructed quantity is shown in Figure
9-8 for both the NO_CL2 and the CL2 mode. While the CL2 distribution has a peak
near 1 with a width of 6%, the NO_CL2 suffers from a low side shoulder which is
caused by a 250 MeV zero suppression imposed by Level 1 and the lack of
calorimeter coarse hadronic information. The mean of the NO_CL2 distribution is
8% less than the CL2 distribution. Thus although N O_CL2 is many times faster than
CL2, the reconstruction is poorer.

The purpose of processing jets in LEVEL 2 is to further reduce the trigger rate
while maintaining efficiency. Figure 9-7 shows efficiency and rate curves obtained
by requiring LZJETS to pass the event only if the calculated Jet ET is above a
specified threshold. Plotted is total rate and target jet efficiency versus L2J ET ET
threshold for target jet ET's of 25, 45 and 90 GeV. As a prerequisite, we added the
Level 1 trigger proposed for that target jet ET in table 9-1. In all three cases, there is

 

an efficiency plateau. Thus a L2JET cut can be chosen which maintains full
efficiency while reducing the rate. Table 9-3 shows a complete set of Level 1 and
Level 2 triggers for various target jets. The signal to noise ratio has been greatly

 

 

 

 

 

improved.
"I‘farget Jet ET L1 Trigger Lfirigger Total Rate signal/noise
25 l tower >3 GeV 1 L2 jeT>20 GeV 400 .3
45 1 tower >7 1 L2 jet >30 60 .28
90 2 towers >7 1 L2jet >50 4.5 .08
110 3 towers >7 1 L2jet >80 .2 .5
155 4 towers >7 1 LZjet >115 .03 .1

 

 

 

 

 

 

 

Table 9-3: Proposed Level 1 and Level 2 triggers and rates. Note that the signal rate is
greatly improved over table 9-1 while full efficiency was maintained with the
exception of the 45 GeV target trigger which dropped to 96%.

Although Level 1 trigger settings are sensitive to factors like noise,
calorimeter resolution and the energy distribution of a jet, we expect that the Level 2
found jets will be relatively insensitive to these. effects and may perform better than
predicted. '

111

 

 

Lag Background rate Log Background rate

Log Background rate

Jet Triggering Efficiency for Level 1 and Level 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m . e
' E" 0 8 :
2 - 3 ' C
.. Q E
0 r_ a 0.4 E-
. . , . E; :
_2 rrrrlrrrrIfil )‘ OilllJLI.L'-l.lillll
o 40 80 g o 40 80
1 Trigger Tower > 3 GeV :1; 1 Trigger Tower > 3 Gev
a
(0
2 _ ‘6 : .....
_ "; 0.8 :-
m I-
0 I
0 '— 9 0.4 E-
’ - . , 5‘3 :
I I L JL L L ILL I L I .I x 0 L I I I I I I I I I I I
o 40 so g 0 40 so
1 Trigger Tower > 7 GeV It} 1 Trigger Tower > 7 GeV
m
- a a . m I. eeeeee
1 :- ' 3:1 :
0 r o E
3 O 0.4 :-
-1 E- T t
- .9 :
.-I I I I L I 4 L L I I I .I >‘ 0 '-I I I L I I I J I I I I L
0 4o 80 g o 4o 80
2 Trigger Towers > 7 GeV :§ 2 Trigger Tower > 7 GeV
LT:

Figure 9-7ZBackgraund rates and jet efficiencies under various Level 1
trigger settings as a function of L2JET Et cut

 

 

 

112

 

 

Frequency

Ratio of Level 2 Jet Et to Reconstructed Jet Et - (40—80)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.. 11" >280
400 _ m m g - m use
_ Ian on: w _ Ilene uses
_ an arm 3 _ 0.:
~ 1 3 .
350 L L: 240 -
r ..
30° T 200 -
: 1~ I
250 L C
: 160 i-
t I
200 "' l-
‘ 120 l—
: r
150 *- ’
' 1'
r b
: 80 r-
100 - C
: .0 ;
50 :- 1'
.- P
L F
Obll IIILIIII ' obI ILILIIIIIII‘IIIIIL
0 0.5 1 1.5 2 0 0.5 1 1.5 2
CL2 L2JET Et/Reconstructed Et NO CL2 L2JET Et/Reconetructed Et

Figure 9—82Ratio of Level 2 Jet to Reconstructed Jet Et for using both
calorimeter (CL2) and trigger (NO_CL2) energies for L2JET S

 

 

 

114

 

1]. Hoftun, Level 2 System Programmers Users Manual, DO Note 909, D0
Experiment at Fermilab, Batavra, IL. December 1989.

2F. N ang and R. Partridge, Level 0 Detector Layout, DO Note 998, D0 Experiment at
Fermilab, Batavia, IL, August 1990.

3M. Abolins, D. Edmunds and B. Pi 0n the Size of Hadronic Trigger Clusters, DO
Note 457, D0 Experiment at Fermilab, Batavia, IL, October 1986.

4R. Astur and H. Weerts, Level 1 Jet Trigger and Level 2 Jet Tool: Rates and
Efiiciencies. D0 Note104-4, D0 Experiment at Fermilab, Batavia, IL. November, 1990.

5R. Astur, Level 1 Calorimeter Trigger "Improvement", DO Note 1297. D0
Experiment at Fermilab, Batavia, IL. December 1991.

6R. Astur, Status Report on LZJETS, D0 Note 1227, D0 Experiment at Fermilab,
Batavia, IL. October, 1991.

 

 

Chapter 10: Results

In this chapter we present the procedure and results for reconstructing the
single jet inclusive cross section from a large sample of Monte Carlo events. The
sample used was about 100,000 events which were generated by ISAJET and
processed by the detector simulator and the reconstruction software. The ISAJET
events were required to have both partons from the original 2—> 2 interaction to have a
transverse energy between 50 and 200 GeV. This does not mean that each event had
a jet in this ET range as the partons are free to radiate quarks and gluons after this
restriction is applied. We will use the jet reconstruction cone algorithm with cone size
R- .7 and compare to a particle PJ ET distribution (modified to match the Ellis
definition as described in chapter 5). The P1 ET distribution was taken from a separate
data sample of about 50,000 generated under the same conditions as the reconstructed
sample. The resulting distributions from the reconstructed sample was scaled by the
relative number of events (approximately 1:2) before comparing to the PJET
distribution. We reconstruct three inclusive distributions versus ET and one
inclusive distribution with respect to pseudo-rapidity. The ET was binned in steps of
5 GeV and the 11 distribution was filled in bins of An - .2. The following distributions
were reconstructed: -'

 

a) 39- (integrated over all n)
dET
dza
b (n = 0.)
)dETdn

115

 

116

dza
c)1—(113 (11)
d2

 

(n= 2)

 

d) 6 (ET =57.5.)

dETdn

Figure 10-5 shows the ratios of these uncalibrated reconstructed distributions
to the corresponding input distributions. These curves would ideally be straight lines
at 1.0. But mismeasurement in jet ET have diminished the reconstruction cross
section to anywhere from 20% to 55% of the input value. Additionally, the shapes of
the distributions have changed by 20% to 35% over the range of the horizontal axis.
The following steps were taken to correct the reconstructed distribution.

 

 

Correction for incorrectly merged jets

Long after the generation and reconstruction of our high statistics sample, an
error in the reconstruction code was found which directly affects the single jet cross
section. As described in the D0 Jet Definition chapter, the reconstruction algorithm
merges two jets if the amount of energy they share is greater than a certain fraction of
the energy of the least energetic of the two. This value is normally .5, however the
error in the code caused this fraction to be set at .01. Thus, some jets were merged
unintentionally. As all merged jets are flagged, a procedure was set up to correct jets
that were wrongly merged. Wrongly merged jets tended to have abnormally large jet
widths. The reconstruction process stores results for jets with smaller cone sizes as
well as the R-.7 size which we are discussing. The correction was based on
resplitting the jets using the relative energies of the same jets which were not merged
under a smaller cone size. Figure 10-1 shows comparisons of the reconstructed ET
distribution to the distribution obtained by using the correct splitting fraction, both to
the incorrect splitting fraction case and for the 'corrected' distribution. A sample set
of events was used to make this comparison. We can see that the distribution
obtained by using a splitting fraction of .01.leads to a measured cross section that is
20-50% higher than that found when the splitting fraction is .5. This is because
smaller ET jets can be merged to form larger ET jets. When we take the sample with
the splitting fraction -.01 and use the correction procedure described above, the
resulting curve matches the correct one to within 10%.

 

117

 

 

Frequency Normalized to Correct Distribution

Correction to Sample with Incorrect Jet Splitting Parameter

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. c .
O
r z -
l- .3 :
2.4 l- ‘5 1.6 _.
r- .1' "
r 0 I
l- i” 1.4 :- __
2 L— 3 : -- "1".r—u—
: 3 I __ _f—
" "' -l- U 1'2 :— -
- S - , , 5
l- 1 .. s E ' E E
: "i. g :5 ' "3"
l + -- “F r; : '
1.2 ti |+ c 0.8 -
-. : :+ "i g :
:i ’.:.:.:. . P b _—-‘ g :
- ' L“ 0.6 —
0.8 - I
: 0.4 I. SalidZSplit=.01
04 t Solid'Split= 01 E DotZSplit=.01 Corrected
' - DatISplit-.01 Corrected 0.2 L.
o I I I I I I I I I o - I I L I I L J. I L
40 60 80 80 100 120
JetE, Jet E.

Figure 10—1 ICorrection of Sample Distribution: Sample made with Split
F raction=.01 was Corrected to Match Sample with Split Fraction = .5

 

 

 

 

118

Jet calibration for single particle response.

We first construct a set of predicted R(ET)'s using the third method described
in the jet calibration chapter. We construct an R(ET) f0! 138 in various 11 bins and
two ET bins. The n bins were .2 in size and covered n-O to n-4. (Jets with negative
n will use the same calibration ratio as their positive 11 counterparts.) Jets were
generated with ET in a 40-50 GeV and a 80-90 GeV range and the predicted R( ET )
values were calculated as described in the jet calibration chapter. A comparison of
these values to the real values for the 40-50 GeV sample is shown in figures 8-18 and
8-19. The predicted R(ET) changes only by a couple percent as we move from the
40-50 GeV sample to the 80-90 GeV sample. The falling distribution of jet ET
within each ET bin means that the mean value is not at the center, the R(ET )'s from
the 40-50 GeV and the 80-90 GeV samples were assigned to 42.5 GeV and 82.5 GeV
respectively. The calibration then can use a linear interpolation to determine the
predicted R( ET ) for a jet with any arbitary ET, We only need to know which ET
value to use and which n to use for a given reconstructed jet. The n of the
reconstructed jet was assumed to be correct. The n reconstruction results of chapter 7
indicate that this is a reasonable assumption, especially since our 11 bins are .2 in size.
ET can be approximated by using the reconstructed value of ET divided by R(42.5)
for that n bin. Now the linear interpolation is done between the 42.5 and the 82.5
curve and the final calibration number is found.

Out of cone showering correction.

Our calibration did not take into account the out of cone effects seen in the
forward and backward regions of the calorimeter. This correction was made by
comparing the R( ET )'s of two identical samples with different cone sizes. Hence
this correction explictly uses a result from the simulation. The motivation is as
follows. Figure 8-6 implies that large cone‘sizes are less vulnerable to out of cone
energy losses. Thus the difference in the R(ET)'s between the sample with a cone size
of R-1.0 and the same sample with cone size of R-.7 is a measure of the out of cone
losses that are seen by the R-.7 algorithm, since the intrinsic response due to single
particle response should be the same for both cone sized jets. This is not strictly true;
one can imagine that the jets found with the larger cone size contain softer particles
along their perimeter that are not present in the R-.7 jets. We can correct for this
however by using the difference in the predicted R(ET)'s for the different cone sizes.

 

 

119

Figure 10-2 shows these R(ET)'s for both cone sizes both as found from the
simulation (real) and as predicted from the ISAJ ET fragmentation. We see in 10—2
that the real R(ET) curves diverge for forward 11. But the R-1.0 curve starts to flatten
at n-3. implying perhaps that it is starting to experience out of cone losses as well.
The predicted curves show that there is a systematic difference in the predicted
response of the different cone sized jets. The smaller cone size has a .8-1.6% greater
response at all pseudo-rapidity intervals. This implies a softer particle structure in the
larger cone sized jets. In any case, we must subtract the predicted differences out.
Thus our R(ET)'s become adjusted in the following way for each n bin:

- 00’”:- 7 cone=1.0
R(ET)adju3ted — R(ET)predic'ed + [R(ETt)real — R(ETlreal i
)cone=.7 )cone=l. 0

Here 'real' refers to the values actually determined in the simulation.

 

 

120

 

 

—b

(El)

.0
to
an

Reconstructed R

0.92

0.88

0.84

0.8

0.76

R(Et) for Different Cone Sizes

 

 

 

 

;

: R210

L Hi

E +1LJr

t +15

Sf..+ .' =.7°

; =‘+i+i«:-

I

L
”IIIIIlLlIIllIlILIII
0 1 2 3 4

Generated Jet 17

1

(Et)

.0
to
or

Predicted R

0.92

0.88

0.84

0.8

0.76

 

 

' I I I I T I 4.9 Ij’I I I I l I I I I I I I I I l I I I I

 

IIIIIIIIIIIIIIILII

 

0 r

1 2 3 4
Generated Jet 1)

Figure 10-22Reconstructed R(Et) for conesizes R=.7 and R=1.0
Distribution is shown both for reconstructed and predicted R(Et)

 

 

 

 

 

121

Zero suppression correction.

As mentioned before, there was no need to use a zero suppression in the
simulation as there was no noise present However, there will be one in real data
taking, so the software needed to zero suppress was present. It was not used in most
of the studies described in the previous chapters. However, the large data sample
which we are using to reconstruct the various cross sections did have a channel zero
suppression of 0.1 GeV. This means that if a cell had less than 0.1 GeV of energy, it
was set to zero. Since our calibration analysis did not have any such suppression, we
must correct for this before we can calibrate this large sample. The correction term
was determined by comparing the R(ET)'s of a sample of jets reconstructed with and
then without the 0.1 GeV suppression. Figure 10-3 compares the two curves and

shows that there was a 4% loss in energy for jets with n-O due to the suppression.
The difference of these curves was subtracted from the adjusted R(ET)'s.

 

 

R(Et 1...... = R(5 1...... +[R031J'ZZIS7R if: '10] [R(5 12:22.1. R(Etli‘l'lilii
+[R(5) )‘°°‘“°"'“" -R(5,)fjf“"]( (10.2)

Final Calibration Numbers
Figure 104 shows the comparison of these adjusted predicted R(ET)'s to the
real ones we determined from the simulation. The predicted responses systematically
underestimate the real response, but the forward region is much better represented
than in figures 8-18 and 819 before the out of cone corrections were made.

 

122

 

 

R(E) Distribution With and Without Zero Suppression

 

—.

(E)

Reconstructed R
.0
co
0:

0.92

0.88

I I I I I I I I I l I I I I l I I I I

No zero suppression

' TF+++

 

 

 

 

 

_ ' i ..1.. ’
: 100 Mev zero suppression
0.76 -
- I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
0 0.5 1 1.5 2 2.5 3 3.5 4

Generated Jet 17

Figure 10—32Reconstructed R(E) with and without a 100 Mev per channel
zero suppression.

 

 

 

 

 

123

 

 

r 45 Gev Jets
.0
on
a:

R(Et) lo

0.92

0.88

0.84

0.8

0.76

Adjusted Predicted R(Et) Distribution

 

IIIIIfITIlIIIIII‘III

Eu
A
'32
V

I I

 

1111+

IIII

 

 

 

111

 

usted R(Et) Rrpdiction

IIII

 

1.
L*IJ.I IAFJ.
0 1

2 3 4
Generated Jet 11

1

R(Et) forOBS Gev Jets
in
a:

0.92

0.88

0.84

0.8

0.76

 

 

 

IIIIIII'IIII'rIjI

 

it

T’Adjusted R(Et) Prediction

 

 

'ILJIIIIIIIIIIIIIIIL

 

0 1 2 3 4

Generated Jet 11

Figure 10-42Final R(Et) prediction compared with actual R(Et) for jets

in the 40-50 and 80-90 Gev Et bins.

 

 

 

 

 

124

Comparison of Calibrated to Generated Cross sectiom

A glance at figure 10-5 is enough to see the poor comparison that the
uncalibrated distributions made. We will display two sets of calibrated plots. One set
will use the distributions made by calibrating with the predicted responses which we
have determined. The second will use the real responses that were seen in the
simulation for comparison purposes. In all cases we plot the ratio of the reconstructed
distribution to the generated. Thus, ideally, the resulting curves would be horizontal
lines at 1.0 Figure 106 shows the ratio of reconstructed distributions to the input
generated distributions using the predicted responses to correct the reconstructed jets.
Most points on the curves move to within 20% of the input distribution. The shape
has been reconstructed to within 40% for the n-O. curve and to within 20% for the
n-2. and E1=57.25 curve. The ET distributions now tend to underestimate the cross
section for low ET and then overestimate for the higher range of ET. This is due, to

 

 

some extent, to the resolution smearing of the sample. The event sample used was
generated with jet E'r's between 50 and 200 GeV. Thus jets generated near 50 GeV
tended to be smeared away from the peak while higher ET received extra entries from
the lower ET portion of the distribution. We can see from figure 107, where the real

calibration responses were used, that the same type of structure is present but not as
severe. Thus the results we obtain in using the predicted responses are not so
different than those we would have gotten had we used the real responses. The 11
distribution tends to be reasonably flat in both.

 

125

 

 

Ratio of Uncalibrated to Generated Cross Section

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A A 0.6 __
u” 5.. o' g.
E 0-5 2" 2. 0.5 :-
b ' b
O "’ P "
v 0.4 E-"T'__ ‘9. 0,4 }++ +
m : -*- ++++ fi : _,_++ ++ + +
0.3 :— +*-H-—l~j.,§ 0.3 ___— + H
0.2 :— 350.2 E-
0.1 E- 0.1 :-
O:IIIIIIIIIIIIJIIII otIIIIIIIIIII_ILIIII
60 80 1 00 1 20 60 80 100 1 20
Jet E1 Jet E7
1: 0.6 E 05 :
ii: 0.5 “l" i E- + +++
R '1' 11 511-4" + + +
U '- 0.4 “'-
15 p -
E 03 +++ ‘9- 0.3 '- +
"v ' ++ “13‘ E
E’ ‘i' E 0.2 '-
+ .1, .
0.1 5? 0.1 :-
OIIIIIIIILIIILIIILI 0:LIIIIJIIIIIILIIIIIII
60 80 100 120 0 1 2 3 4
Jet E1- Jetn

Figure 10—52Ratio of uncalibrated reconstructed jet cross sections to

that of the generated.

 

 

 

 

 

126

 

 

R( da/dE1)

=2. )

R( d'a/dE,dn 11

1.2

1
0.8
0.6
0.4
0.2

0

0.8

0.6

0.4

0.2

Ratio of Predicted Calibrated to Generated Cross Section

 

 

 

 

i ’7 1.6

: -l-l- °

:_ __-"—*-+ +++Fl'+ 1': 1.4

E -- 1‘s: 1.2

" — LIJ

-.- u 1

= e

F ‘3118

a E? 0.6

0.4

E' 0.2

:1 I I l I J LI I I I l I I J 14 0
60 80 100 120

Jet E1

 

 

 

 

: 3 1
:— , . + <1
; .+_ 4‘+‘+' +_ Ficjg
TF4- I... °
.- DJ
. + H
)- f:
__ + 1?. 0 6
.. LU
: Q
:. “g 0.4
l: U
:— E’ 0.2
1:
'1 1 l 1 1 1 1 L1 1 1 1 l 1 1 1 1

60 80 100 120

Jet E1

 

 

 

 

 

 

+ + +
+
IIIIIIIILLIIIIIJ
60 80 100 120
JetE.
+
.1.
ILIIIIIJJILIIILIIJL
0 1 2 3 4
Jetn

Figure 10-62Ratio of Calibrated reconstructed jet cross sections to
that of the generated. The predicted calibration numbers were used.

 

 

 

 

127

 

 

R( do/dE, )

R( d’a/dEydn 11:2.)

Ratio of Real Calibrated to Generated Cross Section

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_..."°_ + p 1 _— ++ +
13 0.8 r“-
0.6 P E
"o 0.6 _-
0'4 °‘ 0.4 —
0.2 0.2 E-
0 I I I L LILILI I J I I I I I I I 0 Z I I I I I I I I I I JLI I I I I
60 80 100 1 20 50 80 100 1 20
Jet E: Jet E1
1 :- A
: _,_++ + iii 0'9 _,_+ .1. +
'- -t- + h 0.8 + +
0.8 Eh..- +++ + “I: 0.7 ++++ + ++
0.5 r- i‘ “.1 0.5
r ‘E 0.5
o 4 E— } 0.4
E “t, 0.3 +
0.2 l;- E’ 0.2
I 0.1
OpIIIIIIIIIIIIIIIII 0 IIIILIIIIIIJIIII+IIII
60 80 100 120 0 1 2 3 4
Jet E1 Jet 11

Figure 10-72Ratio of Calibrated reconstructed jet cross sections to
that of the generated. Real calibration numbers were used.

 

 

 

 

128

Unsmearing the reconstructed distributions
We used two methods to correct for ET resolution smearing. Both make

explicit use of a simulation result. The first method is to smear the PJET distribution
by the assumed jet ET resoluton before doing the comparison. This requires us to
determine the ET resolution. One way to do this would be to use the resolutions of
the single particle pions and electrons and convolute them with the ISAJET jet
fragmentation to predict jet resolutions the same way we predicted jet responses.
Doing this yields only a 6% resolution as opposed to the simulation result which is
more like 10%. Again, out of cone fluctuations probably contribute and we have not
accounted for this. Although the jet ET resolution changes as a weak function of
energy, we assumed it was a constant value of 10%. Figure 10-8 shows the results of
smearing the modified PJET distribution before making the comparison to the
predicted calibration curve. All of the curves become flatter as we expect. The shape
is now reconstructed to within 20% for all the curves. Figure 109 shows the same
comparison but this time the real calibration responses are used. The shapes of the
distribution are flat to within 10% to 15%. We note that the absolute cross section is
still 10-20% less than the PJET distribution.

 

 

 

129

 

 

Ratio

A
.-

R(da/dE

R( d'o/dE1dn 11:2. )

1.2

0.8
0.6
0.4
0.2

.0 .0
01 on A
i"

.0
.p

of Predicted Calibrated to Smeared Generated Cross Section

 

 

1 .4
+++

1.2 ++ ++++ +

1 "' Ti"

++

, , I++++++

IIIIIIII

l

0.8
0.6
0.4
0.2

R( d’O/dEtdn n=0. )

 

 

 

(_IIII'IIIIIIIIII'IIIIIIII

IILIIIIIIIIIIIII 0 IILJIIILIIIIIIII

 

120
Jet E,

60 80 1 00 1 20 60 80 100

Jet E.

 

 

1.2

.l.
+
1
+

1

-1—

+

+IIIITIIII

.I.
‘l’
i,
‘1'

1

++

R( o’er/dean E.=57.25)
+
+
+

+

0.8
0.6
0.4
0.2

Frl""l""|""l'r
+
++
_+...

lIIIIlIIII'IIII'III

.j.

IIJIIIIIIJIIIIIIIII

 

 

 

 

IIIILLIIIIIILIIII

 

O

 

1 2 3 4
Jet 17

o IIII

60 80 100 1 20
Jet E,

Figure 10-81Ratio of Calibrated reconstructed jet cross sections to
that of the smeared generated. Predicted calibration numbers were used.

 

 

 

 

130

 

 

R( act/<15t )

=2.)

R( d’a/dE1d1) 11

Ratio of Real Calibrated to Smeared Generated Cross Section

0.8

0.6

0.4

0.2

9.0.0
scion-t

.0
N

 

 

 

 

 

 

 

 

:- o'
E + n 1
_— -+-
t. *-*—-“‘-'-"' _,_++ + E:
’ ‘3. 0.8
t 11.1
7- Q
E «O 0.6
: U
:— 3? 0.4
E- 0.2
3..1L...1....1.... 0

60 80 100 120

Jet E,

r TS
:" + 61 1
:_“"-+-+ L‘,
: .1. ++++ + L1,; 0.8
":- + 5 0.6
. LU
'_ + Q
: ”b 0.4
. U
:- E’ 0.2
:I I I I LLLLL I I I I I I I I

60 80 100 120

Jet E7

 

fIIIIII

-+- +
+4—l—l— +

l

 

_ IIIIIIIIIIIIIIIIIIIII

IIIJIIIIIIII

+

+++

 

ILIL

 

60 80

100

120
Jet E,

 

+
...+

+

+
”+4.

1""

IIIIIIIIIIIIIIIIIIII

 

IIILIIIIIIIIII

.j.

 

IIILII

 

1 2

O

4
Jet 11

3

Figure 10-92Ratio of Real Calibrated reconstructed jet cross sections to
that of the smeared generated. Real calibration numbers were used.

 

 

 

 

131

The second method used was to try to unsmear the reconstructed distribution.
Again, we assume a jet ET resoluton of 10%. The reconstructed distribution is
smeared again using this resolution. The bin by bin difference is calculated and these
differences are used to correct the original reconstructed distribution. Figures 10-10
and 1011 show the results. In general this method does not produce a distribution
that agrees with the modified PJET distribution as well as the previous method.

Summary of Reconstruction

We will summarize the accuracy of the reconstruction. The error bars in
figures 10-5 through 1011 are purely statistical. The ET distributions tend to run out

of statistics for high ET so we will consider the distribution up to 100 GeV. The 11
distribution runs into both statistical and out of cone problems for very forward 11 so
we will consider that distribution only up to n-2.0. In these regions, the overall cross
section scale is reconstructed to within 10—20%. The shape of the cross section is also
preserved at the 15-20% level. We can compare to this the reconstructions which
used the 'real' calibration numbers. These curves reconstruct the scale to within 10-
20% but the shape reconstruction is slightly better especially for the n-O. curve.

Since the real calibration numbers are used, we are led to believe that errors in jet
definition and how our calibration is applied cause these 10—15% shifts. These are
systematic effects. There are further systematic errors associated with errors in the
ET calibration. Figure 8-16 implies that we can expect a 2% error in the predicted
calibration ratios which we use. We estimate the effect on our reconstructed cross
section by changing the predicted R(ET) values by +/- 2% and comparing the
resulting cross section distribution to the PJET distribution. The results are shown in
figure 10-17. Thus we expect an additional 10% error in the cross section due to an
assumed 2% error in the jet ET calibration for the ET distributions. The 11 distribution
seems more or less insensitive and changes by only 2% with a 2% change in the
R(ET) values.

 

 

132

 

R( da/dE1)

R( d’a/dEtdn n=2. )

 

1.2

1
0.8
0.6
0.4
0.2

O

0.8

0.6

0.4

0.2

Figure 10—102Ratio of Unsmeared Predicted Calibrated reconstructed cross
sections to that of the generated. Predicted calibration numbers were used.

 

 

 

 

 

 

 

 

E— - 1.5
: _._ + 01!: r 4
c -— + -+- «E 1.2
::. laJ

: Q 1
: e

5- ‘1'0 0.8
=_ E? 0.6
E 0.4
:— 0.2
:I I I I I I l I I I I I I I I I I 0

60 80 100 120
Jet E1

_ A 1.2
I -+- (nu
hid-I- - 1
- + rx

: ++++ “i"

; + + 1;,- 0.8
T _j— 5

: + ul’ 0.6
’- E

: + «a 0.4
: U

.— E’ 0.2
1:

bLL LI I I J I I I I LI I I I I 0

60 80 100 120
Jet E,

Ratio of Unsmeared Predicted Calibrated to Generated Cross Section

 

IIIIIII'IIIIIIIII'III

IIIIIIIIII'IIIIIII

 

_[In

I I I I I I I I I I I I I I I I

 

 

60

80

100 120

Jet E1

 

III II

1'

.1 II II [I'II I' II Ilill II II II

 

11111111I111LIlJ—I-l-l-m

 

 

0

1

2

3 4
Jet 17

 

 

 

 

133

 

 

R( da/dE1)

R( d’a/dEdn n=2. )

Ratio of Unsmeared Real Calibrated to Generated Cross Section

1

0.8

0.6

0.4

0.2

d

.0
on

.0
a:

.0
4.

.0
N

 

 

 

 

 

 

 

 

E + + ‘9.
5' § 0.8
- o
E ‘30 0.6
5 °‘ 0.4
:— 0.2
:I I I I I I I I I I L I I I I I I 0
60 80 100 120
Jet E:

t— 3 1

9!
C -l- “tn-j- + 11_ 0'8
.. j w
E. H- g 0.6
L' 11.1
r. + E 0.4
L' “O
: _j. 3 0.2
:- a:
:I I I I I L I I I I I I I I I I 0

60 80 100 120
Jet E1

 

IIIIIIIIIII

IIIIIIT'WITTIIIIII‘

 

l
l

IIIIIIIIILLIIIIIL

++

+

++++

i

 

 

60

120
Jet E1

80 1 00

 

TIITIIIIIIIIII'IIII[*IIIll

 

.j.
t£+

LIIIIIIIIIILIILLIIII

+
++ +
+i

+

 

 

0

1

4
Jet 11

2 3

Figure 10-1 1 Ratio of Unsmeared Real Calibrated reconstructed jet cross
sections to that of the generated. Real calibration numbers were used.

 

 

 

 

134

 

 

Ratio of Predicted Calibrated to Smeared Generated Cross Section

A
p

R(do/dE

 

1.2

 

0.8

0.6

0.4

0.2

IrrIlIIIIrIIIIlIIIITI

 

 

 

o I_ILILLIIIIIILLLILI

60 80 100 1 20

JetE
Figure 10-172Ratio of Calibrated retzonstructed jet cross sections to
that of the smeared generated. Predicted calibration numbers were used.
Also plotted are resulting distributions when calibration is varied by

+/- 2 percent.

R( d'a/dEfln E.=57.25)

1.2

0.6

0.4

0.2

 

 

 

r I I I I l I

  

 

 

 

I I I I I IiI I I l I I I I l I I I I l I fi.!_

 

 

IIIIIJLIIIIIL

 

 

 

135

Cross Section and Structure Functions

We have seen that the next-to—leading-order predictions largely reduce the
theoretical errors in the cross section prediction. However, there are still errors of
order 20% from the choice of parton distribution functions. A precision measurement
of the single jet inclusive cross section could be compared to several NLO theoretical
predictions generated using various sets of parton distribution function. In doing so, it
may be that some sets would be favored over others and thus the parameters used to
generate the p.d.f‘s could be further constrained.1 We will investigate the difference
in the predicted cross sections obtained by using various sets of structure functions
calculated by Martin, Roberts and Stirling. These sets were calculated in the same
way except for two parameters. The first is the QCD A parameter. The second
parameter is 11g which has to do with the gluon parton distribution function which

typically has the form:

 

g(x) = Ax‘ (1 - x)"‘ (10.3)

The best fit of these two parameters was called BO. Four more fits were created by
choosing 4 points along a chi-square contour in A418 space. The chosen parameters

and their labels are shown in table 10-1.

 

 

 

 

 

Set M4) MeV fig

30 190 5.10
3135 135 - 4.65
3160 160 4.25
3200 200 5.65
3235 235 5.20

 

 

Table 10-2: Parameter values for various parton distribution fits.

Figure 10-12 shows the cross sections predicted by using each of these sets
when normalized to the BO fit. The distributions differ by as much as 20% in certain
PT ranges. Changes in A tend to cause normalization changes while changes in 113
changes the shape. Figure 10-13 is the same plot but at n-2. Like figure 10-12, the
high and low PT regions are where there is the largest difference between the curves.
N ote that there are both scale and shape differences. Figure 10-14 is the same type of
plot but this time the 1‘) cross section at fixed PT-IO. GeV is used. The differences are
mostly in the scale, but they are large differences. This is at very low PT, however;
figure 10-15 shows the results for a PT-GO. GeV point which is closer to the sample
we are using. But here the differences are much less. So we see that the predicted

136

cross section distributions vary widely in different kinematic regions, but the sample
we are using seems to be in one of the kinematic regions where the differences are
not as large.

:x -.
. ’P
Q
i
i
g
,5
we
‘2
.1.
5!
1e
Y.

 

 

 

137

 

 

Cross Section Normalized to BO

1.3

1.2

1.1

0.9

0.8

0.7

Jet Et Cross Section for Various Structure Functions

 

 

 

 

 

 

1 _o_ —_.__,_
.0- —°_

9 —0'— —*__*___* *—
. _A:Cl" _°_ —>l<-—

1..

{l- _ _ —*—

L 4} o

W e at r: at 4.: e

E flak»... +—O——o £3 13 43—
_ -0-_ _-fi- +‘
.. * + : 2 ——A'——

+- -0-—*-

;_°_‘*‘ 1:1 8235
l. * B135
_ a 80

.->1<-

9 o 5160
t A 3200
;*.

1..

IIILIIIIIILIILIILIIIIIIIIIIIIIIIIJLLIIIIIII

 

50 1 00 1 50 200 250 300 350 400 450

Jet Pt

Figure 10-122E, cross section for various structure functions at
17=O.0, normalized to 80

 

 

 

138

 

 

Cross Section Normalized to 80

Jet Et Cross Section for Various Structure Functions

 

 

 

 

1.3
1.
1.2 —
El _0_
- ——*—
1.1 5‘0- —0_
. —o-—
_o_
- 4:- -o- —>l<——
f-A-
. #20. __
1 mm
P ‘A‘ -*-
_A._
L -o- a
. $9 A D 3235
. >1: 13135
_ _ a 80
0'9 5 * o 8160
.'°‘ A 8200
1..-*-
0.8 9'
*.
0.7 _ILIIIIIIIIIIIIIIIILIIIJIIIILIIIIIIIIIIIIIII
50 100 150 200 250 300 350 400 450

Jet ET

Figure 10—13ILO E, cross section for various structure
functions at n=2.0 normalized to 80

 

 

 

 

139

 

 

Cross Section Normalized to BO

1.3

12

11

(19

0.8

(17

Jet L0 77 Cross Sections for Various Structure Functions

 

8235
B1 35
BO

Bl 60
8200

Dov-XIII

 

 

 

 

r
1 0:01
.0.
— .0..°.
l- .0.
.0.
.. .0.
l- °°"°:°. -*4
1- .0 .. 0:0 .'°'¢ :0 . *.'*'
l— ‘°'°.-°I0’°’°J°. -*..*.
p-o-o-o—o—oeo-oco—o-ooo-ooo—OvO-o * *d..***--*
, , :*’*‘ "*'- :

w********************’* * * *
bI I I I I I L I I I I I I L I I I L I I I L I I I I I I I I I I I I I I I I I I I
0 0.5 1 1.5 2 2.5 3 3.5 4

Jet 11

Figure 10-14ZLO 1; cross section for various structure functions
normalized to BO. E.=10.

 

 

 

 

140

 

 

Cross Section Normalized to BO

Jet LO 1) Cross Sections for Various Structure Functions

 

1.1

1.3
-D 8235

1.2 ->l< B135
- a so
lo 8160
-A 3200

 

09
'0

{WWW-W '

0

..°' ‘A‘u ,*,..
.. A A A ‘ ‘ ‘ A A A.A‘.A¢A‘<A‘A'*.*.*.°*:*

 

 

 

*‘*‘*‘*’*:** I
0.9 $-*-*-=lv*'*'*'*’*’*’*'*
0.8 -
,
O7 b‘IIILlIIIIILLIIlIIII[ILIIlILLJLIIILlLJIIJ
0 0.5 1 1.5 2 2.5 3 3.5 4

Jet 7;

Figure lO-lSILO 7; cross section for various structure functions
normalized to BO. E.=60.

 

 

 

141

Figures 10-12 through 10—15 were generated using LO predictions only. It is
important to know if the NLO predictions show the same, less or more dependence on
the choice of parton distribution functions. The answer seems to be that the
dependence is the same. Figure 10-16 shows one prediction for both L0 and NLO as
an example of this.

If we were able to reconstruct the cross section precisely enough, we would be
sensitive to the normalization and shape differences between the different sets. The
above plots seem to imply that one must be sensitive to S -10% differences in the
cross section. In the range of our reconstructed sample. even better precision is
necessary. The reconstruction results show that the reconstructed distributions are
uncertain by 20-25%. In figure 10-18 we have superimposed the ratio of our
reconstructed cross section to that of the input PJET distribution to the other structure
function ratios. The reconstruction is not nearly precise enough to differentiate
among them.

 

 

142

 

 

Jet E?Cross Sections for Various Structure Functions: LO vs NLO

 

 

    

 

 

o 1.1 I?
m - Gd]
0 -
B is [3:3
$1.05 ~¢ C} .9
o . a
E . '
O . .
z
c ‘l '.‘.,,..,,
.2 - ¢ - -
1'3 - A O- .*. '
0 l- . .
If") _ {AAA --
(00.95 — l-
8 '- 0 *‘*‘
U - .0. '*'
. .0. *-*
g . .
0.9 - 'i' '*
. *-
- '0- *-
0.85 3‘? ** a 80
_ *-
-*_ >l< B135
0.8 ,
0 8160
A 8200
0.75
D 8235
0.7 L L I I I I I I I L I I I
40 80 120
L0 Jet P,

Cross Section Normalized to 80

1.1

.0
to
UI

IIITerrifirlitllr

0.9

0.85

0.8

0.75

0.7

 

 

 

 

 

 

 

 

 

 

k 80
>l< 3135
O 8160
A 8200
D 8235
I I I k I I_I I L I I
40 80 120
NLO Jet P,

Figure 10-162Et cross section for various structure functions at n=0.
normalized to 80. L0 versus NLO.

 

 

143

 

 

Cross Section Normalized to 80

Jet E, Cross Sections for Various Structure Functions

 

 

 

 

 

 

1.3
1.2 — -<>-
1.1 :- {3102‘}
e 1»
C
: _°_"°‘_*__*_- -’*‘ 0 Sim Data
_o_-°- ->l<- * BO
' -*-*- a: 31.35
0'8 f” o 8160
t A 3200
C a 3235
0.7 I I I I I L I I I I I I L I L i L I I I I I I I I I
20 4o 60 so 100 120
.. Jet P,

Figure 10-182Et cross section for various structure functions at n=0.
normalized to 80. Data points are normalized to modified PJETS

 

 

 

144

 

1A. D. Martin, R. a. Roberts and w. J. Stirling, Preprint RAL-90-084 (1990).

Chapter 11: CONCLUSIONS

The previous sections are the results of simulations and studies done so far and are
by no means complete. It may be useful to summarize some of the main issues raised
along with a general indication of how well it is believed to be understood.

1) Many of the above sections as well as the appendices emphasize the
importance of understanding the definition of a 'jet' when attempting to reconstruct the
inclusive cross section. This analysis focused for the most part on the Ellis prescription
with a cone size of .7 radians. Other definitions may produce different results. It has
been implied here that the standard DO definition of parton jets (PJETS) is not compatible
with the Ellis definition and that the DO reconstructed defmition of jets may indeed be
compatible with the Ellis prescription. But it was also clear that they are not identical and
the effect of their differences on the measured cross section are not understood. For use
in comparing to NLO theory, it would seem to make sense to study how these algorithms
can be tuned or modified to maximally respect the theoretical definition.

2) DO's ability to reconstruct jets over a wide range of ET and 11 space seems
promising but will be very dependent on the quality of the energy calibration. The
calibration method used here is simple and can‘be improved in many ways. The jets
should be calibrated on the basis of the location of the detector in which they were found
and not based on the n of their jet axis. Further, we have seen that a 'jet' may consist of
several subclusters of energy which represent different partons. Calibration should be
applied on the basis of these clusters instead of on the entire jet Finally, out-of-cone
losses threaten to be a very important phenomena for both forward jet physics and for
studies with different cone sizes. We must learn to separate energy that belongs inside

145

146

the cone from energy that belongs outside the cone. This may require changing the fixed
cone into a more flexible object which depends on rapidity and the center of mass frame
of the scattering.

3) This paper deals, for the most part, with the reconstruction of the cross sections
of the particle jets that are created by the underlying parton jets. There is a clear
fragmentation dependent difference in these two distributions and no attempt has been
made here to recreate the partonic distributions which would ideally be compared with
theory.

4) Energy calibration seems to be dominated by the effects of single particle
responses in the calorimeter. A surprisingly good correction can be made by determining
the single particle responses and combining this with an assumed fragmentation. Hence,
careful analysis of the linearity of pions and electrons in DO's fixed target test calorimeter
is crucial in supplying a first order jet energy correction at collider start up. This
correction can be used both for offline analysis as well as online triggering and display.
Such analysis and work is underway.

5) In order to be able to make statements about structure functions via
measurements of the single jet inclusive cross section, the precision of the reconstruction
must be improved over what has been shown here; additionally, any such attempt must
consider the low and high jet Pr regions where the cross section is most sensitive to the

structure functions.

 

 

 

APPENDIX A: Level 1 Trigger Semitivity

Efficiencies and rates have been calculated for various ET jets for various
trigger settings. It is expected, however, that these numbers will be sensitive to
differences between the simulation and the real detector. For example, noise would
tend to increase trigger rates, while wider jets would decrease trigger efficiency. We
have studied the effect of the Level 1 trigger to the different calorimeter resolutions,
noise , and different event generators.

Sensitivity to Event Generator.

Sensitivity to the event generator was done by comparing ISAJET to
HERWIG. CDF has found that HERWIG agrees very well with the fragmentation
dependent quantities they are able to measure with their central tracking detector.
(Unlike DO, they are able to determine the momentum of charged particles by using
their central magnetic field and measuring the curvature of the particle's trajectory.)
Both simulations were run to produce jets between 50 and 200 GeV. The final state
generated jets were defined by looking at the particles produced, applying a cone of
R=.7 and requiring that there be at least 8 GeV in order for the jet to counted. Five
hundred events were generated in each case. ISAJET generated 2921 jets and
HERWIG generated 2848 jets. The results were placed into a toy D0 calorimeter, no
energy cutoffs were made, the energies were smeared with the calorimeter resolution

and longitudinal showers were simulated. NOTE: this is NOT the same as the much
more sophisticated and detailed DOGEANT detector simulation. Thus effects like ch!

147

 

and energy linearity will not show up in this comparison. But we should see effects
of different event topology and jet energy distribution. The ET distributions looked
similar. Table AA-l shows the jet ET breakdown of these events.

 

 

 

 

Jet Et Bin Herwig Isajet
O_5 30% 18%
5_10 16% 22%
30_35 2.8% 2.7
50_55 63% 44%
>120 .25% 0.1%

 

 

 

Table AA-l: Jet ET distribution for Herwig and Isajet. Herwig generates a
higher fraction of higher as well as lower ET jets.

The ET distribution is all in all similar. HERWIG clearly has more lower as well as
higher ET jets. We compared various Level 1 triggers which required various ET
thresholds and various number of trigger towers. The following was observed:

1) The total ET triggers fired the same percentage of the time within 4%.

2) The triggers that asked for l or 2 trigger towers above 3,4,5 or 6 GeV fired
the same percentage of the time within 1%.

3) If 3 or 4 towers are required, then HERWIG was systematically more
efficient especially at the 6 GeV threshold where it was 5% more efficient for
3 towers and 10% for 4 towers. This difference seems to decrease as the ET
of the jets in the sample rises. This would tend to indicate that HERWIG jets
deposit their energy in less space or perhaps that the core is more concentrated
at least for jets up to 40 GeV.

Sensitivity to Noise.
Noise is the presence of a signal (usually with a constant mean and width) in the
absence of particles in the detector. We now would like to compare the trigger
efficiencies based on varying the Lei/e1 l simulator with noise and without. We
should note that at the time the study was done, the Level 1 simulator had much larger
noise than it was programmed to have after the first cosmic ray commissioning run.
The widths of the noise were approximately 250 MeV in the electromagnetic trigger
towers and 700-900 MeV in, the hadronic portion. A 2.5 sigma zero suppression was

149
applied to every tower. We looked at trigger efficiencies for various types of physics
processes.
50 GeV Single Electrons:

For 50 GeV electrons the efficiencies are virtually identical with and without
noise if 1 tower above a threshold is required. At the 3 GeV threshold, the efficiency
doubles if N=2,3 or 4 towers above 3 GeV are required and the noise is turned on in
the simulation. But these efficiencies are low as electrons tend to enter one trigger
tower only.

50 GeV Single Pions:

For 50 GeV pions, we only see an effect when N=3. Without noise, the pion
is very inefficient at these thresholds. But with noise, the triggering rates go up by a
factor of about 5. We theorize that the pions spread out enough energy to allow noise
effects to 'build' upon the lower towers and manage to trigger.

14000 jets in a variety of ET samples:

Table AA-3 shows the multiplicative increase in triggering efficiency when
the noise is turned on in the simulation. We see two trends. First, the lower ET bins
have larger increases in trigger efficiency. Secondly, the lower trigger tower
thresholds are more sensitive to the noise. The 5 GeV threshold is relatively
insensitive to noise while the higher thresholds are insensitive. We expect that the
real determining factor is the ratio of the noise level to the trigger tower threshold.

150

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of T1“ Er Cut 2_5 5_10 10_20 20_40 19180
1 3 1.5 1.6 1.1 1.09 1.0

1 5 1,0 1.0 1.04 1.0 1.0

2 3 3,0 2.5 1.5 1.09 1.0

2 5 1.0 1.1 1.1 1.03

3 3 .008/0. 1.5 2.0 1.2 1.03

3 5 1.0 1.03 1.05
4 3 mm 2.3 1.3 1.05
4 5 1.3 1.1

 

 

Table AA-Z: Ratio of Level 1 Trigger Tower efficiency with noise to without.

We also look at the effect of calorimeter resolution on the Level 1 trigger
efficiencies. We compare an old set of events in which smearing was 30%/V1? for
electrons and 60%NE' to new numbers that are 16%/VF for electrons and 40%/VF
for pions. Table AA-3 shows the ratio ,R, of the rate with the old smearing with
respect to that with the new smearing. This ratio is significantly greater than one only
for the 3 GeV thresholds and the lowest ET bins. But it is here that much of the rate
comes from. Thus it is important to know the Level 1 energy resolution. We see that
the high ET event efficiencies are relatively unchanged at all triggers. But the 2_5
and 5_10 are widely different. Since the QCD jet ET spectrum falls as ET to a power,
these small ET bins can contribute sizable amounts of rate which will decrease the

Sensitivity to Energy Resolution

signal to noise of the events that pass through the Level 1.

 

 

151

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of towers 51‘ Cut 2_5 Sjfl M 20:42 40_80
l 3 7 2.2 1.15 1.02

l 5 3 1.3 1.01

l 7 1.04 1.02

1 9 1.25 1.02

2 3 2 3.7 1.5 1.08

2 5 1.06

2 7 1.09

2 9

3 3 infinite 2.0 1.7 1.18

3 5 3.0 1.11

3 7

3 9

4 3 3.0 1.38

4 5 1.5 1.07
4 7 1.07
4 9

 

 

 

 

 

 

 

Table AA-3: Ratio of Trigger Efficiency with old smearing compared to new

smearing:

 

 

 

MICHran smTE UNIV. LIBRARIES
111|11111111111111111111111"1111111111
31293007929055