first measurement of the proton structure function f2 with ... · the zeus detector is one of two...

First Measurement of the Proton Structure Function F 2 With the ZEUS Detector

by

Frank S. Chlebana

A thesis submitted in conformity with the requirements

for the degree of Doctor of Philosophy

Graduate Department of Physics

University of Toronto

© Copyright by Frank S. Chlebana 1994

Reproduced with permission o f the copyright owner. Further reproduction prohibited w ithout permission.

Abstract

This thesis describes the methods and results o f the first measurement of the proton struc

ture function F2 by the ZEUS collaboration. The ZEUS detector is one o f two large general purpose

detectors at the electron-proton colliding facility HERA located at DESY in Hamburg Germany.

HERA provides collisions of 26.6 GeV electrons with 820 GeV protons, resulting in a center of

mass energy an order o f magnitude higher than previous fixed target electron scattering experi

ments. The kinematics at HERA allows the measurement of F2 in a region o f x ana g 2 phase space

previously unexplored. A total integrated luminosity of 24.7 nb'1, collected during the fall o f 1992,

was used for the measurement o f F2. The results reported here extend the measurement of F2 to

lower values of x by two orders o f magnitude. I11 the parton model the behavior of F 2 at low x is

highly dependent on the unknown gluon distribution and the absence o f data leads to significantly

different expectations of the neutral current cross sections at low x. A measurement of F2 at low x

constrains the gluon distribution. The results show a strong rise at low x.


For Tess, with love.


Acknowledgments

The success of this experiment is the result o f the effort o f the many people involved. The

unique experience gained by working in such an international collaboration is invaluable and re

warding.

I would like to thank Robert Orr for providing the opportunity to work on the Third Level

Trigger (TLT). His concept and design of the TLT has proven to be successful. The flexib ility un

der his supervision is also appreciated. 1 would like to thank my supervisor John Martin. 1 learned from his pragmatic approach to problem solving. I would like to acknowledge Sampa Bhadra for

her leadership of the TLT group at DESY. The TLT would not be a success without her effort. Dinu

Bandyopadhyay’s enthusiasm and calmness is admired.

The other graduate students from the University of Toronto, working on ZEUS, have en

riched the experience and made it fun. Thanks to Mike Crombie, Burkhard Burow, Frederick

Benard, Milos Brkic, Richard Teuscher and Cortney Sampson for answers to questions and tech

nical help. Thanks to John Mayer for putting up with me during my oral exams and printing the

thesis for me in Toronto.

T h e /^ analysis would not have been possible without the dynamic and active participation

of the many members of the working group. The group benefitted by the leadership and direction

provided by Allen Caldwell. His understanding o f the detector and physics allowed the quick con

vergence of the F 2 measurement. Halina Abramowicz provided and continues to provide inspira

tion. Her deep understanding of physics, quick intelligence and devotion to physics is to be ad

mired.

1 would like to thank Maria Roco and Gary Levman for meticulously reading the thesis.

Their comments and suggestions were much appreciated and greatly improved the early drafts.

Any errors in the final version are mine.

Thanks to my family, my brother Michael Chlebana, sister Joanne Neilson and parents

Alois and Anna Chlebana for their support and care.

Special thanks to Maria Roco for support and making me get away once in a while although

not as often as she would like.


Personal Contributions to the ZEUS Experiment

During the first summer while working on the ZEUS experiment 1 participated in the con

struction o f the stacking machine used to build the forward and rear calorimeter modules. 1 wrote

software to control the vertical motion of a reference frame used to ensure the uniform stacking of the depleted uranium plates.

1 contributed to the selection o f the processors used for the Third Level Trigger (TLT). This

required the evaluation of the different processors considered for use in the TLT and testing o f the

Silicon Graphics (SGI) computer which was eventually selected. I contributed to the hardware de

sign o f the TLT. This required the development of a dedicated input/output (lO) device driver

which is linked to the UNIX operating system of the SGI. This routine provides robust and last data

10. I performed rate tests to ensure that the hardware design would meet the bandwidth require

ments o f the ZEUS experiment. 1 wrote online code to access the event data for the TLT. I also

wrote code to append the results o f the TLT to the data stream. 1 participated in the software design

of the TLT and contributed to the trigger studies for the TLT. I represented the TLT at group meet

ings. I wrote code to test a custom built DMA extender built by Silicon Graphics based on speci

fications provided by the University o f Toronto.

I designed and implemented the data transfer from the TLT to the DES Y central IBM where

the data is archived. The combination of the hardware and software used to transfer data is referred

to as the IBML1NK. I maintained the 1BML1NK and was on call during the entire fall running pe

riod. I reported on the status of the IBM LIN K at group meetings. I designed and implemented the

data storage on Exabyte tape. This ensures that luminosity is not lost when the DESY central IBM

is not operating.

During data collection I helped check the data quality and tracked down sources of corrupt

data. I provided utility routines to help check the integrity of the data. I participated in data taking

shifts in the role of an online expert. I was also on call for the TLT during the Fall data period.

1 was an active participant during the structure function analysis of the Fall data. I partici

pated in the selection of the cuts to be applied to the data in order to obtain a clean sample of DIS

events. I interfaced the TLT tracking software to the offline vertexing software. The vertex thus

obtained is used in the measurement of I later modified the ver'exing software to be used on

line. This software is currently used online to filter events. I also suggested that calorimeter time

infonnation can be used to determine the event vertex. I implemented the method used to measure

F 2 - I performed numerous systematic checks for the measurement o f F^1 represented the ZEUS collaboration at the 1993 European Physical Society conference, presenting results on events in

deep inelastic scattering with a large rapidity gap.


Table of Contents

1 Introduction.......................................................................................................... 1

I . I Development o f the QCD Improved Quark-Parton M odel...............................2

1.2 Compact Form of the Differential Cross Section ............................................13

1.3 Small x Behavior of the Structure Function...................................................... 16

1.4 Measured Regions in x and Q Phase Space..................................................... 17

1.5 Parton Parameterizations ................................................................................... 18

2 HERA ................................................................................................................. 21

3 The ZEUS Detector.......................................................................................... 25

3.1 The C5 Veto Counter.........................................................................................26

3.2 Luminosity Measurement ................................................................................. 27

3.3 Central Tracking Detector................................................................................. 29

3.4 Calorimeter ........................................................................................................31

3.4.1 Electromagnetic Showers ........................................................................31

3.4.2 Hadronic Showers ....................................................................................33

3.4.3 Mechanical Description........................................................................... 35

3.4.4 Calibration................................................................................................35

3.4.5 Time Measurement................................................... 37

3.5 Veto Wall ........................................................................................................... 40

4 The ZEUS Online Trigger and Data Acquisition System .......................42

4.1 First Level Trigger ............................................................................................ 42

4.2 Second Level Trigger........................................................................................ 44

4.3 Event B u ild e r.....................................................................................................46

4.4 Third Level Trigger........................................................................................... 46

4.4.1 The Third Level Trigger Hardware Configuration................................ 46

4.4.2 Control Software of the Third Level Trigger.......................................... 50

4.4.3 The Third Level Trigger A lgorithm s...................................................... 51

4.5 Trigger Configurations...................................................................................... 54

5 Monte Carlo and Reconstruction Programs..................................................56

6 Reconstruction of Kinematics at H E R A ..................................................... 58

6.1 Different Methods o f Kinematic Variable Reconstruction............................. 58

6.2 Smearing of Kinematic Variables.....................................................................63

6.3 Selecting the Reconstruction Method .............................................................. 67

i


7 System atic E ffects o f Reconstruction and the T r ig g e r ............................... 70

7.1 QED Radiation.................................................................................................. 70

7.2 Effects of Uranium Noise .................................................................................72

7.3 Electron Finder.................................................................................................. 72

7.4 Determining the Vertex Distribution .............................................................. 74

7.4.1 Vertex Distribution Determined from the C5 Counter..........................74

7.4.2 Vertex Distribution Determined From Photoproduction Events........... 78

7.4.3 Vertex from Tracking.............................................................................. 78

7.4.4 Vertex from Calorimeter T im ing .............................................................70

7.5 Reconstruction of the Event Vertex ..............................................................82

7.6 Trigger Acceptance and Efficiency ..............................................................S3

7.7 Angle Reconstruction........................................................................................ 85

8 Event Selection .......................................................................................................80

8.1 Selection Cuts ....................................................................................................80

8.2 The Effects o f the Cuts ..................................................................................... 00

8.3 Background Subtraction.................................................................................... 08

8.3.1 Photoproduction ...................................................................................... 08

8.3.2 Beam Gas Interactions............................................................................100

8.3.3 Cosmic Muon and Halo Muon Rejection..............................................101

8.3.4 QED Compton........................................................................................103

9 The D e te rm ina tion o f F 2 ..................................................................................... 105

9.1 Bin Selection.....................................................................................................105

9.2 Contribution From the Longitudinal Structure Function.................................108

9.3 Events with a Large Rapidity G a p .................................................................. 110

9.4 Description o f the Unfolding Procedure...........................................................113

9.5 Testing the Unfolding Method........................................................................ 117

9.6 Determination o f F2 Using Different Reconstruction Methods.....................119

10 System atic E ffects on the D eterm ination o f F 2 ........................................... 120

10.1 Systematic Checks ...........................................................................................121

10.2 Determining the Final Systematic Error...........................................................132

11 Presentation o f the F ina l Results and a Com parison w ith M CS im u la tion ..............................................................................................................135

12 C o n c lu s io n s .............................................................................................................139

13 References ...............................................................................................................140

ii


List of Figures

Figure 1-1: Electron scattering from a proton by the exchange o f a single virtual photon 2

Figure 1-2: Dipole approximation...................................................................................................5

Figure 1-3: The baryon octet of the Eightfold Way....................................................................... 6

Figure 1-4: Inelastic scattering cross section compared with elastic scattering crosssection..........................................................................................................................7

Figure 1-5: Evidence for scaling..................................................................................................... 8

Figure 1-6: Evidence for scattering from spin 1/2 partons............................................................ 9

Figure 1-7: Parton distributions of the proton...............................................................................11

Figure 1-8: Lowest order Feynman diagrams which lead to scaling violations..........................12

Figure 1-9: Electron proton interaction mediated by a virtual photon........................................ 13

Figure 1-10: The effect o f Z° exchange on F 2 ................................................................................15

Figure 1-11: Regions in thex and Q2 plane for which structure functions have been measuredby recent experiments................................................................................................17

Figure 1-12: Low x extrapolation of F 2 for some recent parton parameterizations..................... 19

Figure 2-1: The HERA accelerator...............................................................................................21

Figure 2-2: HERA injection scheme.............................................................................................23

Figure 2-3: ZEUS accumulated luminosity for the runs taken during the fa ll data takingperiod......................................................................................................................... 24

Figure 3-1: Elevation view of the ZEUS detector cut along the beam line................................25

Figure 3-2: Event display o f the highest (92 event used in this analysis.....................................26

Figure 3-3: Luminosity monitor................................................................................................... 27

Figure 3-4: End view of the CTD showing a simulated NC event............................................. 30

Figure 3-5: ZEUS FCAL module................................................................................................. 36

Figure 3-6: Timing diagram of the electron-proton interaction..................................................39

Figure 3-7: Average time o f energy deposits in the calorimeter for o f the DIS sample............40

Figure 3-8: The scintillator counters of the Veto Wall viewed from the ZEUS detector......... 41

Figure 4-1: Overview o f the ZEUS trigger and data acquisition system....................................43

Figure 4-2: Calorimeter trigger regions........................................................................................44

Figure 4-3: Detailed schematic of the Third Level Trigger data and control paths...................47

Figure 4-4: Detailed schematic of the IBM Link data path.........................................................50

Figure 4-5: Sustained transfer rates to the IBM as a function of the transfer size.....................51

Figure 4-6: TLT Control Processes and the communication paths............................................ 52

Figure 4-7: Typical TLT online timing histogram...................................................................... 53

iii


Figure 6-1: Scattered energy and angles of the electron and jet................................................ 59

Figure 6-2: Neutral current cross sections obtained using the MRS IVparameterization....................................................................................................... 60

Figure 6-3: Error bands for the measurement of the scattered electron energy and angle....... 61

Figure 6-4: Error contours for the measurement of 0 and y. .................................................... 63

Figure 6-5: Smearing of the kinematic variables for different reconstruction methods...........64

Figure 6-6: Migration true to reconstructed .v and Q~................................................................65

Figure 6-7: Smearing o f the kinematic variables after final selection cuts...............................66>■>

Figure 6-8: Migration o f MC events passing the final selection cuts in .v and Q~......................67

Figure 6-9: Reconstructed electron energy for the left and right side of the rearcalorimeter................................................................................................................ 68

Figure 6-10: Measured electron energy divided by the electron energy determined by theDouble Angle method...............................................................................................69

Figure 7-1: First order QED radiative corrections to the scattering electron............................71

Figure 7-2: Percentage of MC events having initial state radiation with a photon greaterthan 1 GeV................................................................................................................ 7 1

Figure 7-3: Effect of a 10 cm vertex shift on the reconstruction of . v ^ and ...................75

Figure 7-4: Typical histogram from the C5 veto counter............................................................ 76

Figure 7-5: Average interaction point determined from tracking and C5 as a function of therun number................................................................................................................77

Figure 7-6: Vertex distribution of photoproduction events.......................................................77

Figure 7-7: The vertex distribution used as input to the MC simulation..................................79

Figure 7-8: Vertex from different tracking programs................................................................80

Figure 7-9: FCAL time versus z vertex from tracking.............................................................. 81

Figure 7-10: Resolution of the calorimeter z vertex as a function of the FCAL energy............82

Figure 7-11: Trigger and selection acceptance............................................................................ 84

Figure 7-12: Calorimeter FLT efficiency as a function of Q ..................................................... 85

Figure 7-13: Calorimeter First Level Trigger efficiency as a function of energy and electronposition in the RCAL............................................................................................... 86

Figure 7-14: Resolution o f the scattered electron angle obtained from the MC simulation......87

Figure 7-15: Resolution o f the scattered quark angle obtained rrom the MC simulation..........88

Figure 8-1: Calorimeter time for events prior to a timing cut...................................................92

Figure 8-2: Reconstructed x and Q2 of muon candidates.......................................................... 93

Figure 8-3: The distribution of 8 for the Monte Carlo simulation............................................ 94

Figure 8-4: Resolution o f y as a function of the cut on y jg ....................................................... 95

iv


Figure 8-5: Fraction of the visible electron energy as a function of position in thecalorimeter for the MC simulation...........................................................................96

Figure 8-6: Effects of the three stages of event selection...........................................................97

Figure 8-7: Effects of the final selection cuts............................................................................. 99

Figure 8-8: Reconstructed .v and Q2 of MC photoproduction events passing the finalselection cuts........................................................................................................... 101

Figure 8-9: Event display of an electron-gas interaction..........................................................102

Figure 8-10: Event display of a cosmic event passing final selection cuts................................102

Figure 8-11: Event display of a beam muon event..................................................................... 103

Figure 8-12: Event display of an elastic QED Compton candidate........................................... 104

Figure 9-1: Systematic shift and resolution of x and Q2 determined from the MCsimulation................................................................................................................ 106

Figure 9-2: Correction factor and smearing for the final bins determined from the MCsimulation.................................................................................................................107

Figure 9-3: Data passing final selection cuts and the bins......................................................... 108

Figure 9-4: Effect of FLQC0 on Fo for different values of Q2...................................................110

Figure 9-5: FCAL energy versus y jg .........................................................................................111

Figure 9-6: Display of an event with a large rapidity gap........................................................112

Figure 9-7: The distribution of the data and the MC in r|max.................................................... 112

Figure 9-8: Fraction of events with a large rapidity gap versus Q2 in the DIS sample............113

Figure 9-9: Migration in x and Q2 of DIS events compared with events with a large rapiditygap............................................................................................................................ 114

Figure 9-10: Test of the unfolding procedure using the MC simulation.....................................118

Figure 9-11: Measurement of Ft from the data using different reconstruction methods......... 119

Figure 10-1: Systematic effects on the determination of F^...................................................... 131

Figure 11-1: Distribution o f data compared with the MC simulation....................................... 135

Figure 11-2: Measured values o f F2 as a function o f x for different Q2 bins............................137

Figure 11-3: F t versus Q~ for different values o f x .....................................................................138

v


List of Tables

Table 2-1: Design values o f HERA parameters......................................................................22

Table 3-1: The luminosity for the fall 1992 running period.................................................. 29

Table 3-2: Structure of a DU/SCI layer of the calorimeter.................................................... 37

Table 3-3: Summary o f the composition of a layer in FCAL and RCAL............................. 37

Table 3-4: Summary of the depth of the calorimeter for normal incidence.......................... 38

Table 4-1: Trigger configuration and prescale factors of the FLT for the differenttrigger configurations............................................................................................ 34

Table 4-2: Calorimeter trigger tower thresholds used for the different triggerconfigurations........................................................................................................ 33

Table 4-3: Summary of trigger configurations used during the fall runningperiod..................................................................................................................... 33

Table 7-1: RMS in MeV of the uranium noise for different cell types..................................72

Table 7-2: Number of events for the different categories of the vertexprescription............................................................................................................ S3

Table 8-1: Summary of the number o f events removed in the different eventselection stages...................................................................................................... 98

Table 9-1: Summary o f the quantities used in the unfolding procedure............................ 113

Table 10-1: The measured F 2 for different systematic checks............................................. 123

Table 10-2: Measured F2 for different systematic checks, continued................................ 126

Table 10-3: Measured F 2 for different systematic checks, continued................................ 127

Table 10-4: Measured F2 for different systematic checks, continued................................ 128

Table 10-5: Measured F2 for different..systematic checks, continued................................ 129

Table 10-6: Measured F2 for different..systematic checks, continued................................ 130

Table 10-7: Categories covered by the systematic checks.................................................... 133

Table 10-8: The systematic error determined for the different checks is listed for thebins...................................................................................................................... 134

Table 11-1: The measured cross section and F 2 .................................................................... 130

vi


1 Introduction

Early fixed target lepton scattering experiments have provided a powerful tool to study the

structure of the proton. Results from these experiments contributed to the development o f the

Quantum Chromodynamics (QCD) improved quark-parton model. This model describes our cur

rent understanding of the strong interaction, responsible for binding quarks in a proton. In the sum

mer of 1992 the two detectors H 1 and ZEUS began collecting data at the first electron-proton col

liding facility HERA (Hadron Electron Ring Anlage) at the DESY laboratory (Deutsches

Elektronen-Synchrotron) located in Hamburg, Germany. HERA provides electrons with an energy

of 26.6 GeV and protons with energy 820 GeV resulting in a center of mass energy of 295 GeV,

an order o f magnitude higher than at previous fixed target scattering experiments. This allows the

measurement o f deep inelastic scattering (DIS) in a kinematic region previously unexplored. Re

sults from the two collaborations, based on a integrated luminosity of 2 nb'1 collected during the

first running period during the summer of 1992, have been presented for the neutral current differ

ential cross section 111.

The differential neutral current cross section can be expressed as a model independent func

tion o f the two Lorentz invariants x and Q2 In the simplest model o f electron-proton scattering, the

electron scatters from a quark carrying a fraction x o f the proton’s momentum by the exchange of9 9a single virtual photon carrying a four-momentum q, where Q = - q . The proton structure function

F^x, Q2) embodies information about the internal structure o f the proton. In the QCD improved

quark-parton model, F 2 is interpreted in terms o f the momentum distributions o f the constituent

quarks. Both collaborations have presented a measurement o f the proton structure function [2]

based on a total integrated luminosity o f 30 nb"1, delivered by HERA during the second running

period during the fall o f 1992.

HERA is an excellent tool to probe the low x region and can extend the measurement of F^

to lower values of .v by about two orders o f magnitude. Scattering in the Iowa: region is dominated

by the sea quark distribution arising from quark pair production from gluons. Gluons cannot be

measured directly as they do not couple to the photon. Various gluon distributions which have been

postulated lead to significantly different cross section expectations in the low x region. A t very low

.v the standard linear QCD evolution equations have to be replaced by nonlinear equations which

account for recombination of quarks and antiquarks as their density increases. For high parton den

sities, the assumption that the struck quark does not interact with neighboring partons is no longer

valid. These effects make studying the Iowa- region interesting. In addition, a correct and accurate

description of the structure function is needed as input to Monte Carlo (MC) simulations for future

colliders.

1


This thesis presents the method and the results of the first measurement of the proton struc

ture function F i using the ZEUS detector. It starts with a brief description of the historical devel

opment of the QCD improved quark parton model. An overview of physics at low x is presented

in order to give a perspective o f the new phenomena expected. Assumptions and methods used to

obtain parton parameterizations are explained in Section 1.5. Some of the designed and operating

characteristics of HERA are presented in Section 2. The relevant components of the ZEUS detector

and their status during the fall running period, are described in Section 3. A description of the

ZEUS online trigger with an emphasis on the Third Level Trigger is provided in Section 4. The

kinematics at HERA, along with a comparison of different kinematic reconstruction methods are

presented in Section 6. The MC simulation is described in Section 5 and details of the reconstruc

tion is described in Section 7. Selection cuts used to obtain a clean DIS data sample and the meth

ods used to control the background are presented in Section S. A detailed description of the method

used to determine F2 is presented in Section 9, and the sources o f systematic errors are discussed

in Section 10. Finally, the implications of this measurement are discussed in Section 11.

1.1 Development of the QCD Improved Quark-Parton Model

Electron scattering is mediated by the exchange of a single virtual photon transferring

four-momentum q from the electron to the proton as shown schematically in Figure 1-1. The inci-

Figure 1-1: Electron scattering fro m a proton by the exchange o f a single v irtua l photon.

The incident electron has four-m om entum denoted by k and the scattered electron has four-momentum k . The incident

proton has four-m omentum labelled p. The momentum transfer carried by the v irtua l photon is labelled q.

dent electron has four-momentum denoted by k, and the scattered electron has four-momentum la

belled k ' . The initial proton four-momentum is labelled p. By neglecting the proton’s mass, M , and

assuming a head-on collision, the expression for center o f mass energy squared can be related to

the energy of the incident electron E and the energy o f the incident proton H by

s = (k + p ) 2 = 4EH. ( l- i)

2


The lepton’s energy loss in the frame for which the proton is at rest is given by

( 1-2 )

The mass squared of the system recoiling against the lepton is

IV2 = (< /+ /;)2 = 2 M v + M 2- Q 2.

For convenience, the positive quantity Q is defined as

(1-3)

Q2 = - q 2 = - { k - k ' ) 2 = sxy. (1-4)

This quantity and the two scalars defined below are commonly used to describe event kinematics.

In the quark-parton model, the scalar defined as

is interpreted as the fraction of target nucleon’s momentum carried by the struck quark in the parton

model. Finally, the fraction of the energy lost by the lepton in the frame for which the proton is at

rest is

As w ill be seen, the cross section for scattering electrons from a proton has a simple form wheniy

expressed in terms of the scalars x and Q . A detailed derivation of the kinematic variables in terms

of measured quantities relevant at HERA can be found in [3]. In Section 6.1 the kinematic variables

x, y and Q2 are expressed in terms of the measured quantities at ZEUS.

In 1950 Rosenbluth [4] calculated the probability o f elastic scattering of an electron from

a proton assumed to have an extended structure and spin 1/2. The Rosenbluth formula for the elas

tic scattering cross section in the fixed target frame is

dadQ.

+ 2 x 0 ^ (Q 2) tan2 (0 /2 ) (1-7)

where

x = Q2/ {AM2) . ( 1-8)

3


For a fixed electron incident energy, the scattered electron energy E '. in the frame for which the

proton is at rest, is determined by the scattering angle a from

E' = -------------- . U -‘»l + ^ s in - ( 0 / 2 )

In the fixed target frame, the scattered electron energy w ill always be less than the incident energy

since energy is transferred to the recoiling proton. The Mott cross section |5|

a 2 cos2 (0 /2 )a M (£ ) = — , — 1---------- d-io)

M 4 E- sin4 (0 /2 )

is the cross section for elastic scattering of spin 1/2 particles from spin 0 point-like particles. The

fine structure constant a = 1 /137 determines the magnitude of the electromagnetic coupling.

In 1953, Hofstadteretal. | 6 | found evidence for elastic scattering of electrons from a proton

at the newly commissioned linear electron accelerator, MARK 111 in the High Energy Physics Lab

oratory (HEPL) at Stanford. Electrons up to an energy of 225 MeV were scattered from a polyeth

ylene target. The target was later replaced by a hydrogen gas target and in 1955 evidence was pre

sented indicating that the proton form factors decreased with increasing Q~. They estimated thatI -3

the proton was (0.7 ± 0.2) X 10 cm in size. The success of the scattering experiments at HEPL

led to the proposal for a two mile long linear electron accelerator, the Stanford Linear Accelerator

Center (SLAC).

In Equation (1-7) the electric form factor Gpp and the magnetic form factor GMp describe

the structure o f the proton. In the nonrelativistic lim it the squares o f these functions are the Fourier

transforms o f the spatial distributions o f the electric charge and the magnetic moment. For Q2 up>y

to about 10 GeV , the function GMp can be approximated by the dipole formula |7| having the form

G MP = T 2 ( | - " J(1 + Q /0 .7 1 )

ry ry

where Q is measured in GeV . The magnetic moment of the proton is denoted by g and has a value

of 2.79. The electric form factor is related to the magnetic form factor by

r _ GMpE p j p - ( M 2 )

Figure 1 -2 shows the dipole formula fit to the data obtained from SLAC. For high Q the cross sec

tion is dominated by G ^p which gives rise to a 1/Q6 factor relative to the Mott cross section. This

4


30

Figure 1-2: D ipole approximation.The electromagnetic fo rm fa c to r o f the proton fo llo w s the dipole fo rm u la . D ata fro m SLAC. F igure taken fro m [8 ].

steep fall o ff can be interpreted as the target particle having an extended electric and magnetic dis

tribution.

The observation of the production o f heavy mesons and baryons in cosmic ray experiments

was unexpected. They were referred to as ‘strange’ particles due to their strange behavior of being

produced at a short time scale and decaying on a longer time scale. This difference of time scales

suggests that the mechanism for the production of these particles is different from that leading to

their decay. Gell-Mann and Nishijima [9] introduced a new quantum number called strangeness

which is conserved in strong interactions but not necessarily conserved in weak interactions. This

new conservation law was used to explain the observed production o f strange particles and why

other processes were not observed.

In 1961 Gell-Mann introduced the Eightfold Way [10], a classification o f the observed par

ticles based on their charge and strangeness using the SU(3) group. The same scheme was inde

pendently proposed by Ne’eman [11|. The classification was reminiscent o f Mendeleev’s periodic

table, and like Mendeleev they found that their classification scheme had missing entries, leading

to the prediction o f a particle with charge 1 and strangeness -3. In 1964 then ' was discovered [12]

with the predicted characteristics. Hadrons which were subsequently discovered fit into one of the

Eightfold Way multiplets.

In 1964 Gell-Mann and Zweig [13] independently postulated that hadrons consisted of el

ementary constituents. These constituents, named quarks by Gell-Mann, provided a heuristic tool

to classify the hadron spectrum. The quarks, coming in three flavors up («), down (d) and strange

(,v), could be combined to construct hadrons with the same properties and patterns as in the Eight

'S


fo ld Way. The quarks were assigned a fractional charge: u has charge 2/3c and d and s have charge -l/3e, where e is the charge of the electron. Figure 1-3 114| shows the baryon octet which includes

S =

S =

S =

n (add) p (and)

Z + (a as)IT (dds)

A (uds)

(dss) E® (uss)

0 +

Figure 1-3: The baryon octet o f the E ightfo ld Way.

The quark content o f the partic les in this m ttltip let is shown in brackets. The two particles in the center have the same

quark content, however the spin arrangement o f the quarks are different. Particles in the same row have the same

strange (S) quantum number. Particles aligned d iagonally have the same charge (Q).

the proton. The quark content o f each particle is shown in the brackets. The two particles in the

center have the same quark content, however the flavor component of the wave function describing

these two baryons are different. A more detailed discussion can be found in reference 114|.

A t that time, the picture that the proton consisted o f quarks was not widely accepted. A se

ries of electron scattering experiments at Stanford Linear Accelerator (SLAC) 115 1 began in late

1967 which eventually led to the acceptance o f the quark-parton model. The first inelastic scatter

ing results were reported at Vienna in 1968 1161. The measured cross section showed little depen

dence with momentum transfer at fixed .v as shown in Figure 1 -4. This feature is expected for scat

tering from a point-like object.

For inelastic scattering in the fixed target frame, the differential cross section is

d2a= o m {E) [W 2 (v, Q2) -+- 2 W j (v, Q2) tan2 (0 /2 ) (1-13)

6


In e lo s l ic

E lo s t ic

)-3

0 0 .5 1.0 1.5 2.0 2.5Q 2 [ [ B e V / c ) 2]

Figure 1-4: Inelastic scattering cross section compared w ith elastic scattering cross section.

The inelastic cross section shows l itt le dependence with Q2. The data is fro m SLAC. F igure taken fro m [8 ].

The structure functions, W\ and W2, embody all the information at the proton vertex from scatter

ing unpolarized electrons from an unpolarized proton target. For comparison, the elastic differen

tial cross section given in Equation (1-7) can be recast in the form

^ = g m (£ ) [ | ] [K 2 (Q2) + 2 K l (Q2) tan2 (6 /2 ) ] . (1-14)

For inelastic scattering, the target proton can absorb a range of energies and for a fixed electron

scattering angle the cross section has a functional dependence on the scattered electron energy. The

structure functions Wj in Equation (1-13) which replace Kj in Equation (1-14) are functions o f two

variables instead of one as in the case of elastic scattering. Bjorken had postulated [17] that the

structure functions, W\ and vW^, would become functions o f the single variable x = Q / (2Mv)

in the lim it that Q~ approaches infinity where x is fixed:

M lf , (v, Q2) -» F , (x) (1-15)

vW M v,Q 2) -> F 2 ( jt ) . (1- 16)

9 9This property, called ‘scale invariance’, is experimentally observed for Q >1 GeV and W > 2

GeV as is shown in Figure 1-5 [ 18J. In the figure the structure function vW2 (or F2) is plotted versus

Q2 (labelled q2) for.v = 0.25. The data shows that vW^ is not dependent on Q2 for this value of r .

At that time Feynman had been trying to explain hadron interactions at high energies by using a

model assuming constituents he called partons. The naive parton model describes the proton as

7


constructed from point-like partons. from which the electron scatters incoherently. This model pro

vides an explanation for the observed scaling behavior.

+ 6° □ 18*x io* a ?6*

I |» 4 , tfc . |

x = 0.25

j_____ I--------- 1_____ I_____ i_____ I_____ i_____ I0 2 4 E a

q*. GeV/c1

Figure 1-5: Evidence fo r scaling.The structure function vH/; (o r T \) is plotted versus Q~ (labelled i f in tlte fig u re ) f u r x = 11.25. The luck o f dependence

on Q~ indicates scaling. Data fro m reference | 18|. Figure taken fro n t reference |X|. Data was collected at the fo u r fixed scattering angles indicated by the different symbols in the figure.

The ratio of the cross section o f the absorption of longitudinally polarized photons to trans

versely polarized photons is related to the structure functions:

(1 + ( 4 M 2x 2) / Q 2) Fq - 2xF,R = a , / a T = ----------------------- --------------------------------. d -17 )

L 1 2 x F {

Assuming the parton model o f the proton, it was shown by Callan and Gross in I%X 119|, that R

is dependent on the spins of the partons. Callan and Gross predicted that for spin 1/2 partons, the

ratio o f the structure functions 2xF\jF i = 1, while for spin 0 or spin I partons the ratio would

equal 0. This follows from helicity conservation which prohibits the absorption of longitudinally

polarized photons by spin 1/2 partons. As shown in Figure 1-6 the data clearly supports spin 1/2

partons [20].

QCD describes the radiation o f gluons from quarks and the production of virtual pairs of

quarks from gluons and provides equations relating the quark momentum distribution at one scale

of the transferred momentum to the quark momentum distribution at another scale. Quarks arising

from pair production are referred to as sea quarks, u, d and ,v. Valence quarks, u and d, refer to the

quarks giving the proton it ’s quantum numbers. Since the mechanism for production of different

flavors o f sea quarks is the same, one assumes that the momentum distributions of all the sea quarks

are the same

8

0.5

0.4 -

0 .3 -

»w20.2 -

0.1 -


Spin }

SpinO

1.00.5

Figure 1-6: Evidence f o r scaneringfrom spin 1/2 parlous.

In the f ig u re Q~ is denoted us c f . F o r scanering from spin 1/2 parlous, the ra tio o f2 xF j/F 2 is expected to be equal to

one in the lim it o f large Q2 while fo r spin 0 partons the ra tio is expected to be zero. The fig u re taken fro m [8 ] shows compiled published SLAC data.

u (a) = d (a-) s s (a) = sea (a). (1-18)

The it and d quark distributions w ill thus have components arising from a valence quark contribu

tion, denoted by the subscript v, and a sea contribution denoted by sea:

u (a) = uv (a) + sea (a)

d (a) = dv (a) + sea (a) .(1-19)

The naive quark-parton model makes the assumption that the electron scatters from a

charged parton having spin 1/2. During the interaction the quark does not interact with surrounding

partons. In terms of the quark momentum distributions, the structure function can be written as

F 2 (-v) - X [ V(Z/(-v) +a^/ (a )]c ( 1-20)

9


where the sum extends over the number of flavors of quarks and ej is the electric charge of a quark

with flavor/. Since the quark content is dependent on the baryon type, there is a different F i for different baryons. For three flavors. Equation (1-20) can be expressed as

F , (.v) = ^.v |4mv ( a ) + r/v ( a ) + 12,'\ e a ( a ) ] t l-2t>

where the numerical factors are the result of the quark charge. The factor 12 in front of.vrt/ is ob

tained from 4ms + 4i7v + dK + ds + ,vs + ,vv.

Making use of the Callan-Gross relation, the differential cross section expressed in the fixed target frame takes on the simple form

da (x) a 2 2EE' ->i c ,. ,Q /0J ( 1 + , cos- ( 9 / 2 ) ) . (t-22)

dQ.dE' 2M Fsin ( 0 /2 ) v ( £ - £ ' ) 2

This equation describes the cross section in terms of a function which is only dependent on the sin

gle variable a , and F\ and F 2 are related by the Callan-Gross relation, F 2 = 2.vF,.

In the quark-parton model the relation

1 1 1

J V 2 (a :) dx = 5 J [ f ;2 (a -) + F 2 ( a ) ] dx = I « (a ') + u (a ) + i l (.v) + d (x) | r/.v (1-22) 0 0 n

is valid when the strange quark contribution is neglected. The integral on the right side equals 5/1S

o f the total momentum carried by the quarks. The measured value was found to be 0.14 ± 0.005

115], about half the expected value assuming that the quarks carry all the momentum of the proton.

This result suggests that the remainder of the proton’s momentum is carried by something which

does not couple to the photon. Early neutrino experiments also supported this observation 12 11. In

the QCD model, the missing momentum is postulated to be carried by gluons, which are the medi

ators o f the strong color force responsible for binding quarks within a proton.

The addition o f gluons leads to F2 scaling violations and the quark densities become func-9 9 9tions of both A" and Q . The parton distributions as a function of a for Q - 15 GeV are shown in

Figure 1-7 for two different parameterizations. Once the A distribution of the quark density is de-

10


. MRS D_' . MRS D0'

0 .3

xur (x)0.6

xciv(x)

0.2

X

Figure 1-7: Parton d istributions o f the proton.

Two parton parameterizutions [33] are shown which have different assumptions about the gluon distribution. See Section 1.5 fo r more details on parton parameterizutions. F o r lo w x the sea quark d istributions which arises fro m p a ir

production by the gluons dominate. The gluon d istribution is not well known and the different parameterizations lead

to s ignificantly different predictions f o r the cross section.

9 9termined for a given Q , the Q evolution of the quark densities is determined by QCD dynamics

from the Gribov-Lipatov-Altarelli-Parisi equations (GLAP) [22] [23]:

(hii ( v, Q2) _ a ( Q 2) [r dy, . ^2 9 TT I „ I

d\nQ

dg (jt, Q1) _ a , ( g " ) f dy

2tT ~J j \ p t ^ p ^ Q 2^ p q g ( p s ( y , Q 2)x

d \n Q 2 271 - . Ly

(1-24)

(1-25)

The strong coupling constant describing the strength of the strong force is denoted by as and to

lowest order is given by

a S{Q~) =1 2 tc

(33 - 2/y) log (Q 2/ A 2) ’(1-26)

11


where A sets the scale at which ns becomes large and the perturbation description is not justified.

The value of A is not predicted by QCD and has to be determined from experiment. The splitting

function, (as/2ii)Pljcj(x/y), gives the probability of finding a quark with momentum fraction v which

originated from a quark with momentum fraction y. The Feynman diagram which corresponds to

the first term o f Equation (1-24) is shown in Figure 1 -8a. A quark with initial momentum fraction

Figure 1-8: Lowest order Feynman diagrams which lead to sealing violations.

y radiates a gluon and the final quark now curries a momentum fraction x. The second term of

Equation (1-24) is shown in Figure l-8c. A gluon with initial momentum fraction y produces a

quark-antiquark pair, one o f which carries a momentum fraction x. A similar equation for the gluon

density evolution is given in Equation (1-25).

The emission o f gluons gives quarks a transverse momentum leading to a small correction

to the Callon-Gross relation which is valid in the scaling lim it of free quarks. The longitudinal

structure function

g(y.u’ )

Fl = ( \ + 4 x 2M 2/ Q 2) F 2- 2 x F i (1-27)

12


describes this correction and can be predicted by QCD. The size of the correction is largely depen

dent on the gluon distribution and increases with decreasing*. The effect of is described in more

detail in Section 9.2.

To summarize, in the QCD improved quark-parton model, the proton is viewed to be com

posed of quarks having spin 1/2 and which carry fractional electric charge. Scattering is mediated

by the exchange of a virtual photon between the electron and a quark. The interaction can occur

with one of the valance quarks or a quark from the sea distribution. The resolving power o f the vir

tual photon probe increases with Q2 and large Q2 allows probing more virtual processes. The par

ton distributions are universal and describe interactions of different processes. The interaction

shown in Figure 1-1 is shown in more detail in Figure 1-9.

r e m n o n t je tcmi V

w r y

t a r g e t j e t

Figure 1-9: lilectron proton interaction mediated by a v irtua l photon.

The v irtua l photon emitted bv the electron scatters o f f o f a sea cptark created by p a ir production fro m a gluon radiated

from one o f the valance quarks.

1.2 Compact Form of the Differential Cross Section

"7 • .At high Q~ the single photon exchange, discussed above, must be modified to include the

exchange of the Z°. The most general form of the differential neutral current cross section in lead

ing order electroweak theory, including Z° exchange, can be expressed in the compact form

d

where

Y+ = 1+ (1 - v ) -

Y = 1 - (1 - y ) 2.J (1-29)

The nucleon structure functions are related to the quark density distributions by

J L = 7 1- 2 x ‘J x (l-:tO)

J 2 (-v ’ 2 ‘ ) - £ ^ / / ( , , Q1) -\-xc(j (.v, Q 2)^Af(Q~)

xJ?, (x, Q2) = X Q 2) ~xcjf (x, 0 2)]

(1-31)

( 1- 12 )

where the sum extends over the quark flavors. The function y2 is the generalized structure function

which includes the effects of Z() exchange as well as photon exchange. The structure function / ‘2

only includes photon exchange. The quark momentum distributions, given by xc/, are functions of

x and Q2. The coefficients, Ay and By are functions of Q2 and for a unpolarized lepton beam they

are given by

Ay(Q2) = e j - 2 e f vf vcPz (Q2) + (v j + a j) (v2 + a2,) P2 (Q2)

Bf (Q2) = - 2ejajaePz (Q2) + 4 W ,at,B2 (Q2) .(1-32)

The first term of Ay arises from the exchange of a virtual photon and gives F2. The last term is the

result of Z° exchange and the middle term is the interference term. The neutral current axial cou

pling

j3ar = . 4 (1-34)1 sin20(V

and the vector coupling

T2f - 2t'/s in20u/v , = f . - 4 ----- ^ (1-35)j sm 20^

are both expressed in terms of the third component of the isospin, T y , and the Weinberg angle, Qw.

The electric charge of either the quark or the lepton is denoted by ey. The subscript e in

Equation (1-33) refers to the electron.

14


The term

P/SQ2) = - 3 ^ - 2 d-36)QT + My

contains the mass o f the Z() boson, which is about 91 GeV, denoted by My. For small values of Q2

terms with Py can be neglected and the cross section is dominated by the exchange of a single vir

tual photon. The effect that Z° exchange has on Fy is shown in Figure 1-10. In the figure, F2 was

5 |-----------------------------------------------------------------------------------------------7--------- :------------------ 7

F, \ MRS D.' Kinematic Limit

(F ,=26 .6 GeV Ep= 8 2 0 GeV)

F,(?) / / F2 ( y + Z ° y / x = 0.00042 /

S x = 0.00065

c = 0.0017

" V = 0.0049

x = 0.032

10 10 10 10' 10 Q2 (GeV2)

Figure 1-10: The effect o f exchange on F t .

The kinematic l im it at HERA operating with electrons at 26.6 GeV and protons at 820 GeV is shown as the so lid line.

The dashed line shows F t calculated assuming y exchange only. The effect o f /P on F t is shown as the dotted line. The

MRS I ) . ' parameterization was used f o r the quark distributions. The effects o f 7? can be ignored f o r the current range

oxer which F t is measured.

calculated using the MRS D_' parameterization for the parton densities. The x values shown in the

figure correspond to the values of x for which is measured by the ZEUS collaboration. The range

in Q2 that can be reached at HERA operating with electrons of 26.6 GeV and protons of 820 GeV

is shown as the solid line. The dashed line shows F 2 assuming the exchange o f only a photon. The

dotted line shows Fo including the interference term and Z° exchange term. The effect o f Z° ex

change becomes significant only beyond the kinematic reach for the values o f x shown. For this

15


measurement of Fn, the effect o f Z(l is ignored and single virtual photon exchange is assumed. Scaling violation, predicted by QCD, is apparent in the figure.

When considering only single virtual photon exchange, the differential cross section can be

simplified to the familiar form

c fa NC 27ta2K ,, 2° " ° f , = 7 - ^ 3 = — j r (F2 - f F0 •'• dxdQ xQ 1 +

The measured differential cross section, a, can be split into a term arising from the structure func

tion F2 and a second term which is due to F^. FL has nonzero values due to the transverse momen

tum o f the quarks which arises from the Fermi motion of the quarks within the proton and the trans

verse momentum obtained by the radiation o f hard gluons by the scattered quark. When determin

ing F 2 from the measured cross section, the effects of FL has to be taken into account as is discussed

in Section 9.2.

1.3 Small x Behavior of the Structure Function

For reviews of physics at low.v see reference |2S], For small values of.v and high values of

£22, the GLAP evolution equations result in F2 rising indefinitely with decreasing x. The rising F t

is the result o f the increase in the quark density due to pair production from gluons. However, the

increase o f the total cross section with energy is limited by the Froissart bound |24| which requires

that the growth of the cross section does not grow faster than the square of the hadron radius

= ( * • Q2) - 2 k i '2 ( • '') (1 ‘ 3K)

where

r (s ) ~ const • In s. (I-W)

One expects that recombination of quarks and antiquarks w ill occur, preventing the continued in

crease of the parton density and hence F ^ This recombination can be represented by the addition

o f a nonlinear term to the standard GLAP equation and gives rise to the Gribov-Levin-Ryskin

(GLR) evolution equation [25]

? 2 1d (xu (x, O2) ) const a ; ( 2 ) Cdv 2

■■ f ~: = Pgg ® g + P.,q ® q ---------2 -2 -------- [ - 7 yg iy, Q ) • (I-40)d\nQ u 1,1 R2Q2 J y

X

The contribution o f the nonlinear term is controlled by R, which can be interpreted as the size of

the region within the proton from which the gluons originate |26|. This nonlinear term leads to a

16


more slowly rising/-^. For evenly distributed gluons the value o f R is 5 GeV'1. If one assumes that

the gluons are concentrated around the valence quarks, as in the Hot Spot scenario [27], the value

of H would be less, around 2 GeV'1.

1.4 Measured Regions in x and Q 2 Phase Space

The region in the x and Q2 plane for which F2 has been measured by some current lepton

scattering experiments is shown in Figure 1-11. The SLAC data for ep scattering was recently re-

ZEUS

BCDMS NMC SLAC EMC a

a

10

110 1

Figure 1-11: Regions in the x and Q~ plane f o r which structure functions have been measured by recent experiments.

In it ia l results fro m HERA have provided a measurement o f the proton structure function in a region o f x and Qr phase

space previously unexplored.

analyzed with improved radiative corrections [29]. The SLAC data was obtained from scattering

electrons from hydrogen with Q2 in the range 0.6 GeV2 < Q 2 < 30.0 GeV2. The Bologna, CERN,

Dubna, Munich, Saclay (BCDMS) experiment [30] involved the scattering o f muons from a hy

drogen target. The incident beam energies were 100,120,200 and 280 GeV. The range in a : and Q2

covered is 0.06

The European Muon Collaboration (EMC) measured the nucleon structure function by scattering

muons on a deuterium target [36]. The range in Q~ covered is from 7 to 170 GeV" and .v ranged

from 0.03 to 0.75.

1.5 Parton Parameterizations

The QCD improved parton model provides an interpretation of measured cross sections in

terms of quark densities. It does not provide a prediction of the parton distributions: however the

QCD evolution equations allow us to determine the Q~ behavior of the parton distributions starting

from a given distribution in „v at a reference Q~. Usually simple functions are used to parameterize

the parton distributions, with a chosen functional form coming from experimental and theoretical

considerations. The functions parameterizing the parton distributions are then evolved through the

GLAP evolution equations or evolution equations which account for the recombination of quarks

and antiquarks.

The parton distributions at low a- measured in ep interactions are needed as input in MC'

simulations o f hadron-hadron interactions to estimate backgrounds to signals of new physics at

hadron colliders.

A method commonly used to determine the parton distributions is the global fit method.

This method starts with a parametrization of the parton distributions at a reference Q~ and evolves

the distributions in the region in which is measured. The starting parameters are adjusted until

a good f it to the measured structure functions is achieved. Several recent parameterizations have

included the new high precision data available from the NMC collaboration which extends the9 9measurement o f F2 to x of about 0.01 for Q =5 GeV . Values of F 2 extrapolated to the low x re-

gion obtained from some recent parton parameterizations is shown in Figure 1-12 for Q~ = 15

GeV'2. For comparison, an older parton distribution set, Kwiecinski-Martin-Roberts-Stirling

(KMRS) Bq [32], which fails to reproduce the rise in F 2 observed by NMC is shown. The inclusion

o f the NMC data in the global fit, leads to much higher values of when extrapolated to low a .

The behavior at low a* for the parameterizations shown in the figure are quite different. This differ

ence is mainly due to assumptions on the shape of the gluon distribution which determines the sea

quark distribution at low x.

The Martin-Roberts-Stirling (MRS) set 133] is based on a global structure function analysis

using data from the NMC [34], BCDMS [35], EMC [36|, CCFR |37|, CDHSW |38|, WA70 ]39|,

and E605 [40] collaborations. The best f it to the data is parametrized as the MRS D()' set. The usual

assumption o f a flavor symmetric sea was relaxed and u (x ) < d ( x ) was allowed. This inequality

is suggested by the NMC measurements of the ratio of the deuteron to the proton structure function

18


\

\ \ Q2 = 1 5 GeV2 .....MRS D0' MRS D.'

\ \ CTEQ1M\t CTEQ1 MS

__ GRV HO\ KMRS B0

: •,

\\\\

NMC data

............ 1 ............ .,1 ......... . . . i , , ,0 4 1 o3 1 o2 10-1 1

X

Figure 1-12: Low x extrapolation o f I'? fo r some recent parton parameterizations.

The KMRS line is an o ld set which does not accommodate the new high precision low x N M C data. The new sets

using the recent N M C data a ll predict a fas te r ris ing F t at low x compared with o lder sets. The parton parameterizations diverge in the kinematic region available to HERA.

F 2/ F l2 leading to a low value of the Gottfried sum rule [41] in the measured interval at

Q2 = 4 G eV2. The Gottfried sum rule is given as

l l l

= \ \ d x { u s - d v ) + \ ^ d x { M - d ) (1-41)

0 0 0

where the expected value for a flavor symmetric sea is 1/3. The difference FlJ - F 2 can be ex

pressed as F l ~ F n2 = 2Ft (1 - F " /F ? ) / ( I + Fl) / F \ ) where F2 / F \ s 2 F d2 / F \ - \ . The EMC

measured the ratio o f the deuteron to the proton structure function and used published measure

ments of F 2 to obtain the result [42]

0.8

J ^ ( F ? - F 2 ) = 0.227+0.007 (s ta t )±0.014 (s y s ) . (1-42)0.004

19


The MRS D_' set also uses a parameterization for the gluon distribution which tends to a constant

at .v = 0. The MRS D_' parametrization uses a singular distribution for the gluon and the sea.

xg (.v), xq (x) - x~l/2 leading to a stronger rise in F2 at low .v.

The CTEQ collaboration (Coordinated Theoretical/Experimental Project on QCD) also

performed a global structure function analysis with the evolution starting at Q,2 = 4 G eV ' 1431.

They also allowed for a flavor antisymmetric sea u (.v) * d ( x ) . The best fit to the data is given by

the CTEQ1M parametrization which has a finite gluon distribution for.v = 0. The CTEQ IMS pa

rameterizations have a singular gluon behavior with xg (.v) ~.y_1/2. The singular fit leads to a

slightly higher F2 than the nonsingular f it but it is not as dramatic as the MRS D_' set.

An alternative approach to fitting parameterizations to the F2 data is used in the Gliick-Reya-Vogt (GRV) [44J [45] sets. They start with valence-like parton distributions at a low

Q2 scale, p2 = 0.2 - 0.3 GeV2, which tend to zero as .v —> 0. For Q2 > g2 the gluon and sea dis

tributions are generated radiatively by QCD dynamics from the initial valence distributions at9 9 9Q = g . The value o f g is fixed by energy-momentum conservation and is determined from a

measurement o f the nucleon structure function at

2 HERA

The world’s first electron-proton collider HERA [47j, located at the DESY laboratory in

Hamburg Germany, was authorized in April 1984 and began operation for experiments in the sum

mer of 1992. It was built by an international collaboration from Canada, China, CSFR, France,

Germany, Israel, Italy, Netherlands, Poland, United Kingdom, and the USA. HERA consists o f two

separate storage rings. The proton ring uses superconducting magnets and stores 820 GeV protons.

The electron ring uses conventional magnets to store 30 GeV electrons. During the fall 1992 run

ning period, the energy of electrons was limited to 26.6 GeV since not all o f the accelerator cavities

were installed. The layout o f the HERA accelerator is shown in Figure 2-1 and some of the design

characteristics of HERA are listed in Table 2-1.

HallNorth

HallEast

HERAHallWest

60 GeV ( protons

PETRA

16 GeV electrons

HallSouth

Figure 2-1: The HERA accelerator.

The experiment I I I is located in the north h a ll and ZEUS is situated in the south hall. The preaccelerators are located

on the DESY laboratory site and the HERA ring extends into the surrounding neighborhood. The preaccelerators are

shown in more detail in F igure 2-2.

The proton injection system begins with a newly built H" 50 MeV linear accelerator. Before

injection into the DESY III storage ring, the hydrogen ions are stripped. DESY III is filled with 11

bunches, having the same bunch spacing as HERA, 96 ns, and accelerated to 7.5 GeV. The proton

bunches are then transferred to PETRA II. Seventy bunches are accumulated in PETRA II and ac-

21


celerated to 40 GeV, then transferred to HERA. The process is repeated until HERA is filled with 210 bunches.

HERA Parameters electron proton

Energy (GeV) 30 820ry 1

Luminosity (cm s ) 1.5 x lO 31

Circumference (m) 6336

Magnetic Field (T) 0.165 4.65

Energy Range (GeV) 10-33 300-820

Injection Energy (GeV) 14 40

Circulating Current (mA) 58 163

Number of Bunches 210

Time Between Crossings (ns) 96

Horizontal beam Size ox (mm) 0.26 0.29

Vertical beam Size oy (mm) 0.070 0.07

Longitudinal beam Size oz (cm) 0.8 11

Filling Time (min) 15 20

Table 2-1: Design values o f HERA parameters.

The electron injection begins with a 500 MeV linear accelerator (LINAC II) which is used

to f i l l a storage ring (PIA) with a single bunch of 60 mA. The electron bunch is then injected into

DESY II, where it is accelerated to 7 GeV. It is then transferred to the modified PETRA II storage

ring. The process is repeated at a rate of 12.5 Hz until 70 bunches each having about 0.4 x 10*1

electrons are accumulated in PETRA II. The electron bunch spacing in the PETRA II storage ring

is the same as the spacing in HERA. The electrons are then accelerated to the HERA injection en

ergy o f 14 GeV and transferred to HERA. This process is repeated until HERA is filled with 210

bunches. Electrons in HERA are then accelerated to the final energy. The injection scheme is

shown in Figure 2-2.

The two detectors, H 1 and ZEUS started collecting data during the summer of 1992. A total

integrated luminosity of about 3 nb'1 was delivered by HERA during the first running period which

lasted from June 23 to August 1 1992. The second running period began on September 20 1992

and continued until November 8 1992. During the fall running period HERA operated with only 9

colliding bunches having a total current o f 1-2 mA. Unpaired bunches, called pilot bunches, also

22


HERA Injection Scheme

PETRA Halls N

PETRA Hall NEPETHA Hall NW

HERA i Hall West

c'.e'i Cryo- 1 Technic Llnac \\

Positron U nac,PETRA Hall W

i PETRA HallE

PI A«

OESY

PETRA'7 GeV

7 GeV, PETRA HallSEHERA

Proton bypass

Figure 2-2: HERA injection scheme.

The injection scheme is described in the text.

circulated and are used to estimate beam related background rates. The proton bunch length was

typically 12 to 50 cm. The highest luminosity observed by ZEUS during the running period was

1.5 x 10® c m 'V 1. A total of about 30.5 nb'1 was delivered by HERA o f which 24.7 nb"1 is used

for the extraction of F2 by the ZEUS collaboration.

A secondary electron bunch (satellite bunch) was present in PIA following the main bunch

at S ns. The spacing o f the satellite bunch is the result of the 125 MHz RF operating frequency of

PIA. These satellite bunches are accelerated along with the main electron bunches and are injected

into HERA. The satellite bunches result in electron-proton interactions 1.2 m from the nominal in

teraction point. However the online trigger timing cut and the offline timing cut remove these

events from the final sample (see Section 8.1). The satellite bunches contribute to the luminosity

measurement and this effect has to be corrected for in order to obtain the luminosity corresponding

to the main electron bunches. The effect o f the satellite bunches on the determination o f the lumi

nosity is discussed further detail in Section 3.2. A plot of the luminosity versus run number is

shown in Figure 2-3. The solid curve shows the ZEUS accumulated luminosity after corrections

for electron satellite bunches. The luminosity before the subtraction o f the satellite bunches is

shown as the dashed curve.

23


Be fo re sate l l i te bu nc h su b t ra c t i o n

A f te r sa te l l i te bu nch s u b t ra c t io n>, 30V)0 c1 20

•oa)oU003LlJN J

4100 4200 4300 4400 4500 4600 4700R u n

Figure 2-3: ZEUS accumulated lum inosity fo r the runs taken during the fa l l data taking period.The accumulated lum inosity before sttbtractio.: o f the sate llite bunch is shown as the dotted line. The solid line shows

the corrected lum inosity a fter the satellite bunch was subtracted. UlsRA delivered a total integrated lum inosity o f MIS

n b '1. A fte r retaining runs fo r which the detector was operating well, the total integrated lum inosity was 2-1.7 n l r 1.

24


3 The ZEUS Detector

The main components of the ZEUS detector are shown in Figure 3-1. In the ZEUS coordi

nate system, protons travel in the positive z direction and electrons travel in the negative z direc

tion. The x coordinate points towards the center of the HERA ring, and the y coordinate points up

wards. The electron polar angle, e, is measured with respect to the positive z axis. The azimuthal

angle,

enters the FCAL. The shaded regions in the calorimeter shown in the view on the left, represent energy deposits. The electron track can he seen in the ip view of the CTD presented in the top right

corner. The tracks are drawn from the last CTD hit and extrapolated to the distance of closest ap

proach to the beam line. The transverse momentum, p j . of the electron balances the p-y of the had

rons. Only three superlayers of the CTD were active during this running period. The lower right

Zeus Run 4 4 8 5 Event 5 0 8 7 5,ZEUS

Figure 3-2: Event display o f the highest Qr event used in this analysis.The event had a reconstructed Q~ o f4700 GeV2 an dx o f 0.06. The electron is scattered backwards into the I-CAE. The

views shown are described in the text.

view shows energy deposited in the calorimeter. The energy determined from the left and right

photomultiplier tubes (PMT) are shown separately as the histograms in the figure. Details of the

calorimeter readout are described in Section 3.4. The values of the kinematic variables displayed

in the figure do not make use of the event vertex and are different from values determined by this

analysis. The kinematic variables are related to the measured quantities in Section ft. I .

In the following sections, the performance and characteristics of the components used in

the analysis are described in detail. Reference [48| contains further information about the ZEIJS

detector.

3.1 The C5 Veto Counter

The C5 veto counter consists of two scintillator paddles orientated perpendicular to the

beam axis. The U shaped paddles closely surrounds the beam pipe at z = -315 cm. A lead sheet

26


3 mm thick separates the scintillator paddles. Lead sheets are also located in front and behind the

scintillators to suppress synchrotron radiation. The counter is divided into a top and bottom half

and is read out by a total of four PMTs with a time resolution of better than 1 ns. The C5 veto

counter measures the rate and time of interactions produced by the passing beams, thus providing

information about the background rate and the longitudinal distribution o f the electron and proton

bunches. As described in Section 7.4.1, this information can be used to determine the nominal in

teraction point for each run.

A signal from the C5 counter in time with the proton bunch crossing the interaction point

is used to veto calorimeter triggers at the First Level Trigger. This veto effectively suppresses up

stream proton beam gas interactions.

3.2 Luminosity Measurement

The luminosity was measured from the rate o f small angle hard bremsstrahlung photons

produced in the Bethe-Heitler process ep —> eyp [49], A beam pipe exit window located at

z = -92 m allows photons to leave the beam pipe and be measured by an electromagnetic calorim

eter located at z = -106 m. Under test beam conditions the electromagnetic calorimeter had a reso

lution of A E /E - 18%/ jE(GeW). The layout of the luminosity monitor is shown in Figure 3-3.

The photon calorimeter is labelled GDET.

-x (ml

Beam M agnets

GDET

beam

EDET 4i— i— i— i— i— i— i— i— i— i— i— i—0 50 WO - z (ml

Figure 3-3: Luminosity monitor.

r ito tons emitted by brentsstrahlttng are detected by the electromagnetic calorim eter (GDET).

Each electron bunch was followed by a satellite bunch which could produce an ep interac

tion at about z = 1.2 m. Electrons from these interactions reach the RCAL with times greater than

6 ns. During the event selection, cuts on the RCAL timing are used to suppress background from

27


proton beam interactions with the residual gas (see Section 8.1). These timing cuts also remove ep

interactions originating from the electron satellite bunch. However, the satellite bunch is also a

source of bremsstrahlung photons which are included in the measurement of the bremsstrahlung

rate. The observed bremsstrahlung rate has to be corrected to account for the effects of the satellite

bunches in order to determine the rate from the main electron bunches. The correction to the lumi

nosity due to the satellite bunches is about 6% 150]. There is also a contribution to the bremsstrahlung rate from electron interactions with the residual gas in the beam pipe. The bremsstrahlung rate

due to ep interactions is

* c p - / m u h ( « U H - ^ , , a S - « c p d '' 'C ) - ( T l )

The factor /?l01 is the observed rate. Multiple bremsstrahlung, present with high beam currents, is

accounted for by the f a c t o r T h e rate from the satellite bunch is denoted by . The elec

tron beam gas rate

r , ^ t l l t , ,

tfegas = 7 V „ . (3-3)

The expected cross section is determined by the convolution of the Bethe-Heitler cross section and

the photon calorimeter energy resolution function, ry. The cross section is also corrected for the ac

ceptance of the photon calorimeter Ar The expected cross section is

do(3-4)

Y

In Equation (3-4), the expected cross section is determined for photon energies greater than 5 GeV.

The observed rate is typically 5 KHz o f which about 30% is due electron gas interactions. Accep

tance o f the photon calorimeter is dependent on the electron beam angle at the interaction point

which varies from run to run. From MC simulations, the acceptance was determined to be 92-99%.

The following sources o f systematic errors contribute to the determination of the error on

the luminosity measurement [51]:

• Electron gas subtraction (1.5% error is estimated).

» Correction for satellite bunches. The determination of the satellite current requires a fit to

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the C5 time histograms. The error o f this f it resulted in an estimated error on the correction

of the satellite bunches of 1%.

• Determination of the acceptance o f the photon calorimeter. The acceptance was deter

mined from a Monte Carlo simulation which included changing the crossing angle. The

error is estimated at 2-5%.

• Energy calibration of the photon calorimeter (less than 2%).

• Incorrectly measured energies leads event migration and hence an error when determining

the expected cross section from Equation (3-4). The error is less than 1%.

• Accuracy of the Bethe-Heitler cross section (about 1 %).

• Multiple events in one bunch crossing (negligible).

The systematic errors are added in quadrature resulting in a 5% systematic error on the luminosity

measurement.

During the fall running period there were three trigger configurations (see Section 4.5) for

which the integrated luminosity is shown in Table 3-1 [51]. HERA delivered a total integrated lu

minosity o f 30.5 nb"1. In Table 3-1, the ‘usable’ integrated luminosity is listed. Runs for which the

detector was not fu lly functional are excluded. The final integrated luminosity used in this analysis

is 24.7 nb"1 ±5% .

TriggerConfiguration

£.(nb"*) Ls (nb '1)

SEP19 0.92 0.90

SEP25 16.46 15.35

OCT09 8.97 8.48

Total 26.3 24.7

Table 3 -1: The lum inosity f o r the fa l l 1992 running period.

The integrated lum inosity is shown fo r the three trigger configurations (see Section 4.5) used during the fa l l running

period. The integrated lum inosity after correction f o r the sate llite hunch is shown in the last column. These values are

used in the analysis.

3.3 Central Tracking Detector

The Central Tracking Detector (CTD) is a drift chamber consisting of a total o f 4,608 sense

wires. The chamber is divided into nine layers referred to as superlayers. Each superlayer is further

divided into cells containing eight sense wires. The cells have a maximum d rift time o f 500 ns. Odd

numbered superlayers (superlayer one has the smallest radius) contain axial wires, while even

29


numbered superlayers contain stereo wires. Superlayer two has a stereo angle of minus five de

grees, superlayer four has a stereo angle of 5 degrees and superlayers six and eight have stereo an

gles o f seven degrees. Superlayers one, three and five are instrumented with z-by-timing readout

and were active during the data taking. The z-by-timing system uses the time difference between

signals arriving at the two ends of the wires to determine the z position of the hit with a designed

resolution of 3 cm. Only the z-by-timing system was read out during the fall running period.

Figure 3-4 shows the end view of a simulated NC event in the CTD which illustrates the

superlayer and cell structure. Each sense wire is seen to have a left-right ambiguous hit. In the fig

ure the true hits form radial segments such that a straight line can be drawn through the hits in the

axial layers. Stereo hits are drawn at one end of the CTD. As the stereo hits are projected back to

wards the other end, they w ill rotate in cp and at some point along z they align with the axial hits.

This allows z information to be obtained from the stereo layers.

Figure 3-4: End view o f the CTD showing a simulated NC event.The CTD is divided into 9 cy lind rica l superlayers. Each superlayer is partitioned into cells having H sense wires. The

odd numbered superlayers have ax ia l wires and the even numbered layers have stereo wires. D uring the fa l l / 99.1 run

ning period, only the f i r s t three a x iu l superlayers were instrumented with z-by-tim ing readout.

During the fall running period, the CTD Second Level Trigger was used to reject cosmic

muon events. The CTD Second Level Trigger is a software trigger programmed to search for pat

terns of hits within a cell |52j. Hits on adjacent wires are used to form seed pairs. The seed pair is

used to estimate the drift time of a hit on the adjacent wire. If a hit is found having a drift time with

in the estimated error, it is added to the seed pair forming a segment candidate. Further hits are

searched for within an error estimated from the segment candidate. The search continues until the

cell boundary is reached. In superlayer one, having eight sense wires, a minimum of four hits is

30


required to define a segment. In superlayers three and five there are o r'v four sense wires equipped

with z-by-timing readout and for these cells two hits are required to define a segment.

For fully reconstructed tracks, the error on the determination of the z position of the track

is dependent on the resolution o f the z-by-timing and the number of hits included in the track. Us

ing only hits in superlayer one, it was estimated in [53] that the error in the vertex would be about

17.3 cm. For eight hits in superlayer one and four hits in superlayer three, the error is reduced to

3.5 cm.

3.4 Calorimeter

There are several good references on calorimetry in ge

first measurement of the proton structure function f2 with ... · the zeus detector is one of two...

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