First Direct Measurement of FL using ISR Events in Deep Inelastic Scattering

at HERA

Jonathan Paul Scott

University of BristolDepartment of Physics

October 2000

Thesis submitted to the University of Bristolin accordance with the requirements of the degree of

Doctor of Philosophy in the Faculty of Science.

27,000 Words

Abstract

Collisions between positrons and protons with hard photon radiation from the initial

state positron have been used to measure the proton structure functions F2 and FL. Using

an integrated luminosity of 3.78pb-1 recorded in 1996 by the ZEUS detector, F2 has been

measured over the kinematic range of 0.3 GeV2 < Q2 < 40 GeV2 and 8 10-6 < x < 1.8

10-1. These data cover the region between previous F2 measurements at HERA and

other, fixed target experiments.

Also, the structure function FL has been measured for the first time at Q2 = 5.5 GeV2 and

x = 4.4 10-4. Using data recorded by ZEUS during 1996 and 1997 with an integrated

luminosity of 35.9pb-1, the measured value of FL is and is

found to be consistent with perturbative QCD calculations.

To Mum and Dad

Acknowledgements

I would first like to thank my supervisor, Greg Heath, for providing much needed

direction and assistance. Thanks also to PPARC for providing the funding for the

research in this thesis.

For the Field Bus work, special mention goes to Steve Nash, without whom there would

have been no new circuit boards to play with. Thanks also go to Alex Mass and Dave

Newbold for introducing me to the world of digital design.

While I was at DESY, I would like to give a special mention to Adi Bornheim for

passing on his extensive knowledge of ISR and for doing much of the dirty work. Brian

Foster, Stefan Schlenstedt and especially Ken Long also provided suggestions about

where to go when things looked bleak.

Thanks also to Dave Bailey, Rod Walker, Alex Tapper, Chris Cormack, Jo Cole and

Mark Hayes for their words of wisdom on a wide range of subjects, although none of

them warned about the dangers posed by candles in pubs!

Finally, thank you to Nick Brook for reading and providing lots of helpful comments

about my thesis as well as lots of less helpful comments on a great range of subjects

ranging from football to flying!

iii

“Credit must be given to observation rather than theories,

and to theories only insofar as they are confirmed by the

observed facts” – Aristotle.

“Facts are meaningless. Facts can be used to prove

anything that’s even remotely true.” – Homer Simpson.

iv

AUTHOR’S DECLARATION

I declare that the work in this dissertation was carried out in accordance with the

regulations of the University of Bristol. The work is original except where indicated by

special reference in the text and no part of the dissertation has been submitted for any

other degree.

Any views expressed in the dissertation are those of the author and in no way represent

those of the University of Bristol.

The dissertation has not been presented to any other University for examination either

in the United Kingdom or overseas.

SIGNED: DATE:

v

Contents

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

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

2. Theoretical Overview . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Quantum Electrodynamics . . . . . . . . . . . . . . . . . . . . . 6

2.3 Elastic e+p e+p scattering . . . . . . . . . . . . . . . . . . . . 8

2.4 Inelatsic e+p e+X scattering . . . . . . . . . . . . . . . . . . . 10

2.5 Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . 15

2.6 Parton Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.7 DGLAP Evolution . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.8 The Longitudinal Structure function, FL . . . . . . . . . . . . . . 20

3. The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . 26

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2 The Compact Muon Solenoid Experiment . . . . . . . . . . . . . 27

3.3 The Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4 The Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.4.1 The Calorimeter Trigger . . . . . . . . . . . . . . . . . . 31

3.4.2 The Sort ASIC . . . . . . . . . . . . . . . . . . . . . . . 33

3.5 The Test system . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.5.1 The Protocol . . . . . . . . . . . . . . . . . . . . . . . . 37

vi

3.6 The Field Bus Node . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.6.1 The XILINX Field Programmable Gate Array . . . . . . . 40

3.6.2 The Interface . . . . . . . . . . . . . . . . . . . . . . . . 41

3.6.3 The Node Decoder . . . . . . . . . . . . . . . . . . . . . 41

3.7 Simulation of the Design . . . . . . . . . . . . . . . . . . . . . . 45

4. HERA and the ZEUS detector . . . . . . . . . . . . . . . . . . . . 49

4.1 HERA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2 The ZEUS Detector . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.2.1 The ZEUS Coordinate System . . . . . . . . . . . . . . . 56

4.2.2 The Central Tracking Detector . . . . . . . . . . . . . . . 57

4.2.3 The Small Angle Rear Tracking Detector. . . . . . . . . . 59

4.2.4 Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.2.5 The Calorimeter . . . . . . . . . . . . . . . . . . . . . . . 60

4.2.6 The Presampler . . . . . . . . . . . . . . . . . . . . . . . 61

4.2.7 HES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.2.8 The Muon Chambers . . . . . . . . . . . . . . . . . . . . 63

4.2.9 Beam Pipe Calorimeter and Beam Pipe Tracker . . . . . . 63

4.2.10 The VETO Wall . . . . . . . . . . . . . . . . . . . . . . 64

4.2.11 The Collimator, C5 . . . . . . . . . . . . . . . . . . . . . 64

4.2.12 The Luminosity Detector . . . . . . . . . . . . . . . . . . 64

4.3 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . 67

4.3.1 The First Level Trigger . . . . . . . . . . . . . . . . . . . 67

4.3.2 The Second Level Trigger. . . . . . . . . . . . . . . . . . 69

4.3.3 The Third Level Trigger . . . . . . . . . . . . . . . . . . 69

4.3.4 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . 69

4.3.5 DIS Event Selection . . . . . . . . . . . . . . . . . . . . 70

4.4 Measurement of kinematic variables . . . . . . . . . . . . . . . . 70

4.4.1 Event Vertex . . . . . . . . . . . . . . . . . . . . . . . . 72

4.4.2 Positron finding . . . . . . . . . . . . . . . . . . . . . . . 72

4.4.3 Positron energy corrections . . . . . . . . . . . . . . . . . 72

vii

4.4.4 Positron position measurement . . . . . . . . . . . . . . . 74

4.4.5 Reconstruction of the Hadronic Final State . . . . . . . . . 74

4.5 Kinematic Reconstruction. . . . . . . . . . . . . . . . . . . . . . 75

4.5.1 Electron Method . . . . . . . . . . . . . . . . . . . . . . 76

4.5.2 Double Angle Method. . . . . . . . . . . . . . . . . . . . 76

4.5.3 Jaquet-Blondel Method . . . . . . . . . . . . . . . . . . . 77

4.5.4 Sigma Method . . . . . . . . . . . . . . . . . . . . . . . . 78

5. Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.1 QED Compton Monte Carlo . . . . . . . . . . . . . . . . . . . . 79

5.2 ISR Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.3 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.3.1 Simulation of the LUMI- energy response . . . . . . . . .

83

6. QED Comptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.2.1 QED Compton Trigger . . . . . . . . . . . . . . . . . . 89

6.2.3 Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.3 Measuring the Inelastic Contribution . . . . . . . . . . . . . . . . 92

6.4 Luminosity Measurements . . . . . . . . . . . . . . . . . . . . . 94

6.4.1 Calculation of the 1996 and 1997 Luminosity . . . . . . . 95

6.4.2 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . 96

6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7. Measuring the Proton Structure Function, F2 . . . . . . . . . . . . 100

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

7.2 Corrections to the Kinematics due to ISR . . . . . . . . . . . . . 100

7.3 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

7.3.1 The Trigger for radiative events . . . . . . . . . . . . . . 102

viii

7.3.2 The FLT . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

7.3.3 The TLT . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.3.4 Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7.4 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.4.1 Background normalisation . . . . . . . . . . . . . . . . . 107

7.4.2 QED Compton Rejection . . . . . . . . . . . . . . . . . . 109

7.4.3 Cosmic Ray Rejection . . . . . . . . . . . . . . . . . . . 109

7.4.4 Positron and proton beam-gas background . . . . . . . . . 109

7.5 Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7.5.1 Acceptance of the LUMI- calorimeter . . . . . . . . . . . 109

7.5.2 Vertex weighting . . . . . . . . . . . . . . . . . . . . . 112

7.5.3 Beam pipe correction . . . . . . . . . . . . . . . . . . . . 113

7.5.4 Structure Function weighting . . . . . . . . . . . . . . . . 113

7.6 Data and Monte Carlo Distributions . . . . . . . . . . . . . . . . 113

7.7 Measuring F2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

7.7.1 Resolution of Q2 and y . . . . . . . . . . . . . . . . . . . 116

7.7.2 Bin Selection . . . . . . . . . . . . . . . . . . . . . . . . 117

7.7.3 Unfolding . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7.7.4 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . 122

7.8 Comparison with 96/97 F2 measurement . . . . . . . . . . . . . . 123

8. Measuring the Proton Structure function, FL . . . . . . . . . . . . 131

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

8.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

8.2.1 Trigger. . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

8.2.2 Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

8.2.3 Energy scale of the LUMI- calorimeter . . . . . . . . . . 135

8.2.4 The FL Bin . . . . . . . . . . . . . . . . . . . . . . . . . 137

8.3 Measuring FL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

8.3.1 y scaling factor . . . . . . . . . . . . . . . . . . . . . . . 142

8.3.2 Extraction of R . . . . . . . . . . . . . . . . . . . . . . . . 144

ix

8.3.3 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . 145

8.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

9. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

F2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

x

List of Figures

2.1 Feynman diagram illustrating the process e+ e+ . . . . . . 7

2.2 The Feynman diagram for elastic e+p scattering . . . . . . . . . . 9

2.3 The Feynman diagram for inelastic e+p scattering . . . . . . . . . 11

2.4 F2 measured at ZEUS as a function of Q2 in bins of x. The rise

with

Q2 at small x and the fall at high x is clearly visible. Results from

fixed target experiments are shown for comparison . . . . . . . . 18

2.5 Ladder Diagram showing several gluons being radiated from the

parton that interacts with the proton. . . . . . . . . . . . . . . . . 20

2.6 and plotted as functions of y. The effect of non-zero R on the

cross section is only significant at high values of y . . . . . . . . 22

2.7 The emission of an ISR photon in a DIS event. The hadronic final

state is denoted by X . . . . . . . . . . . . . . . . . . . . . . . . 24

2.8 The Longitudinal structure function measured by H1 as a function

of x in bins of Q2 along with charged lepton-nucleon fixed target

experiments. The error bands are due to experimental (inner) and

model (outer) uncertainty for the calculation of FL using a NLO QCD

fit to the H1 data . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1 The LHC Collider showing the relative locations of the four

experiments, CMS, ALICE, ATLAS & LHC-B . . . . . . . . . . 27

3.2 Section of the CMS experiment showing the relative positions of

the major components. . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 The CMS trigger and DAQ . . . . . . . . . . . . . . . . . . . . . 31

3.4 The positions of the trigger towers. Each trigger tower is served by

its own trigger processor crate . . . . . . . . . . . . . . . . . . . 32

3.5 Schematic of the sort algorithm . . . . . . . . . . . . . . . . . . 34

3.6 The Layout of the Sort ASIC Field Bus Test system . . . . . . 36

xi

3.7 The Field-Bus Protocol . . . . . . . . . . . . . . . . . . . . . . . 37

3.8 The overall node design . . . . . . . . . . . . . . . . . . . . . . 39

3.9 The Node Decoder . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.10 The Input/Output module . . . . . . . . . . . . . . . . . . . . . 43

3.11 Simulation of Node Decoder through a Get Node Name command

followed by a write and read data cycle. . . . . . . . . . . . . . 46

3.12 The prototype interface board. The FPGA is shown in the centre

with the socket for connection to the PC shown at top. The TTL

output sockets for the field bus are to the right. Other resources

include 4 seven segment displays and 11 LEDs as well as global

and local reset buttons . . . . . . . . . . . . . . . . . . . . . . 47

3.13 The prototype memory module. Field bus connections are at

bottom right with the FPGA upper centre. Provision for 4 DPR is

made although only one is in place here. This board is designed

to be placed in a VMEbus crate. The resources also include 4

multifunction displays . . . . . . . . . . . . . . . . . . . . . . 48

4.1 The HERA Layout, showing the locations of the ZEUS and H1

experiments along with the preaccelerators, H Linac, e Linac,

DESY and PETRA . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2 The integrated luminosity delivered by HERA for the years

1992-1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.3 The Kinematic Range explored at HERA on the x-Q2 plane. Shown

are results from the standard low and high Q2 analyses together

with results from shifted vertex running and very low Q2 data

obtained using the BPC and BPT. This is shown in comparison with

results from fixed target experiments, including NMC, BCDMS,

CCFR, E665 and SLAC . . . . . . . . . . . . . . . . . . . . . . . 53

4.4 The ZEUS detector. The positions of the major components are

indicated. In this representation, the protons enter from the right

and the positrons from the left . . . . . . . . . . . . . . . . . . . 55

xii

4.5 The ZEUS co-ordinate system . . . . . . . . . . . . . . . . . . . 56

4.6 The arrangement of wires in the CTD . . . . . . . . . . . . . . . 57

4.7 The arrangement of the two layers of scintillator strips in

the SRTD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.8 The area covered by the Forward and Rear Presamplers (shaded)

superimposed on the FCAL and RCAL cells . . . . . . . . . . . . 62

4.9 Overview of the ZEUS LUMI detector. The locations of the four

main components along with the magnets upstream of the main

detector are shown . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.10 The LUMI Calorimeter . . . . . . . . . . . . . . . . . . . . . . 66

4.11 The ZEUS Trigger Layout showing the flow of data from the

detector front-end electronics, through the triggers, to final

storage onto either tape or disk . . . . . . . . . . . . . . . . . . 68

4.12 A reconstructed neutral current event. . . . . . . . . . . . . . . . 71

5.1 The two leading order contributions to QED Compton scattering . 80

5.2 The difference between the measured and true photon energies

for 1996 and 1997 . . . . . . . . . . . . . . . . . . . . . . . . . . 86

6.1 The two leading order contributions to QED Compton scattering . 88

6.2 Elastic and Inelastic QED Compton MC Distributions for

1996 data set (upper plots) and 1997 data set (lower plots) . . . . . 92

6.3 Data v Elastic + Inelastic MC comparison for 1996 . . . . . . . . 93

6.4 Data v Elastic + Inelastic MC comparison for 1997 . . . . . . . . 93

6.5 Effect of systematic checks on measured 1996 luminosity. The

fractional error on each systematic check is shown with the dashed

line indicating no systematic check . . . . . . . . . . . . . . . . . 97

6.6 Effect of systematic checks on measured 1997 luminosity. The

fractional error on each systematic check is shown with the dashed

line indicating no systematic check . . . . . . . . . . . . . . . . . 98

xiii

7.1 The raw LUMI-e and LUMI- energies for 1996 (left)

and 1997 (right). The structure in the plots arises due to the acceptance

of the LUMI-e and LUMI- detectors . . . . . . . . . . . . . . . . . 107

7.2 Total E-Pz distribution for data with the normalised

background contribution. The background is normalised to the data

in the hatched region where the total E-Pz > 62 GeV . . . . . . 108

7.3 The aperture of the LUMI- calorimeter . . . . . . . . . . . . . . 110

7.4 The x and y Beam Tilts for 1996, top, and 1997, bottom, plotted

against relative run number . . . . . . . . . . . . . . . . . . . . . 111

7.5 Acceptance of LUMI- calorimeter for different x and y beam

tilt positions. The tilt ranges from –0.25 mrad to 0.06 mrad in the x

direction and –0.1 mrad to 0.1 mrad in the y direction . . . . . . 112

7.6 Comparison of Data and MC + BGD for the Electron energy and

theta, which are used for the kinematic reconstruction, as well as

the photon energy and z vertex position . . . . . . . . . . . . . . 114

7.7 Comparison of data and MC for hadronic-based quantities along

with E-Pz distributions. The total E-Pz plot indicates the cut on the

signal region (two vertical lines) and the area where the background

is normalised to the data (hatched area) . . . . . . . . . . . . . . 115

7.8 Comparison of data and MC + BGD for the Q2 and yHERA

distributions, used for the measurement of F2. . . . . . . . . . . . 116

7.9 Resolution of Q2 measured using the electron method and y

measured using the sigma method . . . . . . . . . . . . . . . . . 118

7.10 The acceptance and purity for each bin. The shading of the bins

indicates the purity whereas the value for the acceptance is given in

each bin as a percentage . . . . . . . . . . . . . . . . . . . . . 119

7.11 The bins used for the F2 measurement together with previous

results from ZEUS and fixed target experiments. The number

assigned to each bin is also indicated . . . . . . . . . . . . . . 120

xiv

7.12 The fractional error for each systematic check shown as a function

of bin number. . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.13 Data v MC comparison for the 96/97 analysis. The relative

contributions of the diffractive and photoproduction Monte Carlo

are indicated by the green and blue histograms . . . . . . . . . . 127

7.14 Comparison of F2 measured with this analysis and preliminary

96/97 results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

7.15 F2 plotted from the ISR analysis (circles) with the comparison

from the 96/97 analysis (triangles). Error bars for the ISR results

show both statistical (inner bars) and systematic errors added in

quadrature. The 96/97 analysis shows statistical errors only. Also

shown are the results from the ZEUS BPC\BPT and shifted vertex

(SVX) analyses . . . . . . . . . . . . . . . . . . . . . . . . . . 129

8.1 The effect of weighting the y spectrum to three different values of R

As R increases the curve of the ratio becomes steeper . . . . . . . 133

8.2 Kinematic peak study for 1996 . . . . . . . . . . . . . . . . . . . 136

8.3 Kinematic peak study for 1997 . . . . . . . . . . . . . . . . . . . 136

8.4 The maximum values of y obtainable for different minimum

values of the scattered positron energy . . . . . . . . . . . . . . . 137

8.5 The effect of the upper and lower cut of yHERA on the accessible

region of y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

8.6 The bin used for the FL measurement shown on the x, Q2 plane

with the F2 bins superimposed for comparison . . . . . . . . . . 139

8.7 Data v MC + BGD comparison for the 1996 FL measurement. The

y distribution, used for the fit, is shown at the bottom . . . . . . 140

8.8 Data v MC + BGD comparison for the 1997 FL measurement. The

y distribution, used for the fit, is shown at the bottom . . . . . . 141

8.9 The migration and resolution of y in the range used for the

extraction of R . . . . . . . . . . . . . . . . . . . . . . . . . .

142

xv

8.10 The effect caused by fitting over different ranges of y (left). The plot

shows the MC distribution for MC weighted to R=1.4. Two fits

have been made, the black curve covering the range up to y = 0.6

and the red curve up to y = 0.45 (corresponding approximately

to the accessible range in this analysis. As can be seen, the shape of

the curves are different, giving different fitted values of R. The plot

to the right shows the fit made with Sy set to 1.149. This fit yields

the weighted value of R=1.4. . . . . . . . . . . . . . . . . . . . 143

8.11 Fit of ratio of data and MC y distributions for combined 1996

and 1997 data . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

8.12 The effect of the systematic checks on the value of R. Shown for

each test is the fitted value of R together with the error on the fit.

The dashed lines indicate the nominal value together with its error 147

8.13 The fractional effect of the systematic checks on the value of F2 . 148

8.14 The measured value of FL plotted at Q2 = 5.5 GeV2 and

x = 4.4 10-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

8.15 FL measured by H1 over a similar range in x to the ISR

measurement. The yellow band shows the expectation from pQCD

with the dashed lines giving the limits of FL = 0 and FL = F2. The

points are given for different values of Q2 with the FL = F2 also

covering a range in Q2 explaining the fall with decreasing x . . 150

8.16 The hadronic E-Pz distributions using positron energy cut

> 5 GeV (left) and > 8 GeV (right). As can be seen there is a

deficit of Monte Carlo between 5 and 15 GeV for the lower energy

cut. This may be due to more background or problems with

the reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 151

xvi

List of Tables

2.1 The known quarks and leptons . . . . . . . . . . . . . . . . . 5

2.2 The properties of the gauge bosons . . . . . . . . . . . . . . . 6

3.1 Addressing the field bus nodes . . . . . . . . . . . . . . . . . 39

5.1 The LUMI- calibration constants for 1996 and 1997 . . . . . 85

6.1 The kinematic variables used for the COMPTON2.0 program 89

7.1 Summary of the properties of the FLT Trigger bit FLT30,

giving the values of the cuts used . . . . . . . . . . . . . . . . 103

7.2 Comparison between data, DIS01, and background, DIS02,

triggers used for the ISR F2 measurement . . . . . . . . . . . . 104

8.1 Comparison between the triggers used for the ISR analyses.

DIS01 and DIS02 are used for the F2 measurement while

DIS10 and DIS02 are used for the FL measurement . . . . . . 134

xvii

Chapter 1

Introduction

The concept of matter being composed of building blocks called ‘atoms’ was first

introduced by the ancient Greek scholars Leucippus and Democritus in the 5 th century

BC. Based on philosophical considerations, they suggested that matter is composed of

small, indivisible particles moving at random and colliding with each other. It was

however over 2000 years before experiments indicated the validity of this argument

with John Dalton using empirical chemical laws to develop atomic theory. As physics

progressed at the turn of the 19th and 20th centuries it became increasingly evident that

these building blocks of nature were themselves complex objects.

J.J. Thomson discovered the electron in 1897 and Rutherford demonstrated in 1911 by

firing alpha particles at gold, that the atom could be shown to be mostly empty space

with a tiny, dense, positively charged nucleus surrounded by electrons. The nucleus was

found to consist of a number of positively charged particles known as protons.

Chadwick, in 1932, demonstrated the existence of a neutral partner to the proton called

the neutron, therefore explaining the stability of higher mass elements. Together the

proton and neutron are called nucleons.

The model of atoms consisting of a nucleus of protons and neutrons surrounded by

electrons so small they can be considered point-like was further elaborated in the late

1960s by experiments at the Stanford Linear Accelerator Centre (SLAC). These

demonstrated that nucleons themselves contain point-like particles, known as partons.

Today, Deep Inelastic Scattering (DIS) experiments reveal ever-finer structure of

nucleons. The nucleon is now known to be a complex object containing many

interacting partons called quarks and gluons.

1

The HERA accelerator at DESY in Hamburg, Germany, is one such DIS experiment. It

collides a high-energy beam of protons with either electron or positron beams, with

several detectors recording the results of these collisions. Amongst other things, this

allows the accurate measurement of the density of partons within the proton. These have

served to drastically increase our understanding of Quantum ChromoDynamics (QCD),

the theory of nuclear interactions.

In collisions at HERA, the electron can sometimes radiate another particle before

interacting with the proton. This is known as an Initial State Radiative event and is

similar to the bremsstrahlung process. Such events provide a way to extend the

accessible kinematic region at HERA to areas hitherto unexplored. Not only will this

allow us to bridge the gap between previous measurements but also these events also

allow us to make a direct measurement of the structure function known as FL, for the

first time at HERA.

The thesis begins by outlining the theoretical basis of the analysis, starting in chapter 2

with an introduction to Deep Inelastic Scattering, one of the important processes at

HERA. This is followed by a description of structure functions and their importance in

the development of QCD. Finally, Initial State Radiative events and their use in

structure function measurements are discussed.

The problem of filtering out the useful physics events, or triggering, is becoming an

ever more important and challenging problem due to the high rates and large amounts of

data found in modern particle physics detectors. For the ZEUS detector at HERA, high-

speed electronics and farms of computer processors perform the triggering. Future

experiments however, will require solutions that are far more sophisticated. For

example, the Large Hadron Collider (LHC) is a proton-proton collider which, when

completed, will be used to probe physics at extremely high energies. The type of

collision and high energies used will generate conditions that will prove particularly

challenging for triggering. One of the detectors being developed for the LHC will be the

Compact Muon Solenoid (CMS). Chapter 3 describes the development of a system to

test one of the high-speed digital electronic components intended for the CMS trigger.

2

Chapter 4 describes the ZEUS experiment and its major components along with how the

data from these components can be turned into useful variables for physics analyses.

Chapter 5 presents details of the Monte Carlo simulations used in this thesis. These

simulations are important tools in modern particle physics and three Monte Carlo

generators are described.

Chapter 6 introduces QED Compton events. These are radiative events found in a

slightly different kinematic regime to Initial State Radiative events and can also be a

source of background for the measurement of the latter. As the cross section can be

calculated precisely and the event topology is relatively clean, QED Comptons can also

be used as a crosscheck for the measurement of luminosity, which is an indication of the

number of particle interactions.

Chapters 7 and 8 present the use of Initial State Radiative events to measure the proton

structure functions F2 and FL. The process used to select such events is described in

chapter 7 in making the measurement of F2. This is extended in chapter 8 for the more

difficult measurement of FL.

3

Chapter 2

Theoretical Overview

2.1 Introduction

One of the great triumphs of modern physics is the Standard Model of particle physics.

This is one of the most successful models in science and describes with great accuracy

all current measurements in particle physics. The standard model is not without its

problems though, there are many parameters within the model that are not predicted

theoretically and therefore can only be introduced ‘by hand’. Also, many other

questions remain unanswered and so, eventually, we will require a new framework for

the description of elementary particles.

The standard model of particle physics describes nature in terms of elementary

particles, which are acted upon by four forces, electromagnetic, strong, weak and

gravity.

There are three distinct types of particles, quarks, leptons and gauge bosons. The

electron is the most familiar example of a lepton. Quarks on the other hand, bind

together to form hadrons. An example is the proton, which contains three quarks.

Each quark and lepton is also accompanied by its antiparticle, which carries equal but

opposite signed charge, while its mass remains the same.

Quarks and leptons exist in three generations. Particles across the generations have

similar properties but different masses, the first generation of leptons for example,

consist of the electron and electron neutrino, together with their antiparticles, the

positron and electron antineutrino. Similarly, there are two types, or flavours, of quarks

in each generation. In the first generation, these flavours are named up and down with

charm\strange and top\bottom forming the 2nd and 3rd generations respectively.

The elementary particles that are known to exist are shown in Table 2.1:

4

1st

Generation2nd

Generation3rd

GenerationLeptons

(mass)

e (electron)(0.51 MeV)

(muon)(105.6 MeV)

(tau)(1784 MeV)

e (electron neutrino)< 3 eV

(muon neutrino)

< 0.19 MeV

(tau neutrino)

< 18.2 MeVQuarks

(mass)

u (up)(8 MeV)

c (charm)(1.3 GeV)

t (top)(175 GeV)

d (down)(15 MeV)

s (strange)(200 MeV)

b (bottom)(4.8 GeV)

Table 2.1: The known quarks and leptons.

While leptons can exist freely, quarks can only exist in bound states. This is explained

by introducing an extra property to quarks, called colour charge. Each quark has a

‘colour’ of red/antired, green/antigreen or blue/antiblue. A stable particle must have

total colour charge of zero. Therefore, the only allowed combinations are two-quark

states with, say, red-antired (mesons) or three-quark states with, for example, red-green-

blue.

The third class of elementary particles are known as gauge bosons. These mediate the

four forces. The electromagnetic interaction is mediated by the photon () and is

described by the theory of quantum electrodynamics (QED) while the weak force is

carried by the charged W and neutral Z bosons. Electroweak theory is described in

terms of 4 bosons, one positively charged, one negatively charged and two neutral. At

high energies the 4 bosons are similar. However, at lower energies, symmetry breaking

gives masses to 3 of the bosons, which are identified as the W and Z while the other

boson is the photon. This is described by the GWS [1] theory of electroweak

interactions. The strong force, on the other hand, carries colour charge and is described

by quantum chromodynamics (QCD). The mediating particles in this case are an octet

of massless gluons.

It is postulated that gravity is mediated by a spin-2 boson known as a graviton. As

gravity is very much weaker than the other forces, it is neglected in typical particle

physics experiments.

The properties of the gauge bosons are shown in Table 2.2.

5

Gauge Boson Mass (GeV) Charge (e) Spin

photon, 0 0 1

gluons, g 0 0 1

weak, W 80 1 1

weak, z 91 0 1

graviton 0 0 2

Table 2.2: The properties of the gauge bosons.

2.2 Quantum Electrodynamics

Quantum field theory (QFT) attempts to explain the dynamics of elementary particles

in a manner consistent with the postulates of quantum mechanics and the special theory

of relativity.

Quantum electrodynamics is formulated by quantising the electromagnetic field.

Feynman noted that each component of an interaction, for example an incoming

particle, contributes a rule to the calculation of that interaction. By drawing a QED

process as a diagram, the cross section can be calculated by applying the rules to every

component. The cross section, , for a process is a measure of the probability that that

particular process will occur. It is defined as an area, with the naïve interpretation being

the particles must pass through this area before the process can take place.

A simple example of a cross section calculation is e+- scattering, as shown below in

figure 2.1.

6

Figure 2.1: Feynman diagram illustrating the process e+ e+.

In this case Pa, Pb, Pc and Pd are defined as the four-vectors corresponding to the

incoming and outgoing positron and muon and q is the four-vector of the photon.

The 2 2 differential cross section formula in the centre of mass frame is, for a particle

passing through the solid angle d:

(2.1)

where Mfi is a matrix element found by applying the Feynman rules to the diagram and

s is the square of the centre of mass energy. For the process shown in figure 2.1, |Mfi|2

can be written, in the high energy limit, in terms of the Mandelstam variables:

(2.2)

7

where the Mandelstam variables are defined as

(2.3)

and e is the electron charge.

Substituting (2.2) into (2.1) gives

(2.4)

where is the electromagnetic coupling constant.

The next two sections deal with the scattering of a positron off a proton. At HERA

electrons are also scattered off protons. The process is similar however to the positron

case.

2.3 Elastic e+p e+p scattering

In elastic e+p scattering the proton remains intact, while for the inelastic case, the

collision is energetic enough to fragment the proton.

The diagram for e+p scattering is shown in figure 2.2. The four vectors of the particles

are indicated in brackets as well as q, the four vector of the virtual photon.

8

Figure 2.2: The Feynman diagram for elastic e+p scattering.

By considering the proton to be a point-like particle with mass M, the cross section for

elastic e+p scattering can be obtained using the same method as the positron-muon case.

This leads to the Mott Scattering cross section formula:

(2.5)

where the factor is given by

(2.6)

and arises from the recoil of the proton.

Next, in order to take into account the fact that the proton is not a point-like object, two

form factors, G1 and G2 must be introduced.

9

(2.7)

G1 and G2 are related to the electric form factor, GE, associated with the charge density

and the magnetic form factor, GM, associated with the magnetic moment distribution by:

(2.8)

(2.9)

where .

GE and GM are normalised such that GE(0) = 0 and GM(0) = p, where p is the proton

magnetic moment.

The values of GE and GM have been measured in electron and muon scattering

experiments.

2.4 Inelastic e+p e+X scattering

The generalised process for inelastic positron-proton scattering is shown in Figure 2.3.

In this case, the proton fragments into many particles, X, with total invariant mass W.

The four-vectors are the same as before, with the exception that the four-vector of the

outgoing proton is replaced by W.

10

Figure 2.3: The Feynman diagram for inelastic e+p scattering.

Inelastic e+p scattering events are interesting as they can be used as a probe of the

internal structure of the proton. This is the case if the momentum transfer, q,

corresponds to photon wavelengths that are very small with respect to the size of the

proton.

In order to describe the event, a basic set of variables can be defined. These so called

kinematic variables are used in many of the arguments given in this thesis and are

defined below:

The centre of mass energy squared, s, of the event is given by

(2.10)

where Ee and Ep are the energies of the incident electron and proton

respectively and the approximation is for the case where the masses are small

compared to the energies.

The negative four-momentum transfer is defined as

11

(2.11)

This ranges from 0 to s. As Q2 increases, the size that can be resolved by the photon is

reduced and the structure of the proton is probed at ever-smaller scales.

It is also convenient to introduce two dimensionless quantities, x and y, whose values

range from 0 to 1. The Bjorken scaling variable, x, is defined as

(2.12)

and y is defined by

(2.13)

which is a measure of the energy transferred from the electron (or to the proton) in the

rest frame of the initial proton.

Again, assuming masses are small, the variables Q2, x and y are related by

(2.14)

Of these, for fixed s, only two are independent.

Finally, the invariant mass of the final hadronic system (*p), where * is the exchange

photon, is

(2.15)

where mp is the mass of the proton.

12

The double differential cross-section for positron-proton scattering at high energy,

mediated by neutral current is [2]:

(2.16)

In a similar argument to section 2.3, the factors F1 and F2 are introduced as

parameterisations of the structure of the proton and a new factor, F3, is also included.

The form factors F1 and F2, are related to the cross sections for longitudinally (L) and

transversely (T) polarised photons by,

(2.17)

(2.18)

where the total cross section is

(2.19)

xF3 is a parity violating term arising from Z0 exchange. For , this is negligible

and the cross section depends purely on * exchange. In the following xF3 will be

neglected for all calculations.

In the late 1960s experiments at SLAC [3] showed that for fixed x, the measured values

of F1 and F2 become approximately independent of Q2 at high Q2 and are only

dependent on x, i.e.

13

(2.20)

x is interpreted as the fractional momentum of the proton carried by the struck

constituent so, in other words, the scattering has become point-like. This is known as

Bjorken scaling [4]. The quark parton model (QPM) was introduced by Feynman [5] to

explain this.

The quark parton model introduces into the nucleon, point-like, non-interacting

scattering centres known as partons. Scaling is caused by photons scattering off a fixed

number of point-like particles within the proton.

F2 is now defined as the sum of momentum distributions , over all flavours:

(2.21)

where ei is the electric charge of the parton.

F1 depends on the spin of the partons. For spin-½ particles, the Callan-Gross [6] relation

states that:

(2.22)

which is confirmed by experiment. From equations (2.17) and (2.18) this implies that

L = 0.

Experimentally, the proton was found to contain 3 quarks, two up and one down, which

are known as the valence quarks.

By summing over the momenta of all the partons in the proton the momentum sum rule

states that

(2.23)

In the QPM, this would be the case if all the momentum in the proton were carried by

the valence quarks. Experimental evidence however, points to a value of ~0.5 and

14

implies that electrically neutral partons carry the remaining momentum. Such partons

were discovered at DESY in 1979 [7]. These are called gluons and their presence acts

to modify the quark-parton model in a way described below.

2.5 Quantum Chromodynamics

Quantum chromodynamics (QCD) is a gauge field theory, based on SU(3) symmetry,

describing the strong interaction. As stated earlier, quarks carry a colour ‘charge’. QCD

introduces gluons as the mediators of the strong interaction by transmitting the colour

between quarks.

In QED, as Q2 increases, the electromagnetic coupling constant, , also increases. This

is a result of the probing particle ‘seeing’ less of the screening charge caused by the

presence of electron/positron pairs. QCD is different to QED however, in that the

gluons carry colour charge themselves and can interact with each other as well as with

the quarks, in contrast with photons, which carry no electric charge. This leads to a

different behaviour for the strong coupling constant, s, which is given to leading order

in equation 2.24.

(2.24)

where nf is the number of quark flavours and is a constant of integration. This

constant represents the energy scale where the coupling constant becomes large. This

scale parameter is often quoted at values of ~200 MeV.

The coupling falls logarithmically towards 0 as . This behaviour is

known as asymptotic freedom.

Asymptotic freedom is explained by the presence of higher order loops containing only

gluons. The quark loops, similar to the electron/positron loops in QED, screen the

colour charge, i.e. as smaller distances are probed less of the screening charge is seen

and the coupling constant should increase. The gluon loops however, have an

15

antiscreening effect. This has a greater effect than the screening contribution and the net

result is to weaken the interaction at shorter distances.

Gluons are radiated from the quarks as well as gluons themselves. These may then

couple either to more gluons or form quark/antiquark pairs. As this depends on the

strong coupling constant and is a function of Q2, Bjorken scaling is therefore only an

approximation at low Q2 and x. This is evident in variations of the structure functions

with Q2. Such scaling violations have been measured and recent results from ZEUS [8]

are shown in figure 2.4.

In addition to the valence quarks the proton must now be considered to include a ‘sea’

of quark-antiquark pairs formed by gluon splitting. The overall flavour is unchanged as

baryon conservation states:

(2.25)

where xqisea in this case are the probability distributions of the sea quarks.

In this new model, known as the Improved Quark Parton model, F2 must now include

contributions from the sea quarks. It is also a function of Q2 as well as x in order to take

into account the scaling violations. Equation 2.21 can now be rewritten as:

(2.26)

The contributions from the bottom and top quarks have been neglected as the energies

reached in this analysis are not great enough.

16

Therefore, according to the Quark-Parton Model, F2 can be interpreted in terms of the

distribution of quarks and antiquarks in the proton. Unfortunately, the distribution

cannot be calculated from first principles. The QCD factorisation theorem [9] however,

allows the evolution of the parton distributions with Q2 to be calculated using

perturbative QCD. The accurate measurement of F2 provides constraints for fits to these

QCD calculations, therefore allowing the parton distributions to be determined.

2.6 Parton Evolution

The experimentally observed variation of the structure function with Q2 implies an

evolution of the parton distributions. The processes that lead to this are the radiation of

hard gluons by quarks and the splitting of gluons into quark-antiquark and gluon-gluon

pairs.

The probability that a quark contains another quark of lower fractional momentum z is

defined as Pqq(z), that it contains a gluon is Pgq(z), that a gluon contains a quark is Pqg(z)

and that a gluon contains a gluon is Pgg(z). These probabilities are know as the Altarelli-

Parisi splitting functions [10] and, at leading order, are given by equations

(2.27)(2.30).

(2.27)

(2.28)

(2.29)

(2.30)

Figure 2.4: F2 as a function of Q2 in

bins of x. The rise with Q2 at small x and the fall at high x is clearly visible. Results

from fixed target experiments are shown for comparison.

17

2.7 DGLAP Evolution

The splitting functions can be used within the DGLAP equations [10-14] to describe the

evolution of quark and gluon densities with Q2. As stated previously, the quark

distribution evolves via gluons being radiated from quarks and by gluons splitting into a

pair and is given by:

(2.31)

with the evolution of the gluon distributions given by:

(2.32)

A diagram with several such emissions is shown in figure 2.5. This has the effect of

increasing the density of low-x partons.

Parton density functions (pdfs) were first introduced in equation 2.21. The solutions of

the DGLAP equations are used to evolve the parton distributions as a function of x and

any Q2 scale. The x dependence at some input scale, , must be known beforehand.

This is theoretically incalculable and must be derived from fits to structure function data

obtained from experiments.

Pdfs have been published by several groups, with the majority being implemented in the

PDFLIB package [15]. This allows their convenient use in Monte Carlo simulations.

Two such pdfs used in this thesis are the MRS(a) [16] and CTEQ4D [17]

parameterisations.

18

Figure 2.5: Ladder diagram showing the effect of several gluons being radiated from the

parton that interacts with the virtual photon.

2.8 The Longitudinal Structure function, FL

In the naïve quark-parton model the valence quarks carry no transverse momentum. The

emission of a hard gluon from the quark however, introduces a small component of

transverse momentum due to momentum conservation rules. The measurement of FL

can therefore give the gluon distribution within the proton.

In order to parameterise this, the structure function FL, is introduced where

(2.33)

19

Substituting the above into equation (2.16), the cross section for e+p scattering can be

written in the form:

(2.34)

where

(2.35)

Again, the xF3 term is neglected and equation (2.34) can be written as:

(2.36)

where

(2.37)

The quantity, R, is defined to be

(2.38)

and is introduced into equation (2.36) to give:

(2.39)

As equation 2.39 shows, the relative contribution of F2 and FL to the cross section is

dependent on and hence y. Also, as the structure functions themselves are functions of

x and Q2, the extraction of FL requires a measurement of the cross section at fixed x and

Q2 while varying y, in effect varying the (1-) factor in the FL term. As can be seen from

equation (2.14), such a variation in y can only be achieved by changing the centre of

mass energy squared of the event, i.e. changing the beam energies.

20

Also, as the plot of as a function of y shows in figure 2.6, there is only a large

deviation of at large values of y. With the term in the cross section involving R

rewritten as:

(2.40)

this can also be plotted as a function of y and is shown in figure 2.6. Here, R is set to

0.3, a value resulting from the prediction of perturbative QCD. It is clear that the effect

on the cross section from non-zero values of R (FL) will only be visible at large values

of y.

Figure 2.6: and plotted as functions of y. The effect of non-zero R on the cross

section is only significant at high values of y.

The resulting requirement of making measurements at different centre of mass energies

and high y makes the measurement of FL extremely difficult.

Many fixed target experiments can run beams at different energies and have published

results on FL [23-32]. However, changing the beam energies at an e+p collider, such as

HERA, presents enormous challenges, ranging from understanding the response of the

detectors under different conditions to the engineering problems involved with changing

the beam energies. Such a move would also have a large impact on other analyses.

21

Although Monte Carlo studies of the effect of changing the beam energies at HERA

have been made [18,19], there are no plans for changing the beam energies.

A potential way of achieving the necessary variation in centre of mass energy is to

make use of the emission of hard photons by the incoming positron, as illustrated in

figure 2.7. These events are known as Initial State Radiative Events and serve to lower

the energy of the positron and therefore change the kinematics. The variable, z, is

defined as the fraction of the initial electron’s energy remaining after the emission of

the photon, where:

(2.41)

Thus, the incident energy of the electron becomes zEe and the centre of mass energy

squared of the event becomes:

(2.42)

Equation 2.14 can therefore be rewritten as:

(2.43)

As can now be seen, a change in y can now be achieved by changing z, or having

photons of different energies. Monte Carlo studies of the potential of this method have

also been made [20,21]. These show using ISR events to measure FL from their effect

the absolute cross section would require much larger data sets than currently available.

However, the effect of R on the shape of the distribution should be observable using

the current available data and will be discussed further in chapter 8.

22

Figure 2.7: The emission of an ISR photon in a DIS event. The hadronic final state is

denoted by X.

The H1 collaboration has made use of another approach to determine FL that doesn’t

require changing the centre of mass energy of the interaction [22]. This method first

utilises data at low y where there is a negligible contribution from FL to the cross-

section. The resulting measurement of F2 is evolved to high y using the NLO Altarelli-

Parisi equations. In this region, where there is believed to be a sizeable contribution

from FL, the evolved value of F2 is subtracted from the measured cross section, leaving

the extracted value of FL. Resulting values for FL are shown in figure 2.8.

23

Figure 2.8: The Longitudinal structure function obtained by H1 as a function of x in

bins of Q2 along with charged lepton-nucleon fixed target experiments. The error bands

are due to the experimental (inner) and model (outer) uncertainty of the calculation of

FL using a NLO QCD fit to the H1 data.

24

Chapter 3

The Large Hadron Collider

3.1 Introduction

The Large Hadron Collider (LHC), currently under construction at CERN in Geneva, is

a proton-proton machine that will be the most important colliding beam facility in the

world for many years after it is commissioned in 2005. The LHC will probe conditions

at much higher centre of mass (CM) energies than current experiments. This will allow

it to probe a kinematic regime which, it is believed, will provide direct experimental

evidence for extremely important processes. For example, the Standard Model explains

the origin of mass via the Higgs mechanism [33,34]. The discovery of the Higgs particle

is therefore fundamental in our understanding of particle physics. There is also potential

to discover physics beyond the Standard model, possibly in the shape of supersymmetry

[35]. A schematic of the LHC is shown in figure 3.1.

The LHC will have a CM energy of 14 TeV, operating at extremely high luminosities in

the region of 1034cm-2s-1. It will be built inside the existing LEP tunnel with new halls

being built for the experiments. The experiments being built for the LHC include LHC-

B, a B factory for the investigation of CP violating processes, ALICE, a heavy ion

detector for nucleus-nucleus interactions and two general-purpose detectors, ATLAS

and CMS.

25

Figure 3.1: The LHC Collider showing the relative locations of the four experiments, CMS, ALICE, ATLAS & LHC-B

3.2 The Compact Muon Solenoid Experiment

The Compact Muon Solenoid (CMS) Experiment is designed to record general physics

events, in particular those events that are the signature of new physics. Furthermore, this

has to be done at the high luminosity and background conditions at the LHC. Figure 3.2

is a section of the CMS experiment showing the relative locations of the components.

To achieve these aims, a symmetrical detector has been designed. Innermost will be

silicon trackers that will reconstruct charged tracks and provide important vertex

information. Surrounding these will be high-resolution electromagnetic and hadronic

26

calorimeters that will measure the energy of particles to a high degree of accuracy. The

solenoid will generate an extremely high magnetic field of 4 Tesla and will enable the

identification and momentum measurement of charged particles.

Finally, outermost will be Muon chambers that will allow the detection of muons,

which pass directly through the calorimeter.

Figure 3.2: Section of the CMS experiment showing the relative positions of the

major components.

The rest of this chapter will concentrate on some of the electronic components

associated with the calorimeter.

27

3.3 The Calorimeter

The calorimeter consists of an electromagnetic calorimeter (ECAL) surrounded by a

hadron calorimeter (HCAL) that work in conjunction to measure the energies and

positions of particles produced in the interaction as well as providing hermetic coverage

for the measurement of missing transverse energy.

The purpose of the ECAL is to measure, with high resolution, the energies and positions

of the electrons and photons produced in each event.

The Higgs decaying to two photons channel [36] is used as the benchmark process to

assess the calorimeter performance at the LHC. Although the cross section for this

process is very low, the background is very small and it will be the best way of

detecting the Higgs if it has a mass 130 GeV. As such, the performance of the ECAL

is determined by the di-photon mass resolution. This depends on the energy resolution

of both photons, , as well as the angular resolution of the two photon separation

angle, , .

The design chosen is an active ECAL array consisting of scintillating lead tungstate

(PbWO4) crystals [37,38]. In an active design, the crystal acts as both the scintillator

and the absorber. Lead tungstate was chosen because of its properties as a good

scintillator with short radiation length as well as good radiation hardness, important in

the extreme conditions at the LHC.

Light from the crystals is detected using silicon avalanche photodiodes in the barrel, and

vacuum phototriodes in the endcaps, whose signal is digitised by the front-end

electronics.

On a larger scale, the ECAL consists of a Barrel calorimeter covering the range in

rapidity || 1.48 and two endcap calorimeters covering 1.48 || 3.00, where

28

=-ln(tan/2). In order to reduce systematic errors, the design is arranged such that no

crack between two crystals is aligned with the interaction point.

The HCAL measures the jets produced by p-p collisions, it must be as hermetic as

possible as well as having sufficient depth in order to contain the hadronic showers. The

size of the HCAL is limited by the super-conducting coil that surrounds it. The choice

of design uses copper absorber interleaved with plastic scintillator tiles. Copper was

chosen for the absorber as it has a short interaction length and is non magnetic.

The HCAL also covers the region || 3.0 in a barrel and two endcaps. The calorimeter

coverage is extended to || 5.0 by two forward calorimeters with copper absorber and

quartz fibres for readout.

3.4 The Trigger

At the design luminosity of 1034cm-2s-1 there will be an average of 20 interactions per

bunch crossing, every 25ns, leading to an input rate of 109 interactions per second. The

maximum rate with which data can be stored on tape for analysis is ~100Hz, therefore a

reduction in rate by at least a factor of 10-7 is required. The trigger and Data Acquisition

(DAQ) System are shown in figure 3.3.

The level-1 trigger consists of front-end electronics operating on a subset of the data.

These generate trigger primitives and perform level-1 trigger processing. Information is

then passed to the Global Trigger Processor (GTP), which, on a positive decision causes

the data to be read from pipelines into front-end buffers.

The higher level triggers are implemented in a processor farm that receives inputs at a

maximum rate of 100kHz. Several levels of filter will be performed to reduce the rate to

the final output rate of ~100Hz.

29

Phenomena have been identified which may be indicative of signatures of new physics

processes. A successful trigger needs to select these events with a very high efficiency.

For example:

Muons and electrons from inclusive W bosons.

Muons with high transverse momentum, pt.

Jets at high pt.

High pt photons and electrons.

Missing Et.

Figure 3.3: The CMS trigger and DAQ.

The only two components used in the level-1 trigger are the calorimeter and muon

chambers. The muon trigger identifies muons and measures their transverse momentum,

pt, before passing information to the global first level trigger. The calorimeter trigger is

presented in detail in the following sections.

3.4.1 The Calorimeter Trigger

The calorimeter trigger has to identify and select electrons, photons and jets as well as

measure the missing ET. The calorimeter is divided into 4176 trigger towers,

corresponding to the HCAL tower structure. In the barrel, a trigger tower corresponds to

30

0.087 in and 0.0873 (5) in , corresponding to 25 ECAL crystals. Endcap trigger

towers cover a larger range in . Trigger primitives generated by the front-end

electronics are processed in regional crates. For this purpose, the calorimeter is split into

18 regions, each served by its own crate as shown in figure 3.4. A crate can process 256

ECAL-HCAL trigger tower pairs.

Figure 3.4: The positions of the trigger regions. Each trigger region is served by its own

trigger processor crate.

The electron/photon trigger selects individual energy deposits determined using a

sliding window algorithm [39]. This takes groups of 3x3 trigger towers and performs

cuts on the ECAL energy in each tower as well as the ratio of energy of the

corresponding HCAL towers to the ECAL. Candidates are then sorted and the top four

in each crate are passed to the next stage. Jets are found by summing jet E t over 4x4

trigger towers as well as searching for isolated hadrons. Following this, another sort is

performed and the four top electron, jet and isolated hadron candidates are passed to the

global calorimeter trigger.

31

The Missing Et trigger combines the transverse energy in 0.35 x 0.35 (,) regions,

taking into account the tower angular co-ordinates, over the entire calorimeter. This

provides an estimate for the missing Et.

3.4.2 The Sort ASIC

As can be seen from above a fast sort algorithm is important for the calorimeter first

level trigger. The sort process will be implemented using 2-stage sort trees. The first

stage uses 3 sort ASICs each receiving 24 objects over 4 clock cycles and outputting 4

objects while the second stage takes the resulting 12 objects and outputs 4 objects. The

requirement of the Sort ASIC is therefore to output the four highest ranked objects from

a set of input trigger objects at a clock speed of 160MHz. The design for the

implementation of this algorithm is shown in figure 3.5.

Before the main sort stage, a pre-sort is performed and objects are arranged into input

groups. The objects in each input group are arranged into rank order.

The first stage of the sort algorithm places the input groups in order of the highest

ranked object in each group, with the highest ranked group labelled A(0,1,2,..), followed by

B(0,1,2,..) etc. As the groups have been pre-sorted, the highest ranked object in group A

must therefore be the highest ranked overall. Furthermore, if for example, there are four

input groups each containing four objects the four highest objects overall must come

from the set {A0, A1, A2, A3, B0, B1, B2, C0, C1, D0}. As the highest ranked object overall

is A0 because of the pre-sort, the second ranked object must therefore be either A1 or B0.

This is repeated for the lower ranks.

32

Figure 3.5: Schematic of the sort algorithm.

As part of the early development of the system, the sort algorithm was implemented on

an ASIC. The ability of the design to work under the required conditions is however

unknown. Therefore several such prototype sort ASICs have been built and require full

testing.

Due to the rapid developments in integrated circuit technology however, this approach

has been rendered obsolete. The test system described below therefore remains a

development exercise.

33

3.5 The Test System

The requirement of the test system is to send simulated trigger signals at the LHC clock

speed to the sort ASIC and to monitor its output for errors. The sort ASIC requires 32

8-bit words input at a speed of 160MHz but a testing device should be able to raise the

input to 200MHz. This requirement is too high for current commercial chip testing

platforms to test it to its full capacity. Therefore, a specialist chip-testing device has

been designed. Ideally, the design of a test system should be modular where

components can be removed and replaced at any time and can have more than one

application. For example, it is envisaged that further components of the CMS trigger

will be tested on the same platform.

For this reason a field bus design was chosen. The principle of the design is to store the

high-speed output from the device under test onto a series of memories located on a bus.

The data can then be read and analysed at a slower clock speed using currently available

technology. By placing several such memories on the bus a single computer can analyse

a large amount of data. An overview of the field bus is shown in figure 3.6.

The output of the device under test is readout at high speed onto memory modules on

the field bus. Several such modules can be located on the bus at any one time. The

contents of these memories can then be read at the slower speed of 40MHz onto the

controlling computer, in this case a PC, before being analysed and checked for errors.

The input to the ASIC is provided by four pseudorandom number generators giving the

required bit rate with the output sent though a demultiplexer onto a 16-bit bus running

at 40MHz.

The following description however, is independent of the device under test.

34

Figure 3.6: The Layout of the Sort ASIC Field Bus Test system.

The 16-bit bus then interfaces with memory modules, each holding 4 Dual-Port RAM

(DPR) memory chips. Modules on the field bus and are linked to the other modules with

an 8-bit loop. This loop can include more memory modules where necessary, as well as

other devices. For example, the Clock and Control module provides clock distribution

and triggering facilities. The nodes have a common design and decode the field bus as

well as providing the control of each module.

Dual Port RAM (DPR) was chosen as it contains two sets of address and data lines,

labelled left (L) and right (R), as compared to conventional memory with just one set.

Both sets of lines in DPR access the same memory locations on the chip and as such

allow simultaneous reading and writing to the memory.

Finally, the field bus requires a driver. Signals are generated and analysed by a remote

computer terminal that can send control signals and data packets to the field bus.

Furthermore, the computer can read data from the field bus and analyse the output from

the device under test as well as check for errors.

The field bus driver module simply converts the PC signals to the field bus, which uses

either copper cabling or fibre-optics.

35

3.5.1 The Protocol

Messages and commands sent around the ring by the field bus driver are received by all

nodes, which then decode them. The message content should then determine the action,

if any, that the node performs. In order to achieve this any protocol has to include

commands for the full set of actions available to the nodes. In addition, addresses for

selecting nodes individually as well as for selecting memory locations on the DPR, a

data payload and finally error checking facilities should also be included. As the field

bus design implements an 8-bit bus, the protocol consists of a set of 8-bit words in the

order shown in figure 3.7.

Each node of the system is designed to be 16-bit. Therefore, every two words in the

field bus protocol correspond to one word used by the node. The aim of this is to allow

the major functions of the node to run at half the clock speed of the field bus, thereby

allowing for easier implementation using current technology.

Figure 3.7: The Field-Bus Protocol

36

One complete cycle of the bus first consists of a Header, consisting of 10 8-bit words.

The header starts with the token, which defines the operation to be performed, followed

by the address of the node that is intended to carry out this command. If the command

involved reading or writing to the DPR the starting address and data length follow,

otherwise these are set to zero. Two error check words follow.

Next, comes the data payload, the length of which is defined in the header up to a

maximum length of 215 words. This length was determined by software constraints.

Finally, come another two Error Check words.

The bit naming convention used has the least significant bit (LSB) in the top left hand

corner of a 16-bit word double and the most significant bit (MSB) in the bottom right

hand corner.

Six tokens control the general actions of the nodes. They are:

Bus Reset

Get Node Name

Write Data Word

Read Data Word

Write Data Block

Read Data Block

The Bus Reset and Get Node Name tokens are global and act on every node on the

system. The Bus Reset token, as its name implies, resets all the signals and registers of

the nodes on the network.

The Get Node Name token loads the first node in the network with an 8-bit address, a,

specified by the user in the Node address word. This address is then incremented by 1

and the protocol, otherwise unchanged, passes to the next node and so on. In this way,

all the nodes are given addresses as shown in table 3.1

37

Node 1 Node 2 Node 3 Node 4

Address Address+1 Address+2 Address+3

Table 3.1: Addressing the Field bus nodes

3.6 The Field Bus Node

The aim of the node design is to make the field bus nodes modular. Therefore, all

nodes, regardless of the function of the board on which they are situated, have the same

general design. This overall design is shown in figure 3.8 and is described in the

following sections. This is implemented onto a Field Programmable Gate Array

(FPGA), which is the core component for each board.

Figure 3.8: The overall node design.

38

3.6.1 The XILINX Field Programmable Gate Array

The XILINX FPGA is an integrated circuit consisting of an array of complex logic

blocks connected by reroutable links. This gives the device a large amount of flexibility.

A huge range of digital circuits can be designed and then downloaded to the FPGA.

Furthermore, the FPGA can be reset allowing different designs to be implemented.

When the final design has been completed, a Programmable Read-Only Memory

(EPROM) can be used to store it and reload the FPGA whenever it is reset or when the

power is switched on.

In general, the size and complexity of modern digital circuits is such that it is

impossible to design them by building circuits at the schematic level. It is evident

therefore that a way of synthesising these from a set of standard instructions is required.

VHDL (Very High Speed Integrated Circuits Hardware Description Language) [41,42]

is a programming language that allows the design of such large and complex integrated

circuits.

VHDL uses objects called ‘entities’ which are descriptions of some logical process with

the input and output to the process also defined.

An entity can be as simple as a description for a simple logic operation, for example

(3.1)

defines a logical ‘and’ operation with inputs A & B and output C.

Another entity could be a state machine with many different states and input signals, the

transition from state to state depending on a complex interaction between these signals.

Entities are joined in a hierarchical structure to form the overall design. The advantage

in this case is that neither a top-down nor a bottom-up design methodology is favoured.

One could just as easily start with the top-level design as start from the individual

components.

39

After the VHDL has been written it must be converted into a form that can be

downloaded to the FPGA. This is called implementation.

The first stage of the implementation of the design after the code is written is known as

Elaboration. Here, the entities are placed in the correct hierarchical structure. Then,

follows the architectural synthesis stage. Here the synthesis of the required logic

components is performed.

It is after this stage that the physical pin locations on the chip of the inputs and outputs

are assigned. Of theses pins, some are reserved for power supplies, resets and loading

the design. The others however, can be assigned to whatever purpose is required.

Finally, the Logic is optimised for either speed or area and the circuit diagrams are

created. These diagrams must then be converted into a netlist, or list of the connections

used within the FPGA, which is then used in the final stage to create a bit-file that can

be downloaded to the chip.

3.6.2 The Interface

The interface is the only part of the design dependent on the hardware being used. Its

function is to provide the necessary connection to external resources that may vary from

board to board. For example, the memory module board will require address, data and

control lines for the DPR. There may also be the requirement for control lines to any

displays or LEDs mounted on the board. Also, the interface to the field bus itself may

vary from board to board, i.e. from coaxial cable to fibre optic inputs.

The design should allow the greatest amount of flexibility in order to make changes as

simple as possible.

3.6.3 The Node Decoder

The Node Decoder monitors and, if necessary, acts upon the field bus protocol. It has

four main components, the Input/Output (IO) module, a clock divider, a Header decoder

and internal bus control. The layout of the Node Decoder is shown in figure 3.9.

40

Figure 3.9: The Node Decoder.

The clock divider provides a control signal with double the period of the field bus clock.

CLK2 = high is used throughout the design to synchronise the 16 bit words. The signal

is generated using a 2-bit counter clocked with the field bus clock.

The IO Module converts the 8-bit field bus to internal 16-bit words used by the decoder.

These 16-bit words are then passed into the rest of the system. The data however also

passes through a shift register that delays it by the same number of clock cycles that are

required by the Node Decoder. In this way, the header always passes though unaffected

by any other process. An illustration of the IO module is shown in figure 3.10. Data is

only written to the field bus if the output enable signal is set high. The latches in the

shift register are clocked with the field bus clock while the input latch is clocked with

the internal CLK2 signal. On CLK2 = high the first 8 bits of the 16 bit internal words

are filled while on CLK2 = low the last 8 bits of the 16 bit words are filled.

41

Figure 3.10: The Input/Output module

The Header Decoder decodes the protocol. The main component is a state machine that

waits for the arrival of a valid token and, for those tokens that require it, a node address.

Then, on each subsequent CLK2=high signal it cycles through the states:

Load Address 1

Load Address 2

Load Length

Header Error Check

IO Data

Data error check

Error word

End State

Idle

If however, the token is the Bus Reset token a bus reset signal is set high for 2 Clock

cycles, performing a ‘soft’ reset, as the state machine will continue to its end state.

42

During the Load states, appropriate registers are loaded with the current data word. The

Address and IO Data Counters are loaded with the contents of these registers during the

Header Error Check state. The Address counter counts up starting from the loaded

address while the IO data counter counts down from the load length to 0. On reaching 1,

a terminating signal is sent to the State Machine.

If the token is Read/Write Data, the state machine will remain in the IO Data state until

the terminating signal is received.

Error checking is done by performing an XNOR on each word with the previous one.

The result is compared with the check word. If the two are equal, no error is returned.

This is equivalent to an odd parity check.

The Get Node Name Token is implemented by a separate module. If this token is

received, the state machine sets a get name valid signal and a node address register is

then loaded with the word in the data payload. An address-loaded signal is also set. The

data word is then incremented by one and sent to the IO module to be sent on to the

next node on the field bus.

Data will only be sent to the field bus if the right conditions are met. Firstly, for the Get

Node Name token the signal Data to Bus enable is set during the Header Error check

state. Secondly, if the token is Read (word/data), Data to Bus enable is only set on the

correct state and if an output enable signal is set. This only occurs when the node is

being addressed.

The memory manager controls the necessary address and read/write enable signals

necessary for reading and writing data to memory.

A node also possesses an internal memory comprising of a set of 8 16-bit registers

that can be used for control and testing purposes.

43

0 - control register - Read/Write

1 - Node address register - Read only (except on Get Node Name)

2 - Type and Version Number - Read Only

3 - Status Register - Read Only

4 - Reserved for future use - Read Only

5 - General Purpose/resources - Read/Write

6 - General Purpose - Read/Write

7 - General Purpose - Read/Write

3.7 Simulation of the Design

In order to simulate the design a test bench was defined. The test bench simulates the

field bus inputs and clock. It is applied after the architectural synthesis stage. The

current state of any signal within the design can then be monitored throughout the

duration of the simulation.

Figure 3.11 shows the signals monitored during the running of a typical testbench on a

simulation of a field bus node. The simulation runs three tokens. First, a Get Node

Name command loads the node address with the address 1. This is followed by a write

data command that writes six 8-bit (three 16-bit) words to the node with address 1

starting at the address 0101. Finally, a read data command is again sent to the node with

address 1. This reads three words from the starting address 0101.

Points 1,2 and 3 show the starting points of each data packet. The inputs are clocked on

the rising edge of the field bus clock. However, the 16 bit signals of the node decoder

have to be synchronised with the rising of the clock 2 signal. Points A show the actual

‘CLK2’ signal used in the node can either be equal to or a NOT of the nominal CLK2

signal.

44

Figure 3.11: Simulation of Node Decoder through a Get Node Name command,

followed by a write and read data cycle.

This ensures that the node decoder is always synchronised regardless of which point in

the CLK2 cycle that the field bus data bunch arrives. Point B shows the output-enable

signal set to high, this allows data from the internal registers or memory to be written to

the field bus. At all other times the signals pass through the input-output module with

appropriate delay. As can be seen, the output to the field bus is delayed by 10 clock

cycles.

The prototype consisted of a PC running a Windows based Graphical User Interface,

coded in C++, with a physical interface to the field bus provided by a dedicated circuit

board. This was connected to a board via a 40-way cable. For testing, the PC also

provided the clock. The node on the board is linked to the field bus via ECL-TTL chips

that drive the 8-bit bus. The clock is also delivered around the field bus. A picture of

this board is shown in figure 3.12

45

A prototype memory module was also included on the field bus. This was designed to

be placed in a VMEbus crate and was run successfully in tandem with the first node.

The memory module is illustrated in figure 3.13

Figure 3.12: The prototype interface board. The FPGA is shown in the centre with the

socket for connection to the PC shown at top. The TTL output sockets for the field bus

are to the right. Other resources include 4 seven segment displays and 11 LEDs as well

as global and local reset buttons.

46

Fig 3.13: The prototype memory module. Field bus connections are at bottom left with

the FPGA upper centre. Provision for 4 DPR chips is made although only one is in

place here. This board is designed to be placed in a VMEbus crate although it only

draws power from the crate. The resources also include 4 multifunction displays.

The field bus was successfully tested with two nodes, on separate cards. The node

addressing and ability to read and write data to the internal registers on the nodes was

demonstrated.

The next stage required reading and writing operations to the DPR. This required

overcoming synchronisation problems caused by the distribution of the clock around the

field bus and hence required the introduction of the clock distribution card. Also, the

entire design required running at much higher clock speeds than that provided by the

PC.

The progress of technology though, finally ended the field bus design. Due to a large

increase in speed and reduction in cost of FPGAs, it is now possible to implement the

sort algorithm on one of these rather than a specialist chip. This therefore enables the

FPGA simulation to be used directly for testing the operation of the chip.

47

Chapter 4

HERA and the ZEUS detector

4.1 HERA

The Hadron Electron Ring Accelerator, HERA [43], is an electron-positron collider

located at the DESY Laboratory in Hamburg, Germany. Built by an international

collaboration it was commissioned in 1991 with the first collisions observed in May

1992.

The two main storage rings are each 6.3 km in circumference; one contains a beam with

820 GeV protons, the other a counter-rotating beam of 27.5 GeV positrons. This gives a

centre of mass energy of 300 GeV. (For the 1998 running period onwards, 920 GeV

protons were used.) The design luminosity is 1.5 x 1031cm-2s-1. Figure 4.1 shows the

layout of HERA along with the locations of the main experimental areas. The North and

South Halls house the H1 and ZEUS experiments respectively with the HERMES fixed

target experiment in the East Hall and the HERA-b experiment located within the

PETRA ring.

Both the protons and electrons are collected into 220 bunches, crossing at each

interaction point every 96s. Some of the bunches are left unfilled and are used for

background studies. In order to study all possible beam-related backgrounds there are

unpaired electron bunches (no protons), unpaired proton bunches and completely empty

bunches.

48

The protons are initially accelerated to 7.5 GeV in DESY III before being transferred to

PETRA, here they are accelerated to 40 GeV and injected into HERA. When all of the

bunches are filled the beam is then accelerated to 820 GeV. The high energy of the

protons requires a bending field of approximately 4.7T, requiring the use of

superconducting magnets.

Figure 4.1: The HERA Layout, showing the locations of the ZEUS and H1 experiments

along with the preaccelerators, H Linac, e Linac, DESY and PETRA.

The positron beam, however, only needs a field of 0.164T and conventional magnets are

used. The positrons are initially accelerated in a 500 MeV linac and accumulated in a

49

single, 60mA bunch before being injected at 7 GeV into PETRA from DESY III. Once

there are 70 such bunches in PETRA they are accelerated to 14 GeV and injected into

HERA. Once the required bunch structure has been reached the positrons are then

ramped to 27.5 GeV.

Figure 4.2 shows the accumulated luminosity delivered by HERA for the years of

running up to 1999. For the 1996 and 1997 running periods, ZEUS collected

approximately 10.7pb-1 and 27pb-1 of data respectively.

Figure 4.2: The integrated luminosity delivered by HERA for the years 1992-1999. The

early 1999 running period used electrons before being switched to positrons for the

remainder of the year.

50

The HERA accelerator allows the study of lepton-proton scattering in previously

unreachable kinematic regimes. For example, to achieve the same centre of mass energy

a fixed target experiment would require an electron(lepton) beam with energy of several

TeV. Furthermore, a wide variety of physics can be studied, from accurate

measurements of the proton structure functions to photoproduction and searches for

physics beyond the Standard Model.

Figure 4.3 shows the kinematic regime reached by HERA DIS data taken using the

ZEUS experiment, alongside regions probed by fixed-target experiments. The ZEUS

data include results from shifted vertex running in 1995 [44] where the nominal

interaction point was moved in order reach lower Q2. The Beam Pipe Calorimeter

(BPC) and Beam Pipe Tracker (BPT) are two detectors placed close to the beam pipe in

order to measure scattered positrons at very small angles and low Q2. The data shown

were taken over a short period in 1997 [45]. The fixed target experiments included are

NMC [46], BCDMS [47], CCFR [48], E665 [49] and SLAC [50].

As can be seen, very low values of x as well as very high values of Q2 can be probed at

HERA. There is also potential for overlap with fixed-target data. Also, low Q2 and low

x regions can be reached, probing the transition region between perturbative and non-

perturbative QCD.

4.2 The ZEUS Detector

The ZEUS detector [51,52] is a general-purpose detector designed to record all the

physics processes at HERA. The imbalance in the beam energies results in a boost in

the direction of the proton. The detector is therefore asymmetric and is split into three

distinct regions, forward, barrel and rear. The forward region contains more particles

with higher energies and therefore has the most instrumentation. The general layout of

the ZEUS detector is shown in Figure 4.4.

51

Figure 4.3: The Kinematic Range explored by the ZEUS experiment at HERA shown

on the x-Q2 plane. Shown are results from the standard low and high Q2 analysis

together with results from shifted vertex running and very low Q2 data obtained using

the BPC and BPT. This is shown in comparison with results from fixed target

experiments, including NMC, BCDMS, CCFR, E665 and SLAC.

52

The interaction point is surrounded by a central tracking detector (CTD) and forward

and rear tracking detectors. All of these detectors are drift chambers. In the forward

direction is the Forward Tracking Detector (FTD), consisting of three modules with the

Transition Radiation Detector (TRD) sandwiched in between. The TRD provides

electron identification in the momentum range 1 to 30 GeV. In the rear direction is the

Rear Tracking Detector (RTD), which is of the same form as a single FTD module.

Surrounding the drift chambers is a superconducting solenoid providing a field of 1.43T

that allows the measurement of track momenta.

Enclosing the drift chambers and solenoid is a uranium-scintillator calorimeter. It is

split into three sections, the forward calorimeter (FCAL), barrel calorimeter (BCAL)

and rear calorimeter (RCAL) and is used for accurate position and energy measurement

of particles in jets as well as the scattered positron.

The backing calorimeter (BAC) serves to measure leakage from high-energy jets that

are not fully contained within the calorimeter. It also acts as the return yoke for the

superconducting magnet.

Finally, the outermost components are the muon drift chambers, FMUON, BMUON

and RMUON. These allow measurement of muons, which pass directly through the

calorimeter.

53

Figure 4.4: The ZEUS detector. The positions of the major components are indicated. In

this representation, the protons enter from the right and the positrons from the left.

54

4.2.1 The Zeus co-ordinate system

The ZEUS co-ordinate system [53] is defined with the +z direction aligned with the

direction of the proton beam, the +x direction pointing toward the centre of the HERA

ring while the +y direction pointing vertically upwards.

Angles are defined around the interaction point. The polar angle, , is measured relative

to the z-axis and the azimuthal angle, , is measured relative to the x-axis in the xy

plane. This is shown graphically in figure 4.5.

Figure 4.5: The ZEUS co-ordinate system.

The components used for the analyses in this thesis are described, innermost outwards

in the following sections.

55

4.2.2 The Central Tracking Detector

The Central Tracking Detector (CTD) [54] is the innermost detector of the ZEUS

experiment. It is a cylindrical drift chamber, 2m long, with nine radial superlayers each

divided into cells containing 8 sense wires. The arrangement of these wires in part of

the chamber is shown in figure 4.6. The total number of anode (sense) wires is 4608.

The wires in the odd-numbered superlayers run parallel to the beam direction while

those in the even-numbered superlayers have a small stereo angle to allow

determination of the z co-ordinate of the hits.

Figure 4.6: The arrangement of the wires in the CTD.

56

The angle (~5) was chosen such that the polar and azimuthal angular resolutions are

approximately equal. An accuracy of 1.4mm in the z measurement can be obtained.

The chamber operates in a high magnetic field in order to obtain information about

particle momenta. The electrostatics and choice of gas combined with the magnetic

field cause the electron drift trajectories to rotate through a Lorentz angle of 45 relative

to the electric field direction. Furthermore, the cells are aligned at 45 relative to the

radius vector therefore ensuring the drift direction is perpendicular to high momentum

tracks. The resulting configuration brings advantages with track finding, in particular

with the left-right ambiguity, i.e. with two field wires either side of a sense wire, it is

not immediately obvious which side of the sense wire the track passes through. Also,

the maximum drift distance is ~2.5cm. This helps to resolve close tracks by reducing

the likelihood that they pass through the same cell.

The gas used is an 85:8:7 Argon: CO2: Ethane gas mix with a trace amount of ethanol

(0.84%) added to prevent whisker growth on the chamber wires [55]. This choice was

made to provide a high enough drift velocity (50 m ns-1) to allow a fast readout time

and enable the CTD to be used in the triggering.

Signals from the CTD are amplified before being digitised by 104MHz Flash Analogue

to Digital Converters (FADCs). The digitised signal is stored in a digital pipeline until a

decision to keep or reject it is received from the trigger. Events that pass the trigger are

processed to remove pedestals.

An additional measurement of z is provided by measuring the difference in arrival time

from pulses at each end of the wires. All wires in superlayer 1 and alternate wires in

superlayers 3 and 5 are instrumented for this. The resolution for this time difference is

~300ps which implies a resolution of ~4.4cm in the z position. The system can resolve

multiple hits with a minimum time separation of 48ns. Although z by timing resolution

is worse than that provided the stereo superlayers, the speed with which the information

is obtained allows it to be used in the trigger.

57

4.2.3 The Small Angle Rear Tracking Detector

The Small Angle Rear Tracking detector (SRTD) [56] is mounted on the face of the

RCAL (z = -146cm) and covers the hole surrounding the beam pipe. It is built from an

array of scintillator strips, arranged into two layers, one with horizontal strips, the other

vertical. The SRTD covers the angular range 162 to 176 and has an area of 68 x 68cm2

with the exception of a 20cm x 20cm hole in the centre for the beam pipe. The layout of

the scintillator strips is shown in figure 4.7.

Figure 4.7: The arrangement of the two layers of scintillator strips in the SRTD.

Due to the fine segmentation of the scintillator fingers, the SRTD gives a position

measurement with a better resolution than the calorimeter. The SRTD position

resolution is ~3mm.

The SRTD is also used as a presampler to correct the energy of positrons for the energy

loss caused by the crossing of the dead material between the interaction point and

calorimeter. This is related to the resulting shower multiplicity and therefore to the

energy deposit in the SRTD. The correction is done on an event-by-event basis.

These two considerations allow improved reconstruction of positrons at high angles,

therefore improving the ability to do accurate low Q2 analyses.

58

4.2.4 Magnets

In order to measure the momentum of charged particles in the inner region, a

superconducting solenoid is located between the CTD and the calorimeter. The magnet

provides a 1.43 T field. The flux return consists of the iron in the yoke and in the

Backing Calorimeter (BAC). The field in the central region is calibrated to a precision

of 1%. The effect of this magnetic field on the beams is compensated by another

superconducting solenoid, called the compensator, located in the rear endcap of the iron

yoke.

4.2.5 The Calorimeter

The calorimeter is designed to measure accurately the energy and position of isolated

positrons and jets [57]. The design is such that the response should be equal for both

hadronic and electromagnetic particles. Furthermore, it has to cover as much solid angle

as possible.

The coverage obtained is 99.5% in the forward hemisphere and 98.8% in the rear

hemisphere with the calorimeter divided into 3 separate components, the forward

calorimeter (FCAL), barrel calorimeter (BCAL) and rear calorimeter (RCAL). The

energy of incident particles is much higher in the forward regions due to the relative

energy of the proton and positron. The depth of the calorimeter therefore varies, with

the FCAL being deepest in order to contain the highest energy jets. The overall

absorption length of the sections is 7 for the FCAL, 5 for the BCAL and 4 for the

RCAL.

The calorimeter is made from layers of depleted uranium (238U) and plastic scintillator

arranged into modules. Each module is further segmented into EMC and HAC sections,

with the EMC sections on the inner face of the module and the HAC sections behind

them. For the FCAL and BCAL there are two HAC sections, HAC1 and HAC2.

Wavelength-shifter bars carry light pulses from each cell to photomultiplier tubes

(PMTs) at the back of each module. There are two PMTs per cell. These provide both

redundancy and an indication of faulty PMTs by examining the difference in readout.

59

The calorimeter is arranged so that no cracks between modules point directly at the

interaction point. This reduces the chance of energy leaving the calorimeter undetected.

The choice of uranium arises from the desire for equal hadronic and electromagnetic

response. While electromagnetic showers reach the scintillator with high efficiency,

hadronic showers tend to be partially absorbed in nuclear binding energy in the

absorber. Depleted uranium, 238U, was chosen as the absorber as it has the property of

releasing extra neutrons as it absorbs energy. These neutrons can be absorbed in the

scintillator to produce extra scintillation light. This process is known as compensation.

The relative thickness of the absorber and scintillator was adjusted to achieve a required

ratio of electromagnetic to hadronic response of 1 0.05. In test beam an

electromagnetic energy resolution of 18%/E and a hadronic energy resolution of

32%/E was achieved. A further advantage in the use of 238U is that, due to its high

atomic number, Z, it has a shorter radiation length, allowing the calorimeter to be more

compact.

Several methods are employed for calibration of the calorimeter. These include utilising

the natural radioactivity as a calibration signal, which provides a steady reference

calibration [58]. Also, a cobalt source scan, charge injection [59] and laser calibration

pulses [60] are used.

In order to improve energy resolution and particle identification, two components, the

presampler and Hadron Electron Separator (HES) are placed in front of the calorimeter.

4.2.6 The Presampler

The presampler [61] is a segmented scintillator array placed immediately in front of the

calorimeter. It consists of a layer of scintillator tiles, connected by wavelength shifting

fibres to photomultiplier tubes. The tiles have a 20cm segmentation that maps directly

onto the hadronic cells. The area covered by the rear and forward presamplers in

relation to the RCAL and FCAL is shown in figure 4.8.

60

From the beginning of 1999 running, the Barrel Presampler (BPRES) was introduced.

This consists of 32 cassettes each containing 13 scintillator tiles orientated along the z-

axis. These cassettes are installed directly in front of the BCAL modules.

The presampler is used to correct for the loss in energy due to the showering of

positrons in dead material in the same way as the SRTD, on an event by event basis.

Figure 4.8: The area covered by the Forward and Rear presamplers (shaded)

superimposed on the FCAL and RCAL cells.

61

4.2.7 HES

The HES is a plane of 3cm 3cm silicon diodes located 3 radiation lengths inside the

electromagnetic calorimeter both in the forward (FHES) and rear (RHES) directions.

This position corresponds to the electron shower maximum and therefore

electromagnetic showers provide higher deposits in the HES. The segmentation is

significantly better than the F/RCAL and allows the HES to improve the detection of

electrons and 0s.

4.2.8 The Muon Chambers

The muon chambers are divided into three components, the Forward Muon (FMUO),

Barrel Muon (BMUON) and Rear Muon (RMUON) located in the forward, barrel and

rear directions respectively. The chambers are drift chambers and measure tracks

created by the passage of muons through them.

In addition to the main detector components, there are several forward and rear

components that aid the detection of very low angle particles or provide a control of the

background.

4.2.9 Beam Pipe Calorimeter and Beam Pipe Tracker

The Beam Pipe Calorimeter (BPC) is a small tungsten-scintillator calorimeter located

close to the beam pipe to the rear of the RCAL, 3m from the interaction point. It is

designed to detect electrons scattered through very small angles and therefore at very

low Q2. Using the BPC, scattered positrons scattered through the angular range 18mrad

< < 32mrad can be detected, thereby extending the accessible Q2 range to 0.1 GeV2.

In 1997, the Beam Pipe Tracker (BPT) was installed in front of the BPC. It consisted of

two silicon micro-strip detectors providing extra information on the track of the

electron, therefore allowing better control of the background and systematic effects

associated with the measurements made by the BPC.

62

4.2.10 The VETO Wall

The VETO Wall is an 87cm thick iron wall located 7.5m from the interaction point in

the rear direction near the tunnel exit. Its primary purpose is to protect the detector

against particles from the beam halo accompanying the proton bunches. However,

scintillator detectors are placed on both sides of the wall and provide a veto on beam

gas background events.

4.2.11 The Collimator, C5

The collimator C5 is connected to the support of the compensator coil 3.1m from the

interaction point in the rear direction. It protects the central detector from radiation

reflected by absorbers which are designed to absorb the direct synchrotron radiation

produced both up and downstream of the interaction point. Connected to the collimator

are four scintillation counters that provide an accurate timing signal of the background.

This allows the ability to distinguish the background from the positron or proton side

and to veto the showers produced by the proton beam halo scattering off C5 itself.

4.2.12 The Luminosity Detector

Measurement of luminosity is achieved using the bremsstrahlung process

e+p e+p (4.1)

where the final-state photon is emitted at very small angles with respect to the initial

positron direction. This process has a clean experimental signature and a large cross

section, well known from QED. The bremsstrahlung differential cross section is given,

in the Born approximation, by the Bethe-Heitler formula:

(4.2)

63

where is the photon energy, , are the incident and scattered electron energies,

is the proton mass, M and m are the proton and electron masses, is the fine

structure constant and is the classical electron radius.

For photon energy > 10 GeV, this results in a cross section of 37.08mb and a rate of 10 6

events per second for the HERA luminosity of 1031cm-2s-1.

As the luminosity, L, is simply given by

(4.3)

where N is the measured number of events and is the cross section, Bremsstrahlung

events can therefore be used for fast and accurate luminosity monitoring. In this case,

the luminosity measurement requires the detection of the bremsstrahlung photon [62].

The luminosity monitor (LUMI) consists of a photon detector and positron detector.

The position of these components is shown in figure 4.9. The positron detector is

located 35m from the interaction point and is used to measure the energy of positrons in

coincidence with the bremsstrahlung photon.

Figure 4.9: Overview of the ZEUS LUMI detector. The locations of the four main

components along with the magnets upstream of the main detector are shown.

The photon detector, LUMI-, is located 107m from the interaction point in the

direction of the positron beam. It consists of a 24X0 depth lead-scintillator calorimeter

64

with two radiation-lengths of absorber placed in front for the 1996 data taking period

and 3 radiation lengths of absorber from 1997 onwards. The change in absorber length

was made in order to prevent radiation damage to the calorimeter. The energy resolution

was for the 2X0 absorber and for the 3X0 absorber. The absorber is

required to shield against the large flux of direct synchrotron radiation. Inside the

calorimeter at a depth of 3X0 are two crossed layers of scintillator fingers that act as a

position detector. The design of the LUMI- calorimeter is shown in figure 4.10

showing the positions of the filter, the layers of scintillator and lead and the location of

the position detector (POS-DET).

Figure 4.10: The LUMI Calorimeter.

In addition, there are also taggers used to identify electrons from photoproduction.

These consist of further positron detectors found at 8m and 44m from the interaction

point. They are not however used directly for the luminosity measurement. The 44m

tagger is a 24X0 deep tungsten-scintillator calorimeter located 44m from the interaction

point. It is designed to detect electrons in the energy range 22-26 GeV.

4.3 Trigger and Data Acquisition

65

The large amount of data from the detector components coupled with the short bunch

crossing interval means there is an enormous amount of data to store. As each event

produces approximately 100Kbytes of data, it is therefore impossible to store all the

data produced.

Most events however are caused by background processes and the rates from interesting

physics processes are much lower. An efficient trigger must therefore select the

interesting events with a high efficiency while rejecting as much of the background as

possible.

At ZEUS, a three level trigger is used. An overview of the trigger and data acquisition

system is shown in figure 4.11.

4.3.1 The First Level Trigger

The aim of the first level trigger (FLT) is to reduce the input rate from the bunch

crossing rate of 10.4 MHz to an output rate of 1 kHz.

Individual FLT component processors process the data of their component then make a

decision after 1.0-2.5s before sending a summary of the trigger information to the

Global First Level Trigger (GFLT). This combines all the information and decides

whether to reject the data or not. The GFLT trigger calculations take 46 bunch crossings

(4.42s), during which time data from the components is pipelined, ensuring the

process is deadtime free. If it accepts the event, the GFLT sends a Trigger_1_Accept

signal, which includes the bunch crossing number, to each component in order to read

out the data. On receipt of this, each component keeps a Busy_Bit set for the duration of

the readout. All components must reset their Busy_Bit before the GFLT can send

another Trigger_1_Accept.

66

Figure 4.11: The ZEUS Trigger Layout showing the flow of data from the detector

front-end electronics, through the triggers, to final storage onto either tape or disk.

The Fast Clear (FCLR) can reject events between the FLT and SLT. It uses calorimeter

information to identify signatures for background processes and can send an abort to the

component buffers. The FCLR was active during the 1995 to 1997 running period but

was never used in the trigger as the FLT rates were never high enough to make it

worthwhile.

67

4.3.2 The Second Level Trigger

The Second Level Trigger (SLT) has more precise and complete data available to it than

the FLT. After a GFLT accept is received the data is digitised and processed by second

level component triggers using a network of transputers operating in parallel. The

Global Second Level Trigger (GSLT) combines the results from the components and

sends the decision to the Event Builder (EVB). The requirement of the GSLT is to

reduce the rate from 1kHz to 100Hz.

The Event Builder stores the data from the components until the Third Level Trigger is

ready to process it and combines all the component data into one coherent event. The

EVB can build up to 75 events in parallel.

4.3.3 The Third Level Trigger

The Third Level Trigger (TLT) consists of a computer farm running a software trigger.

The software is a simplified form of the offline reconstruction. Tracking reconstruction

is performed by the VCTRAK software package [63] and other electron finding and jet

finding routines are used to tag physics events. These events are then allocated a

physics category depending on which physics filter is used. The input rate from the

SLT of ~100Hz is reduced in the TLT to an output rate of 3-4Hz. Events that pass this

level are written to tape at the DESY main site over a dedicated connection (FLINK).

4.3.4 Reconstruction

In order to reconstruct the event fully, the raw data is processed using the reconstruction

software package ZEPHYR [52] some time (usually a few days) after the data was

taken. The reconstruction code uses the raw data from the detector to determine the

variables that can be used for physics analyses. This includes running the processor

intensive code, not otherwise used at the TLT, as well as including calibration constants

that are not available online. For each event, a set of tables containing relevant

information from all the components of the ZEUS detector is then filled.

68

Finally, similar physics events are selected using a filter and allocated a code, or DST

bit. This is in effect a 4th level trigger as events with a common DST bit can be easily

selected therefore saving computer time.

An example of a reconstructed event shown using the LAZE event display package is

shown in figure 4.12. The event shown is a relatively high Q2 neutral current event. The

tracks, clusters in the calorimeter and electron candidate can be seen.

4.3.5 DIS Event selection

As the dominant process at HERA is photoproduction, various criteria must be used in

order to select DIS events. The most significant cut is applied to the E-Pz of the event

where E is the total energy measured and Pz is the z component of the momentum.

Photoproduction events are characterised very low Q2, i.e. Q2~ 0 GeV2 and the positron

travels down the beam pipe. It is therefore not detected in the calorimeter and E-P z is

low, with most of the detected energy of the event being in the direction of the proton.

Selecting events with minimum E-Pz therefore serves to eliminate most of the

photoproduction.

4.4 Measurement of kinematic variables

Following reconstruction, the data must then be used to generate the kinematic variables

required for physics analyses. This process is described in the following sections.

69

Figure 4.12: A reconstructed neutral current event.

70

4.4.1 Event vertex

The reconstruction of the position of the event in z, the z vertex, is required for the

measurement of angles used for the determination of kinematic variables and also has

an effect on both the detector and trigger acceptance. For example, at a fixed low Q2

positrons scattered from events closer to the RCAL have a higher probability of passing

down the beam pipe and remain undetected.

The vertex is reconstructed using VCTRAK. In this case, only information from the

CTD is used. If no vertex is found, the vertex is set to the nominal value of Z = 0cm

4.4.2 Positron finding

The signature of a neutral current event is the presence of an isolated positron in the

final state. Event selection therefore relies on the efficient detection of this particle.

In the analysis reported in this thesis, positron candidates are identified using the

SINISTRA95 electron finder [64]. SINISTRA95 uses a neural-net based algorithm to

identify the scattered electron using information from the calorimeter. First, calorimeter

objects, which may belong to the shower of a single particle, are clustered to form cell

islands. Each cell is considered and, if it has enough energy, becomes a candidate to be

connected to its neighbouring cells. The process is repeated with cells being joined with

their highest energy neighbours to form islands.

SINISTRA95 then processes all islands in the electromagnetic section of the

calorimeter and returns a probability P, for each island. This ranges from 0, where the

island is of hadronic origin, to 1, the island is a positron.

If there is more than one positron candidate in an event the routine FINDIS95 selects

the candidate with the highest probability.

4.4.3 Positron Energy corrections

The precise measurement of the energy of the scattered positron is vitally important for

the kinematic reconstruction. The energy measured in the calorimeter cells

corresponding to the positron is subject to various detector effects which must be

corrected for. In the RCAL region, where most of the scattered positrons are found,

three different corrections are applied.

71

First, a global correction to the energy of the calorimeter is applied. This is done on a

cell-by-cell basis with the aim of matching the measured positron energy in data and

Monte Carlo simulation. This offset is caused by inadequate simulation of the dead

material within the detector. Details of the simulation of events at ZEUS using Monte

Carlo techniques are given in Chapter 5. The energy scale of the data is corrected

upwards to improve agreement with Monte Carlo.

The correction factors are as follows:

FCAL – no correction to data.

BCAL – data corrected upwards by 5%

RCAL – data corrected by a factor varying from 2% downwards to 5% upwards in

order to account for variations in the response of the different RCAL cells.

Following this, the energy of the scattered electron in the RCAL is corrected using the

SRTD and presampler. If there is SRTD information present, the preshowering of the

electron is measured in terms of the number of MIPS (Minimum Ionising Particles) in

the SRTD. This is proportional to the energy loss and the calorimeter energy is

corrected accordingly. If there is no SRTD information, the presampler is used to

correct the energy. Again, the approach is based on the number of MIPS in the

presampler.

Finally, a further correction is made to the scattered positron energy to take into account

the non-uniformity of the RCAL. This results in energy loss due to part of the

electromagnetic shower passing through gaps and cracks between modules, towers and

cells. A correction is determined by comparing the measured energy at a certain

position with the energy predicted by measuring the kinematics using the double angle

method, described in section 4.5.2. The double angle method uses only the angles of the

positron and hadronic system for kinematic reconstruction and is therefore independent

of the calorimeter energy scale. The correction is determined separately for data and

Monte Carlo due to inaccuracies in the simulation of the cracks in the Monte Carlo.

72

4.4.4 Positron position measurement

The precise measurement of the scattered angle of the positron is also important for

kinematic reconstruction. The scattering angle is defined as the angle between the z-axis

and the line joining the z vertex to the position of the positron on a well-defined plane

perpendicular to the z-axis. The measurement of this position makes use of the best

available detector component, i.e. if there is a signal in the SRTD associated with the

positron, the SRTD position is used.

4.4.5 Reconstruction of the Hadronic Final State

For the hadronic reconstruction, all energy in the calorimeter except the scattered

positron is considered. Therefore, an important aspect of the energy measurement is

calorimeter noise suppression. The sources of the noise in the calorimeter range from

sparks in the PMTs, electronic noise in the DAQ system to general background noise

from the radioactivity of the uranium. This is controlled by setting the energy of these

cells to zero.

All cells with EEMC < 80 MeV, EHAC < 110 MeV are removed while for isolated cells i.e.

those without neighbouring cells with energy above some threshold value, the cut is

raised to EEMC < 100 MeV, EHAC < 140 MeV. Furthermore, a cut on the imbalance

between the two PMTs in a cell helps to remove sparking PMTs as generally in this

case only one of a pair sparks. Finally, hot cells, which have on average much higher

activity than other cells over certain run ranges, are removed ‘by hand’ from calorimeter

tables used for the reconstruction.

In order to reconstruct the hadronic kinematics in the event the simplest method would

be to use the calorimeter cell information only. There are possible sources of inaccuracy

with this approach however. For example, the energy measurement can be affected by

so-called backsplash; i.e. scattering or showering in the material in front of the

calorimeter can send some energy back into the detector. This is particularly significant

at low y where the hadronic energy is concentrated in the forward region. Any

extraneous energy in the RCAL can therefore strongly bias the E-Pz measurement.

73

A more subtle method therefore would include information from tracking, which for

low energies has better resolution than the calorimeter. An algorithm that uses this

approach is the hadronic energy flow algorithm, which combines calorimeter and

tracking information into objects called ZUFOs (ZEUS Unidentified Flow Objects).

The first step of this algorithm involves applying the calorimeter noise and energy

corrections before creating cell islands. Following this, cone islands are created, where

islands belonging to either a single particle or a jet of particles are collected together.

Here, cell islands are taken and a clustering in - space is performed. Cell islands from

different calorimeter sections are matched, starting from the outermost HAC2 cells and

moving inwards. After the clustering has been completed, tracks are matched to these

islands. This leaves three types of objects, islands with a matched track, islands with no

and tracks with no islands. Finally, the algorithm decides for each object which

information to use, employing various selection criteria. For example, where there is a

calorimeter object with no track it is considered a neutral particle and the calorimeter

information is used.

The backsplash correction uses a cut on ZUFOs found at large polar angles from the

angle of the current jet, h.

4.5 Kinematic Reconstruction

In deep inelastic scattering the interaction of interest is electron-quark scattering. This is

a two-body process with two degrees of freedom and as such only two measured

quantities are required to completely reconstruct the event kinematics. As ZEUS is, to a

good approximation, a hermetic detector, both the scattered positrons and jets are

detected thus allowing several reconstruction methods to be used. The choice of which

method to use depends largely on the kinematic region being probed.

The two kinematic variables calculated in each of the following sections are Q2 and y,

as defined in equations 2.11 and 2.13 respectively.

74

4.5.1 Electron Method

The electron method reconstructs the kinematics purely using information from the

scattered electron. In this case, the energy of the electron and the angle through

which it is scattered e are used. Using the electron method, Q2 and y are given by:

(4.4)

(4.5)

At high y and moderate Q2 the electron method provides a good reconstruction of the

event kinematics. However the resolution at low y is poor.

4.5.2 Double Angle Method

The double angle method makes use of the fact that angles are often measured more

accurately than energies. The angles of the scattered positron, , and hadronic system,

, only are used for the reconstruction. This method yields Q2 and y of

(4.6)

(4.7)

In the analyses described in this thesis however, the angle of the scattered positron is

usually too low to make this method practicable.

4.5.3 Jaquet-Blondel Method

75

In principle, as all the particles are detected, the hadronic angle and energy can be used

for reconstruction of kinematics as well as the electron variables. This however, is

complicated by the fact that the struck quark, as well as not being completely

independent from the proton remnant, also fragments into a number of particles. The

Jaquet-Blondel method therefore uses all the detectable final state particles, including

the proton remnant, with Q2 and y given by:

(4.8)

(4.9)

where

(4.10)

(4.11)

and the summations exclude the scattered positron.

These variables are chosen as they are not affected significantly by events lost down the

beam pipe nor affected by final state fragmentation. However, at high y, the Jaquet-

Blondel method has very poor resolution for the measurement of both Q2 and y.

4.5.4 Sigma Method

76

In an attempt to use the advantages of the electron and Jaquet-Blondel methods, the

sigma method was introduced [65]. This method uses hadronic as well as the scattered

electron quantities in order to utilise the benefits of both in the high and low y regions.

In the sigma method, Q2 and y are given by:

(4.12)

(4.13)

In the kinematic region covered by the following analysis, i.e. low Q2 and high y, the

sigma method provides the best reconstruction of y while the electron method will be

used for the reconstruction of Q2.

77

Chapter 5

Monte Carlo

Monte Carlo simulations are extremely important tools in modern particle physics. They

are useful both for determining the acceptance and resolution of detectors as well as for

checking the validity of many theories. By simulating well-understood interactions and

comparing with the data an understanding of the detector can be built up. Conversely,

comparing a simulated process with data corrected for the response and behaviour of

the detector can shed light on areas of physics that are not yet understood. Monte Carlo

simulations therefore provide an invaluable handle for comprehending the complex

interactions that take place in a modern particle physics detector.

This chapter describes the Monte Carlo event generators used for the analyses described

in this thesis, beginning with generator used for simulating QED Compton events and

moving onto the two generators used for simulating ISR events. Finally, the ZEUS

detector simulation is described, whereby the response of the detector for each

simulated event is determined.

5.1 QED Compton Monte Carlo

For the simulation of QED Compton events, the reaction considered is ep eX and

corresponds to the diagrams shown in figure 5.1.

78

Figure 5.1: The two leading order contributions to QED Compton scattering.

These diagrams also describe Bremsstrahlung and both initial and final state radiative

events. The QED Compton case however, corresponds to the case where is finite.

Here, the scattered positron and photon are observed and the hadronic system travels

down the beam pipe.

The program used to generate QED Compton Monte Carlo events is COMPTON 2.00

[66]. This generates events in two steps. In the first step ep eX are generated

according to an approximation of the cross section. For elastic events, similar to the

interaction described in section 2.3, the conventional expressions for the proton’s

electromagnetic form factors are used, while, for inelastic events, which are similar to

the interaction described in section 2.4, a structure function is used. In the second step,

these events are weighted by comparing the value of the cross section from the first step

to the exact cross section. However, as one moves into the radiative regime where >

, these weights become large. Therefore in order to keep the weights small, a cut on

the angle | - | < 45 is made, where is the difference in azimuthal angle between

the scattered electron and photon. This quantity is known as the acollinearity and is a

measure of the transverse momentum balance between the two particles.

The cross section is also affected by radiative corrections, in particular, Initial State

Radiation. This is taken into account by reducing the incident positron’s energy

according to a probability law,

(5.1)

79

where

, (5.2)

E is the energy of the beam electron, E the energy of the ISR photon and me is the mass

of the electron.

Again, the events are given weights according to this correction. So, in order to limit the

size of the weights, the hard photon tail of the spectrum is removed by a lower limit

on the e- visible energy of 10 GeV.

Chapter 6 describes analyses of QED Compton events taken in 1996 and 1997 with

different detector and trigger configurations. Therefore, for the 1996 analysis, 60000

elastic and 20000 inelastic events were generated, corresponding to 23.4pb-1 and 23.5pb-

1 respectively.

For the 1997 analysis, 120000 elastic events (47pb-1) and 40000 inelastic events

(47pb-1) were generated.

5.2 ISR Monte Carlo

Simulated ISR events are generated using the Monte Carlo programs DJANGO 6.24

[67]. The DJANGO 6.24 program contains four separate components. Initially the

primary electron-quark interaction is simulated using the program HERACLES 4.5.2

[68,69]. At this stage, deep inelastic e+p collisions via both neutral and charged current

interactions are simulated at the parton level to order 2. Input parameters to the

simulation therefore include the parton distribution functions that parameterise the

interaction at the quark vertex. The functions are taken from PDFLIB 7.06 [15] using

the parameterisation from MRS set (A) [16]. The longitudinal structure function, FL, is

set to zero. This stage also includes QED radiative corrections to the cross section at the

electron vertex.

80

ARIADNE 4.08 [70-72] describes the development of the parton shower. In this case,

the colour dipole method is used to perform the gluon radiation. The conversion of the

partonic final state into the observed hadrons is performed by the JETSET 7.409 [73,74]

program using the Lund string model.

There is also a class of events observed at HERA, known as Diffractive events, that are

not described by DJANGO.

Diffractive events are defined by a large rapidity gap in the hadronic final state. In other

words there is nearly no energy filling the angular region between the hadrons coming

from the struck quark and those originating from the proton remnant. Such events could

be thought of as involving a colourless object, known as a pomeron, in the interaction.

Diffractive events are generated using RAPGAP 2.06/26 [75]. In order to take into

account QED radiative effects RAPGAP is interfaced to HERACLES to produce the e -

* - e vertex. Furthermore, in order to take into account initial state QCD radiative

corrections, the simulation of parton showers is performed by interfacing to PYTHIA

[76] and LEPTO [77]. The final state partonic showers however, are again simulated by

JETSET.

As the initial kinematic distributions for the diffractive and non-diffractive events are

similar, the two samples can be mixed in order to obtain the correct final distribution.

This mixing ratio is found by optimising the agreement between data and MC in the

distribution of max [45], with the fraction of diffractive events found to be 15%1.

Four samples of non-diffractive MC were generated, Q2 > 0.1 GeV2, Q2 > 0.2 GeV2, Q2

> 0.5 GeV2 and Q2 > 2 GeV2 while for the diffractive MC, three samples of Q2 > 0.1,

0.2 and 0.5 GeV2 were generated. The samples include a cut of > 3 GeV on the energy

of both the photon and scattered positron plus a cut on the polar angle, , of the

hadronic final state of less than 11mrad.

Finally, in order to increase the MC statistics for the FL measurement, further non-

diffractive samples at Q2 > 0.75 GeV2 were generated. In addition, these samples also 1 max refers to the pseudorapidity, = -ln(tan/2), of the most forward energy deposit or track in the event.

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include a cut of y > 0.04 in order to increase the luminosity corresponding to a given

number of events generated. This is acceptable as there is a high minimum y cut in the

FL analysis. In total, 51.74pb-1 of non diffractive and 4.6pb-1 of diffractive Monte Carlo

were generated.

5.3 Detector simulation

The output of the Monte Carlo event generators consists of a list of the 4-vectors of all

the final state particles. These are entered into a simulation of the detector that describes

the response of all the components and the efficiency of the triggers. This simulation of

the detector is performed by the MOZART [52] package, which is based on GEANT

[79]. The simulation of the trigger is done by the ZGANA package [80] with the same

trigger logic simulated as that used online. After simulating the response of the detector

to the passage of the individual particles, the reconstruction code used is identical to the

online code. Hence, the output is given in an identical format to the data format,

allowing a direct comparison between Monte Carlo and data.

5.3.1 Simulation of the LUMI- energy response

Although most of the detector is well simulated by MOZART, the energy response of

the LUMI- calorimeter does not adequately take into account the energy loss due to

the filter. Also, a new filter was introduced for the 1997 running period, further

changing the response. It is therefore necessary to perform the simulation of this

component separately.

For the 1996 data-taking period, the energy response of the calorimeter is described by

introducing an energy smearing function and then correcting for the energy loss in the

filter. This is given by the following expression:

(5.3)

where,

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ETrue is the true energy of the photon.

offset is a constant that shifts the endpoints of the photon energy spectrum to

smaller values in order to take into account the energy loss in the absorber in

front of the calorimeter.

nonlin is another constant that takes into account the nonlinearity in the energy

measurement, caused by effects in the detector electronics.

Ee is the energy of the positron beam.

res is the resolution of the calorimeter, this is calculated on an event by event

basis by performing a smearing of the true photon energy using a gaussian of

width E.

The extra filter used for the 1997 data-taking period changed the form of the energy

response. The new spectrum is described well by the gamma function, with two new

parameters, Add and introduced in order to take into account the asymmetric response

of the calorimeter, i.e. the smearing for low photon energies is relatively wider.

(5.4)

= 19.5or, in the limit:

(5.5)

So, the energy response becomes:

83

(5.6)

where,

(5.7)

(5.8)

The calibration constants [81] are summarised in table 5.1.

Calibration Constant 1996 1997

offset 0.2 GeV 0.38 GeV

E 0.23 0.323

nonlin 0.0011 -0.0005

- 19.5

Add - 0.3

Table 5.1: The LUMI- calibration constants for 1996 and 1997.

The simulation of the photon energy compared to the true energy for the two years is

shown in figure 5.2. As can be seen, the extra filter serves to widen the distribution as

well as shift the simulated energy to slightly lower values. Finally, only simulated

photons that pass through the LUMI- calorimeter are considered by performing a cut

on the physical aperture of the calorimeter. This is defined in section 7.5.1.

84

Figure 5.2: The difference between the measured and true photon energies for 1996 and

1997.

85

Chapter 6

QED Comptons

6.1 Introduction

The classes of events including QED Compton events, Radiative events and

bremsstrahlung, all have the same final state and may therefore be difficult to

distinguish. In this thesis, QED Comptons are a possible source of background to initial

state radiative events. A good understanding of QED Comptons would therefore enable

them to be efficiently tagged and removed.

This chapter describes the use of QED Compton events as cross check for the standard

luminosity measurement. This measurement is both useful in its own right and also

requires a good understanding of the process. The event selection can therefore be used

to efficiently remove QED Comptons from the ISR analysis.

The leading order diagrams for radiative events were shown in figure 5.1 and are given

again here in figure 6.1. QED Compton events are in principle distinguished from

Bremsstrahlung and initial and final state radiative events are in principle distinguished

by the values of the 4-momentum transfer and . The bremsstrahlung process is

characterised by 0 and 0. Here both the scattered photon and positron travel in

the direction of the electron beam. Initial State Radiative Events have a large value of

and 0. In this case the photon travels in the direction of the electron beam while

the positron can be scattered at large angles. QED Compton events however, have

0 but is non zero. In this case both photon and positron can be scattered at large

angles and measured in the main detector. The 4-momentum between the proton and the

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positron is very small in this case and as such the positron-photon pair and hadronic

final state have transverse momenta close to zero.

Furthermore, the QED Compton process can be defined as either elastic or inelastic. In

the elastic case the proton remains intact and passes undetected down the beam pipe. As

the elastic form factors of the proton are well known the cross-section for this can be

precisely calculated.

In the inelastic case the proton fragments and as such the cross-section calculation isn’t

well known. As the final state has little transverse momentum most of the hadronic

activity also passes undetected down the beam pipe. This can become a significant

background when making measurements using elastic Comptons.

The experimental signature of QED Compton events is therefore a positron-photon pair,

balanced in pt with little or no detected hadronic activity.

Fig 6.1: The two leading order contributions to QED Compton scattering.

QED Compton Monte Carlo events are generated using the COMPTON 2.00 program

described in section 5.1. The kinematic cuts used for generating the events are given in

Table 6.1

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Parameter Min Max

Positron Beam Energy (GeV) 27.5 27.5

Proton Beam Energy (GeV) 820 820

Scattered Positron Energy (GeV) 3 -

Photon Energy (GeV) 3 -

Energy Sum (e+ and ) (GeV) 10 -

Invariant Mass of e (GeV/c2) 1 300

Acollinearity () - 45

Angle between outgoing e+ and () 3 177

Total transverse momentum (GeV) - 20

Table 6.1: The kinematic variables used for the COMPTON 2.00 program.

6.2 Event selection

6.2.1 QED Compton Trigger

The trigger used for the selection of QED Comptons requires that events pass the third

level trigger bit DIS11. At the FLT this requires that global first level trigger bit 62 is

set. For 1996 running, GFLT62 requires an isolated cluster of calorimeter cells and a

veto from the C5 and VETO wall. These vetos remove so called ‘beam gas’ events

where a proton interacts with a gas molecule upstream of the detector. In addition, for

1997 running there are further requirements on the presence of good SRTD and CTD

tracks.

At the second and third trigger levels, there is a cut on the presence of hadronic and

electromagnetic islands in the calorimeter. Particles entering the calorimeter will

shower and deposit their energy over several adjacent cells. An algorithm runs over

clusters of such cells and those whose neighbouring cells pass energy and probability

cuts are added to the island. The trigger requires that there are no hadronic islands

present. Furthermore, one electromagnetic island must be present with energy greater

88

than 2 GeV accompanied by a second electromagnetic island with energy greater than 4

GeV and the total energy in the FCAL inner ring must be less than 50 GeV. The FCAL

inner ring takes into account only the FCAL modules nearest the beam pipe and acts to

suppress the background from the proton remnant. Finally, there is a requirement that

the total E-Pz of the event is greater than 30 GeV and the acollinearity is less than 90 or

/2 radians.

As an initial selection, events that fire the QED Compton trigger bit are taken. In

addition at least one of the electron candidates, identified using the SINISTRA95

electron finder must have a probability > 0.5. The corrections outlined in section 4.4 are

then applied to the data before a more detailed set of cuts are made.

6.2.2 Cuts

After the preselection described above, 247782 events remain for the 1996 data set and

567968 events for the 1997 data set.

The following cuts are then applied:

Two electromagnetic clusters, “electron candidates”, are found using

SINISTRA95, both with probabilities greater than 0.9.

The energy of both candidates, measured by the calorimeter or SRTD is greater

than 8 GeV, i.e. Ee > 8 GeV and E > 8 GeV.

No more than one cluster has an associated track.

Only RCAL clusters outside a region of 13cm x 13cm around the beam pipe are

accepted. This ‘boxcut’ prevents leakage out of the electron shower into the

beam pipe and ensures the complete reconstruction of the electron and photon

candidates. It also acts to suppress the initial state radiative background.

89

The z position of the event vertex must be within 50cm of the nominal

interaction point.

The total E-PZ of the event must lie in the range 35 GeV – 65 GeV.

The total hadronic component of the calorimeter energy, i.e. not including the

electron or photon, is not greater than 2 GeV. This is made to reduce the

inelastic QED Compton contribution.

Finally, two further cuts were applied to reduce the ISR and DIS backgrounds.

To remove the ISR background, the acollinearity, .

The removal of the DIS background requires the quantity , where

and are the polar angles of the electron and photon respectively.

After the above cuts 6183 events remained for 1996 and 14540 events for 1997.

Figure 6.2 shows some resulting distributions for elastic and inelastic Monte Carlo

normalised to the same luminosity as each other. The plots show the acollinearity, the

total transverse momentum, PT, the invariant mass of the electron/photon system Me

and the difference in polar angle, . As 1996 and 1997 data will be treated

separately later, the distributions for 1996 and 1997 are given separately. The difference

between the elastic and inelastic distributions can clearly be seen. The largest difference

is in the acollinearity and PT distributions where the elastic QED Comptons have

relatively more events with lower total transverse momentum.

90

Figure 6.2: Elastic and Inelastic QED Compton MC Distributions for 1996 data set

(upper plots) and 1997 data set (lower plots).

6.3 Measuring the inelastic contribution

In the data, the sample of elastic QED Compton candidates is contaminated by inelastic

QED Comptons. As the Q2 of such events is generally low, in many cases it is likely

that the proton remnant passes down the beam pipe and remains undetected therefore

faking an elastic candidate. In order to correct for this contamination inelastic MC is

added to the elastic MC.

The elastic MC are scaled to the data luminosity while the inelastic fraction is

calculated by varying the relative proportions of elastic and inelastic Monte Carlo to

find the minimum 2 of a fit to the data. The fraction of inelastic events found from the

1996 Monte Carlo is 14.7% 2.2% while for 1997 the percentage is 12.2% 2.7%.

Comparisons between the data and Monte Carlo for 1996 and 1997 are shown in figures

6.3 and 6.4 respectively.

91

Figure 6.3: Data v Elastic + Inelastic MC comparison for 1996

Figure 6.4: Data v Elastic + Inelastic MC comparison for 1997.

92

In general, there is a good agreement between data and Monte Carlo. However, for the

acollinearity plots there is a deficit of MC at values of higher than 2.5. This is due to

the poor description of the inelastic contribution. The probable cause of this is the

inadequate simulation of the hadronic final state in the COMPTON2.0 Monte Carlo.

The simulation of the parton shower and hadronic final state is not performed by the

generator and therefore any hadrons produced in inelastic events cannot be tagged in the

Monte Carlo. The use of DJANGO to produce QED Compton events would overcome

this problem as the hadronic components are produced in full by ARIADNE and

JETSET and would be seen in the final event.

6.4 Luminosity Measurements

An upgrade to the luminosity at HERA is being planned for the second half of 2000 and

early 2001. This will involve both improvements to the accelerator in the form of

magnet upgrades, changes to the interaction regions, and improvements to the ZEUS

detector in the form of new tracking detectors. The integrated luminosity that has been

provided by the HERA accelerator for the years 1994 - 1999 has now reached over

80pb-1. After the upgrade the luminosity that will be available will increase to an

expected 150 pb-1 per year.

The increased event rate however will have profound implications for the measurement

of luminosity using the current luminosity monitor. Indeed, even with improvements,

the required accuracy of 1% may not be achieved with this monitor. Therefore two

new detectors will be installed in order to provide complementary luminosity

measurements while the current LUMI detector will be upgraded in order to act as a

cross check.

There are three different aspects to the upgrade in Luminosity measurements at ZEUS.

First, the current LUMI- calorimeter will have the current filter replaced by an active

aerogel filter [82]. This gives the advantage of increasing the radiation length of the

filter, reducing the damage to the calorimeter from synchrotron radiation while using

the Cherenkov radiation emitted by converted photons to maintain the bremsstrahlung

signal.

93

Also, at 92m from the interaction point, a photon spectrometer will be installed [83].

Bremsstrahlung photons convert with an efficiency of ~11% in the beam pipe exit

window into e+e- pairs. These in turn will be split by a dipole magnet and detected in the

current Beam Pipe calorimeters, moved into the new position. Finally, a new electron

tagger will be introduced at 6m [84] to detect electrons in the range 6-9 GeV (5-8 GeV

positrons). This will reduce the contribution of the acceptance & energy scale of the

photon detectors to the overall systematic error of the luminosity measurement.

Like the bremsstrahlung events used for the current luminosity measurement Elastic

QED Comptons have a precisely calculable cross section and therefore are suited to

luminosity calculations. As they are detected in the calorimeter however, they are not

affected by the above problems caused by the Luminosity upgrade and are a potential

way of cross checking the luminosity measurement.

6.4.1 Calculation of the 1996 and 1997 luminosity

The integrated luminosity is calculated using elastic QED Compton candidates via the

equation

(6.1)

NCandidates is the total number of candidates corrected for the fraction of inelastic

candidates. is the cross section for the elastic process and A is the acceptance, or

fraction of all events that are detected. The Luminosity is calculated by taking the

scaled number of elastic and inelastic MC candidates, using the method described in

[85].

(6.2)

A Acceptance

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= cross section for the elastic MC generated Comptons (in this case,

2556.6nb)

For the 1996 luminosity calculation the result is:

L = 10.77 0.19 (stat) pb-1

The 1997 luminosity is also calculated using equation (6.1), with

L = 28.05 0.40 (stat) pb-1

6.4.2 Systematic errors

It is important to assess the uncertainty in the measurement caused by the choice of cuts

and the extraction method used. In addition to knowing the statistical limitation of the

measurement, this indicates the extent to which the precision of the measurement is

limited by detector effects

Systematic errors are estimated by independently varying the cuts by the error on the

measured value and measuring the difference of this result with the nominal result. The

individual shifts are then added in quadrature to give the total systematic error.

The changes to the cuts are as follows:

1. Increase the Boxcut to 14cm.

2. Decrease the energy cut for the electron/photon by 1 GeV.

3. Increase the energy cut for the electron/photon by 1 GeV.

4. Change the cut on the z vertex to 60cm.

5. Decrease the |1 - 2| cut to 84.

6. Increase the |1 - 2| cut to 86.

7. Change the Total E-PZ cut to 25 – 65 GeV.

8. Change the Total E-PZ cut to 35 – 75 GeV.

95

9. Change the assumed fraction of inelastic Comptons to 12.5% for 1996 and 9.5%

for 1997.

10. Change the assumed fraction of inelastic Comptons to 16.9% for 1996 and

14.9% for 1997

11. Change the cut on hadronic energy to < 3 GeV.

12. Increase the cut by 1.

13. Decrease the cut by 1.

The effects of these systematic checks on the 1996 and 1997 luminosities are shown in

figures 6.5 and 6.6 respectively.

Figure 6.5: Effect of systematic checks on measured 1996 luminosity. The fractional

change for each systematic check is shown, with the dashed line indicating no

systematic shift.

96

Figure 6.6: Effect of systematic checks on measured 1997 luminosity. The fractional

change for each systematic check is shown, with the dashed line indicating no

systematic shift.

The largest contributions to the systematic error are from the calculation of the inelastic

contribution and the acollinearity cut. The uncertainty in both these systematics could

be reduced by using Monte Carlo that describes the final hadronic components. This,

unfortunately, is not performed by the COMPTON 2.0 Monte Carlo. Also, the use of

forward tagging detectors could provide more information about the proton remnant.

The resulting value for the 1996 luminosity is

(10.710.12 pb-1)

While the value for 1997 is

(27.870.42 pb-1)

97

In both cases, the value given by the standard luminosity measurement is given in

brackets.

6.5 Conclusion

The integrated luminosity obtained for 1996 using the luminosity monitor is

10.7050.12 pb-1. A comparison with the result from the 1996 QED Compton analysis,

shows that they are in good agreement

within experimental error.

Also, the value obtained from the luminosity monitor in 1997 of 27.870.42 pb-1

compares well with the value measured using elastic QED Comptons of

.

With the use of improved Monte Carlo with full simulation of the hadronic final state,

the dominant systematic errors from the measurement of the acollinearity and inelastic

contamination could be significantly reduced. Also, as the 1997 measurement shows,

with sufficient luminosity the statistical error for the QED Compton measurement is

comparable to the error from the standard luminosity measurement. Therefore, with

better control of the systematic errors this method may become competitive.

However, even if the use of QED Comptons proves unable to measure the luminosity to

the required accuracy of 1%, it would provide a useful independent crosscheck to the

proposed new detectors.

98

Chapter 7

Measuring the structure function F2

7.1 Introduction

Initial State Radiative events lower the energy of the incident positron and hence the

centre of mass energy of the event. This results in a shift of the kinematic regime

accessible by such events towards lower Q2 and x. This new regime is interesting as it

allows us to bridge the gap between the low Q2 events measured with the BPC and BPT

and the region covered in the standard F2 analysis. The range accessible in x also results

in some overlap with results from fixed target experiments.

7.2 Corrections to the Kinematics due to ISR

As the ISR photon takes with it some of the energy of the incident electron the

kinematics of the event are changed accordingly. The quantity, z, was defined in chapter

2 as the fraction of the electron beam energy available for the interaction after the

emission of the ISR photon, i.e. restating equation (2.40):

(7.1)

In order to take the ISR correction into account this factor is now applied to the

kinematic variables defined in section 4.5 [86].

As the electron method uses the scattered electron for reconstruction the kinematics are

changed by scaling the initial electron energy by z, i.e. Ee zEe. Q2 and y therefore

become:

99

(7.2)

(7.3)

This also applies to the Jacquet-Blondel method where the scaling due to ISR

results in:

(7.4)

(7.5)

In principle, the sigma method requires no correction due to ISR. This can be seen by

rewriting (4.13) in terms of yel and yjb:

(7.6)

It can be shown that the correction to the top and bottom of (7.6) cancel.

The above result however, gives y at the reduced centre of mass energy caused by the

emission of the ISR photon. Therefore, in order to achieve consistency with previous F2

analyses which are performed at the nominal centre of mass energy, a new variable,

yHERA, is introduced such that:

(7.7)

The true y of the event, including the reduced centre of mass energy is given by:

100

(7.8)

This ensures that F2 values measured using yHERA can be directly compared with F2

measured using standard analyses.

7.3 Event Selection

7.3.1 The Trigger for radiative events

In order to identify Initial State radiative events from 1996 and 1997 data taking,

purpose-built trigger configurations were used. Two separate triggers are used in the

analysis, one was active for part of the 1996 data taking period and is used for the F 2

analysis while the other ran over the whole 96/97 period and is used for the FL analysis.

The trigger used is based on the neutral current trigger, which is well understood and

simulated.

7.3.2 The FLT

At the first level, trigger bits are set using calorimeter information, essentially triggering

on isolated electromagnetic clusters. The F2 trigger uses the first level trigger bit FLT

30.

FLT 30 is the inclusive-DIS trigger and is used for the measurement of F2 using non-

radiative events. After vetos from the C5 counter and veto wall are applied, the trigger

bit is described as follows2:

(7.9)

where ISOE means the energy was isolated in one trigger tower, EREMC refers to energy

measured by the CFLT in the Rear electromagnetic calorimeter, 1st ring means the

energy in the innermost ring around the beam pipe and SRTD implies the GOOD SRTD

TRACK bit is fired.

2 The notation introduced here is set notation where A B is a logical ‘and’ of A and B, A B is a logical ‘or’ of A and B.

101

A summary of the cuts on trigger bit FLT30 is shown in table 7.1:

FLT Variable FLT30

EISOE [GeV] 2.08

EREMC [GeV] 2.032

EREMC (1st inner ring) [GeV] 3.75

ECAL [GeV] 0.464

SRTD YES

LUMI- [GeV] -

Table 7.1: Summary of the properties of the FLT Trigger bit FLT30, giving the values

of the cuts used.

As well as FLT30, which is used for 14.8pb-1 of data in 1996 and 1997, FLT46 is used

for 19.01pb-1 of data in 1997. This bit requires that there is an energy deposit in the

LUMI- calorimeter of > 0.8 GeV in addition to the standard energy cuts.

7.3.3 The TLT

At the TLT, higher-level calculations are performed using most of the detector

information. In this case the trigger uses 4 electron finders with an energy cut of > 4

GeV. If any finder finds a candidate electron a further cut on its position is applied. A

boxcut is applied for |x| > 12cm, |y| > 6cm cutting electron candidates that are too close

to the beam pipe and cannot be reconstructed well. E-Pz is calculated at this stage and a

cut implemented on its value.

A further trigger, DIS02, is used to measure background events. This is a Neutral

current trigger with a relaxed E-Pz cut and passes more events at the lower E-Pz range,

which can be characteristic of photoproduction events. The reduction of the cuts for this

trigger result in an increase of the trigger accept rate. Therefore, in order to restrict the

number of events to a manageable size, the trigger is prescaled i.e. only a fraction of the

102

events passing the trigger are stored. Table 7.2 shows the differences between the two

triggers for the F2 measurement.

TLT Variable DIS01 DIS02

FLT BIT 30 30

E-Pz SLT [GeV] - 19

Ee [GeV] 4 4

Box Cut [cm] 12 x 6 12 x 6

E-Pz [GeV] 30 20

LUMI- [GeV] - -

Prescale 1 40 – 100

Table 7.2: Comparison between data, DIS01, and background, DIS02, triggers used for

the ISR F2 measurement.

7.3.4 Cuts

An initial sample is selected by requiring, in the run range where the DIS01 trigger was

turned on in 1996, that there is at least one electron found using the SINISTRA95

electron finder with probability greater than 0.5 and energy > 3 GeV. Also, a photon

must be detected with the LUMI- calorimeter with energy > 3 GeV. This gives an

initial sample of 341551 data events.

The energy corrections and reconstruction described in section 4.4 are performed. In

addition, the LUMI- energy is scaled upwards by 0.36% in order to overcome an

additional calibration offset introduced by the LUMI group [87]. The scaling factor for

1997 photons is 1%.

The following cuts are then applied:

The energy of the electron found using SINISTRA95 after all corrections is > 8

GeV.

The probability given for this electron by SINISTRA95 is > 0.9.

103

The hadronic energy in a cone drawn from the interaction point through the

electron cluster is < 5 GeV.

The energy of the ISR photon measured by the LUMI- calorimeter > 6 GeV.

The total E-Pz of the event measured by the calorimeter alone > 20 GeV. This

serves to remove the photoproduction background.

The total E-Pz of the event (i.e. E-Pz + 2E) lies in the range 48 – 60 GeV.

The so-called ‘H-boxcut’ is applied [88]. This cut is required to reduce

differences in data and Monte Carlo caused by the incorrect modelling of copper

cooling pipes in the rear direction.

The z position of the event vertex must be within 50cm of the nominal

interaction point.

In order to remove Bremsstrahlung background, the energy in the 35m Tagger <

2 GeV.

The energy in the 44m Tagger is less than 60 ADC counts.

The value of yjb, corrected for ISR is > 0.001.

In order to remove photoproduction background, y, measured using the electron

method and corrected for ISR is < 0.95.

The total hadronic energy of the event is > 2 GeV.

104

Events with sparking cells, muons from cosmic rays, and QED Comptons are

rejected.

7.4 Background

The major sources of background in this analysis include:

Non-radiative DIS events with an overlay photon in the LUMI- calorimeter

from bremsstrahlung.

Photoproduction fake electrons with an overlay bremsstrahlung photon.

ISR-photoproduction events. These events occur mainly at low E-PZ and are

mostly rejecting by applying the lower E-PZ cut.

A sample of events is taken from the same runs as those used by the analysis by

selecting the TLT-bit DIS02. As noted previously, this is characterised by a lower E-PZ

cut, therefore allowing relatively more photoproduction events to pass. The overlay of a

bremsstrahlung photon can cause these events to be shifted up into the signal region so,

in addition to this, LUMI-e and LUMI- energies from bremsstrahlung events are added

randomly to each DIS02 event, creating an artificial overlay sample. Bremsstrahlung

events from 1996 are selected using a random trigger while those from 1997 are

selected using triggered data. The electron energy distribution for the two years is

shown in figure 7.1. As can be seen, the 1997 events include a cut on the LUMI-e

energy of < 2 GeV which is not present in 1996. Performing the same cut on the 1996

LUMI-e energy yields LUMI- distributions that are almost identical. Differences in

these can be explained by the change in LUMI- filter for 1997. The fine structure in

the LUMI-e energy for 1997 is caused by a stuck bit in the DAQ and is also present in

the 1996 distribution, although not visible on this scale.

105

Figure 7.1: The raw bremsstrahlung LUMI-e and LUMI- energies for 1996 (left) and

1997 (right). The structure in the plots arises due to the acceptance of the LUMI-e and

LUMI- detectors.

7.4.1 Background normalisation

In order to determine the number of background events and subtract them from the data,

the artificial overlay sample has to be normalised to the data.

The Total E-PZ distribution above 62 GeV contains very few ISR-DIS events. Most of

the events in this region are non-radiative DIS processes measured in the calorimeter

together with an overlay bremsstrahlung photon.

106

If the artificial sample is normalised to the data above total E-Pz > 62 GeV, the data is

well described in this region, as shown in figure 7.2. The assumption is therefore made

that the artificial background sample at lower total E-Pz is also a good description of the

background. The normalised background is then added to the Monte Carlo sample for

all kinematic distributions in order to fully describe the data.

Figure 7.2: Total E-Pz distribution for data with the normalised background

contribution. The background is normalised to the data in the hatched region where the

total E-Pz > 62 GeV.

In addition to the major sources of background described above, other, minor sources of

background are also considered.

7.4.2 QED Compton Rejection

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QED Comptons are rejected by applying the set of cuts used in Chapter 6. Over the run

range used here, 383 QED Comptons are rejected, roughly 3% of the number of events

that pass the cuts.

7.4.3 Cosmic Ray Rejection

Cosmic rays provide a continuous background signal. Such events generally involve the

passage of muons through the detector. These can look like a single track passing

though the BMUON on two opposite sides, and the CTD. Cosmic events are rejected if

two BMUON tracks are found on opposite sides of the detector pointing to each other.

7.4.4 Positron and proton beam-gas background

Particles from the unpaired positron and proton beams used for beam related

background studies can hit residual gas in the beam pipe and the resulting interaction

can be measured in the detector. This effect can be measured by examining the bunch

crossing number for the event. The backgound from beam gas in this analysis however,

is negligible and is ignored.

7.5 Corrections

7.5.1 Acceptance of the LUMI- calorimeter

A certain fraction of the ISR photons remain undetected by the LUMI- calorimeter.

The ratio of number of photons detected to the total number of photons defines the

acceptance of the LUMI- calorimeter. The data must be corrected by this fraction and

so an accurate determination of the acceptance is important.

As the probability for the detection of photons in the sensitive range of the calorimeter

is very high, it can be approximated to 1. Therefore the acceptance depends mainly on

the geometrical acceptance, i.e. whether the photon actually hits the LUMI-

calorimeter. This, in turn, depends on the physical size of the aperture of the LUMI-

calorimeter. The dimensions of the aperture are shown in figure 7.3.

Several parameters can affect the incidence of ISR photons on the LUMI detector. The

vertex position of the event as well as the direction of the positron beam at the

108

interaction point can both change the direction of the outgoing photon to such an extent

that it misses the LUMI- calorimeter entirely. The latter can be defined by beam tilt

and beam divergence. Furthermore, these can change run by run. Changes over the

duration of a run are smaller and therefore the average over a run is used. The beam tilt

is measured by fitting a gaussian curve to the measured position of the LUMI- photons

from a given run. This position is measured with respect to the nominal position of x=0,

y=0 for the LUMI calorimeter. The run-by-run values of the beam tilt are shown in

figure 7.4.

Figure 7.3: The aperture of the LUMI- calorimeter

The geometric acceptance is calculated using the Q2 > 0.5 non-diffractive Monte Carlo

sample as described in chapter 5 [92]. The true photon angle is first randomly smeared

according to the beam divergence and LUMI- resolution and a correction applied to

take into account a small twist of the beam. Given that the LUMI- detector is located

107m from the interaction point, this angle is easily converted into a position and a cut

is applied according to the physical aperture of the LUMI- calorimeter.

109

Figure 7.4: The x and y Beam Tilts for 1996, top, and 1997, bottom, plotted against

relative run number.

This process is repeated for 187 different values of beam tilt, 17 in the x direction, from

–0.26 mrad to 0.06 mrad, and 11 in the y direction, from –0.1 mrad to 0.1 mrad. The

acceptance for these values is shown in figure 7.5 and is on average 70% over the range

of tilts with drops in acceptance at the extreme tilts as expected.

110

Figure 7.5: Acceptance of LUMI- calorimeter for different x and y beam tilt positions.

The tilt ranges from –0.25 mrad to 0.06 mrad in the x direction and –0.1 mrad to 0.1

mrad in the y direction

7.5.2 Vertex weighting

The correct position of the z vertex of the event is of vital importance to the MC

simulation. However, due to trigger effects and biases from reconstruction the simulated

vertex generally does not agree with the measured one and therefore needs to be

weighted. By selecting a minimum bias sample, the underlying vertex distribution can

be determined and used to weight the MC.

A minimum bias sample is selected by introducing the following cuts:

111

No vertex cut.

electron < 150.

45 < hadronic < 135.

This is repeated using MC. Then 5 gaussians are fitted to the primary vertex distribution

and satellite bunches. The MC is weighted using these fits.

7.5.3 Beam pipe correction

An additional correction is made because the forward cooling pipes around the beam

pipe are not simulated in the MC. The simulation of these pipes has been performed on

a small set of Monte Carlo therefore allowing its effect to be parameterised. A

correction routine is then used to weight the existing MC accordingly [89].

7.5.4 Structure Function weighting

Finally, for the measurement of F2, the parameterisation from ALLM97 [78] is used.

ALLM97 uses a Regge motivated approach based on all available F2 measurements,

including those made in the very low Q2 region using data from the BPC. It is extended

into the high Q2 region in a way compatible with QCD expectations. In addition data

from measurements of the total photoproduction cross section are included. Due to this,

it can be used over the Q2 and x range covering 3 10-6 < x < 0.85 and 0 GeV2 < Q2 <

5000 GeV2 and gives a good description of all data within this region.

As the Monte Carlo was generated using the MRS(a) parameterisation. Each event is

therefore weighted by the factor .

7.6 Data and Monte Carlo distributions

After the cuts and corrections, distributions of data are compared with summed

distributions of Monte Carlo and background. Comparisons for the main kinematic

variables are shown in figures 7.6, 7.7 and 7.8.

112

Figure 7.6: Comparison of Data and MC + BGD for the Electron energy and theta,

which are used for the kinematic reconstruction, as well as the photon energy and z

vertex position.

113

Figure 7.7: Comparison of data and MC for hadronic-based quantities along with E-Pz

distributions. The Total E-Pz plot indicates the cut on the signal region (two vertical

lines) and the area where the background is normalised to the data (hatched area).

114

Figure 7.8: Comparison of data and MC + BGD for the Q2 and yHERA distributions, used

for the measurement of F2.

As can be seen, there is in general a good agreement between data and Monte Carlo.

Overall, though, there is a 1.6% normalisation offset. The error on the luminosity

measurement for 1996 is 1.1%. There is also a slight excess in the lower region of the

total E-Pz plot. This could indicate that there is still some photoproduction background

contributing to the signal after the background subtraction.

7.7 Measuring F2

7.7.1 Resolution of Q2 and y

In order to check the reconstruction of the kinematics of the event, the Monte Carlo

sample is used to estimate the resolution and migration of the kinematic variables used.

The migration is a measure of the mean difference between the reconstructed and true

values while the resolution is defined as the spread on the difference between these

values.

The migration and resolution are determined by fitting a gaussian to the fractional

difference between the measured and true values, . The mean of this fit

gives the average kinematic migration and the width the resolution of the reconstructed

variable.

Figure 7.9 shows the resolution and migration of the two kinematic variables used for

the measurement of F2. In this case, Q2 is measured with the electron method and y is

115

measured with the sigma method. As can be seen Q2 is well measured over the whole

kinematic region of interest. The migration is much less than 5% for Q2 values ranging

from ~3 GeV2 to 100 GeV2 with only a slight increase at the high and low Q2 ends. The

resolution is less than 20% over the whole range.

The measurement of y is subject to greater uncertainties with the resolution being

between 20 and 40% over the whole y range. Migration to lower values of y is also

evident, being of order 10% over most of the y range with some improvement towards

lower y. Other reconstruction methods for y show more migration and worse resolution

however. For the measurement of F2 therefore, the electron method and sigma method

are used for Q2 and y reconstruction respectively.

7.7.2 Bin Selection

The bins used for the measurement of F2 are selected according to the criteria that as

well as the presence of enough statistics, the purity and acceptance in each bin should

be sufficiently high. The acceptance and purity are defined such that:

(7.10)

(7.11)

116

Figure 7.9: Resolution of Q2 measured using the electron method and y measured using

the sigma method.

The acceptance and purity in each bin used are shown in figure 7.10. For consistency

with the nominal 96/97 F2 measurement, the criteria for the use of a bin is that the purity

> 30% and the acceptance > 20%. As can be seen all the bins defined meet the selection

criteria.

117

Figure 7.10: The acceptance and purity for each bin. The shading of the bins indicates

the purity whereas the value for the acceptance is given in each bin as a percentage.

Figure 7.11 shows the bins used, with the regions covered by previous analyses and

experiments shown for comparison.

As has been previously stated, this measurement spans the region between the low Q2

BPT analysis and medium to high Q2 analysis, as well as some overlap with the fixed

target results.

118

Figure 7.11: The bins used for the F2 measurement together previous results from ZEUS

and fixed target experiments. The number assigned to each bin is also indicated.

7.7.3 Unfolding

The measured number of events in a bin gives the raw cross section but, as illustrated in

figure 7.10, this is subject to inefficiencies in the detector performance and

reconstruction method, which together result in a probability of detection of somewhat

less than 100%. In order to correct for the effects of smearing, migration and acceptance

a procedure known as bin-by bin unfolding is used.

119

The unfolding uses the Monte Carlo simulation to correct the data. Here, the unfolded

number of data events, Ni, is calculated be multiplying the measured number of events

Ni, meas by a correction factor ci.

(7.12)

where

(7.13)

This method requires that the Monte Carlo simulation describe the data well over the

whole kinematic region used for the measurement. This is valid however, as in general

there is good agreement between data and Monte Carlo in the distributions shown in

figures 7.6, 7.7 and 7.8.

Restating equation (2.34), the differential cross section is:

(7.14)

where Y+ = 1 + (1-y)2. Here FL is set to zero as it has a negligible effect on the absolute

cross section and F3 is ignored as it only arises from Z0 exchange and is not relevant in

this kinematic regime.

The unfolded number of data events in each bin, i, Ni is related to the cross section by:

(7.15)

As previous ZEUS and H1 results are used in the structure function parameterisation,

the values of the structure functions of data and Monte Carlo are related to the ratio of

the number of unfolded events in the bin

120

(7.16)

It follows that the ratio of observed events is related to the ratio of unfolded events

(7.17)

where . The second term here refers to the artificial overlay

sample described in section 7.4.

The structure function is now given by,

(7.18)

F2 can therefore be measured using only the measured number of data and MC events in

the bin and the known MC structure function.

7.7.4 Systematic Errors

As in section 6.4.2, the systematic errors are determined by varying each cut by the

error on the quantity used for the cut. In this case, the following checks are made:

1. Vary the electron energy cut by 1 GeV.

2. Vary the photon energy cut by 0.5 GeV.

3. Vary the Total E-PZ cut from 46 – 62 GeV to 49 – 59 GeV.

4. Change the Cal E-Pz cut to 22 GeV.

5. Vary the Boxcut by 0.5cm.

6. Change the cut on the Z vertex to 60cm.

7. Normalise the Background in the E-PZ region > 64 GeV.

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8. Change the diffractive fraction to 11% and 19%.

9. Worsen the LUMI- resolution from 23% to 25%.

10. Remove the veto on the 35m Tagger.

11. Remove the veto on the 44m Tagger.

12. Instead of the ‘offline’ trigger, use the TLT for data and no trigger for MC.

13. Scale the hadronic energy by 3%.

14. Vary the SRTD or presampler correction by 10%.

15. Remove the backsplash correction.

The effects on each bin for the above checks are shown in figure 7.12.

As can be seen the dominant systematic over all the bins is the simulation of the LUMI-

energy and electron energy and E-Pz cuts. These all have greatest effect on the high

y/low x bins These bins also have the worst statistics for each Q2 bin. The other

systematic effects are well controlled.

7.8 Comparison with 96/97 F2 measurement

ZEUS has recently published [8] a preliminary F2 analysis using data from 1996 and

1997. The 1996 low Q2 results use the same trigger (DIS01) as the ISR analysis. These

F2 results are in good agreement with previous results [90] and theoretical predictions.

In order to check the ISR F2 measurement the 96/97 F2 analysis is repeated using events

from the same run range as that covered by the DIS01 trigger i.e. the same data set as

the ISR measurement.

122

Figure 7.12: The fractional error for each systematic check shown as a function of bin

number.

The initial selection takes all events that pass the DST bits 9 and 11. These bits select all

events in which a positron is found with energy > 4 GeV and with total E-Pz > 30 GeV.

This leads to an initial sample of 939496 events. The cuts then applied are:

An electron is found with the Sinistra95 electron finder with a probability rising

from > 0.96 at 8 GeV to > 0.99 at 20 GeV, falling back to > 0.9 at 30 GeV and

above. This cut is intended to remove photoproduction background, which is

more evident at lower probabilities.

The energy of this scattered electron is > 8 GeV.

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The hadronic energy in a cone drawn from the interaction point through the

electron cluster is < 5 GeV.

38 GeV < E-Pz < 65 GeV.

ye < 0.95.

The ‘H’ shaped boxcut is used.

Outside a radius of 80cm, a track is required to the electron. This must have

momentum > 5 GeV and a distance of closest approach to the electron candidate

< 10cm.

The total hadronic activity in the event must be > 2 GeV.

The PT balance, PTh/PTe < 0.3. For low values of PTh/PTe there is a large deficit of

Monte Carlo compared to data. This cut therefore selects events with a well

reconstructed hadronic final state.

The z position of the event vertex must be within 50cm of the nominal

interaction point.

Events with sparks, muons from cosmic rays, and QED Compton events are

rejected.

The Monte Carlo in this case again consists of diffractive and non-diffractive MC

generated with the CTEQ4D parameterisation. In addition, Monte Carlo is also used to

simulate the photoproduction background. Two samples of photoproduction Monte

Carlo are generated, direct and resolved.

124

In direct photoproduction the photon has a point-like interaction with the proton and

does not appear to have any substructure. For resolved photoproduction however, the

photon appears to have substructure, which can be using a photon structure function.

The photoproduction MC is generated at low Q2 (< 1 GeV2) and high y (> 0.36). Lower

y events are not generated since the scattered positron would carry so much energy out

of the detector that the event is rejected by the other cuts.

The data and Monte Carlo comparison for these events are shown below in figure 7.13.

As with the ISR distributions, there is good agreement between the data and MC with

the exception of a small excess of MC at high y.

Again, a bin-by-bin extraction of F2 is performed. This time however, the CTEQ4D

parameterisation is used.

A comparison of F2 results from this analysis and the preliminary 96/97 F2 figures [8] is

shown in figure 7.14. The Q2 range shown is roughly the same as the range covered by

the ISR events. As can be seen there is good agreement and therefore a direct

comparison with the ISR results can be made.

Following this, F2 is extracted in the same bins as the ISR analysis using the ALLM97

parameterisation. This is shown in figure 7.14 along with the results from the ISR

analysis.

125

Figure 7.13: Data v MC comparison for the 96/97 analysis. The relative contributions of

the diffractive and photoproduction Monte Carlo are indicated by the green and blue

histograms.

126

Figure 7.14: Comparison of F2 measured with this analysis and preliminary 96/97

results.

127

Figure 7.15: F2 plotted from the ISR analysis (circles) with the comparison from the

96/97 analysis (triangles). Error bars for the ISR results show both statistical (inner

bars) and systematic errors added in quadrature. The 96/97 analysis shows statistical

errors only. Also shown are results from the ZEUS BPC/BPT and shifted vertex (SVX)

analyses.

128

In general, there is a good agreement, within errors, between the ISR F2 and the 96/97

F2 values and ALLM97 parameterisation. In the Q2 = 10 GeV2 and Q2 = 20 GeV2 bins

however, the ISR F2 values are generally higher.

The results in kinematic region covered by the Q2 = 0.6 GeV2, Q2 = 1.3 GeV2 and Q2 =

2.5 GeV2 bins, where the gap between ZEUS medium and low Q2 results lies show good

agreement with the ALLM97 curve.

The errors for the ISR measurement are much larger than the 96/97 result. This is in

part due to the reduced statistics. Improving statistics, especially at low x, where the

systematic errors are also worst, could be achieved by lowering the electron energy cut

to 5 GeV. The advantages of this would also be of benefit for the measurement of FL

and this will be discussed in the next chapter.

129

Chapter 8

Measuring the Proton Structure

Function, FL

8.1 Introduction

As stated in section 2.8, the emission of a gluon from the quark introduces a small

component of transverse momentum. This can be parameterised by the structure

function, FL, which can give a determination of the gluon distribution within the proton.

Indeed, a measurement of FL at y ~ 2.5x is almost a direct measure of the gluon

distribution [91]. The measurement of FL requires varying y at constant x and Q2, in

other words, varying the centre of mass energy, s. Varying s can be achieved through

reducing the beam energy [18,19]. This however, has the drawback that the detector is

not being run in optimal conditions. Also, a large amount of luminosity is lost for high-

energy physics. Finally, there is a significant source of systematic error due to the

relative normalisation of data sets under the different beam conditions due to the

difference in luminosities, caused, for example, by an increase in the proton beam

divergence at lower energies.

Instead of physically changing the beam energy, the use of Initial State Radiative events

has been proposed [20] as a means to effectively vary the centre of mass energy without

physically changing the beam conditions.

As has been shown in Chapter 2, the differential cross section for deep inelastic e+p

scattering can be written as:

(8.1)

130

where , and , the polarisation parameter is

(8.2)

In the above equation, y is the true kinematic y, as given in equation 7.16, i.e.

where y is measured using the sigma method.

Since depends on y, which is related to x and Q2 through , changing s implies

changing .

One method of extracting R using ISR events is to plot the cross section as a function of

and perform a linear fit to the points [20]. This method is independent of F2 but

requires a large integrated luminosity of ~200pb-1 in order to gain sufficient statistics. A

second approach however, uses the knowledge of F2 from previous measurements at

HERA. This exploits the influence of R on the shape of the distribution [21, 92],

where was defined in equation 2.40 as

(8.3)

Since the ISR Monte Carlo is generated with FL=0, the measured y spectrum for data

can be compared with that for the Monte Carlo. This gives the difference in the cross

section which, as shown in figure 2.6, becomes larger with increasing y. In order to

illustrate this, the ratio, MC, is defined as:

(8.4)

As shown in figure 8.1, MC has a different shape for different values of R. It is clear

that as the value of R increases the ratio curves downwards more steeply at higher

values of y

131

Figure 8.1: The effect of weighting the y spectrum to three different values of R. As R

increases the curve of the ratio becomes steeper.

The comparison shows unweighted Monte Carlo and Monte Carlo weighted to values of

R of 0.2, 1.4 and 10 . As can be seen this shows the same fall at high y as figure 2.6.

With ascending y the overall effect on the cross section increases. For the highest values

of y this can have as much as a 15% effect for R=0.3 but, for small values of y, FL has a

very small effect. This renders the measurement of FL using the absolute cross-section

difficult, if not impossible.

In order to measure R, the ratio R is defined such that

(8.5)

This is measured as a function of y and is equivalent to . Therefore, instead of

measuring the absolute cross section, R can be extracted by fitting the measured R to a

function of the form

(8.6)

where NFit is a factor introduced to take into account the relative normalisation.

132

The method is possible because the structure function, F2, has been measured very

precisely at HERA and there is a good understanding of deep inelastic processes with

initial state radiation.

8.2 Event selection

8.2.1 Trigger

Unlike the F2 analysis, the trigger DIS10 is used for the FL analysis. At the first and

second level triggers, this is identical to DIS01. However, at the TLT, DIS10 includes

an ISR specific cut on the energy of the photon in the LUMI- calorimeter of E > 4

GeV. Also, a cut on y measured using the electron method is included. The DIS10

trigger corresponds to 35.9pb-1 of data.

As before, the DIS02 trigger is used for the background determination.

Table 8.1 shows the properties of the DIS10 trigger compared with the DIS01 and

DIS02 triggers described in the previous chapter.

TLT Variable DIS01 DIS02 DIS10

FLT BIT 30 30 30/46

E-Pz SLT [GeV] - 19 -

Ee [GeV] 4 4 4

Box Cut [cm] 12 x 6 12 x 6 12 x 6

E-Pz [GeV] 30 20 30

ye - - 0.1

LUMI- [GeV] - - 4

Prescale 1 40 – 100 1

Table 8.1: Comparison between the triggers used for ISR analyses. DIS01 and DIS02

are used for the F2 measurement while DIS10 and DIS02 are used for the FL

measurement.

8.2.2 Cuts

133

Initial event selection was the same as the F2 measurement with the events being taken

from the DIS10 run range. This yielded 861 860 events for 1996 and 1 331 496 events

for 1997.

The cuts are the same as the F2 analysis with the following exceptions:

Calorimeter E-PZ cut raised to 22 GeV.

Total E-PZ for 1997 changed to 46 GeV – 60 GeV. (The cut for 1996 is unchanged.)

An outer boxcut of 30cm x 30cm is added. This is to restrict events to those within

the SRTD acceptance.

The Trigger bit selected is DIS10.

The same corrections, reconstruction and background subtraction as used for the F2

measurement were performed.

8.2.3 Energy scale of the LUMI- calorimeter

The correct simulation and measurement of the ISR photons is vitally important for the

measurement of FL.

The simulation of the LUMI- calorimeter is therefore checked by performing a

kinematic peak study on the data and MC for both 1996 and 1997 events. The kinematic

peak arises at low y and low Q2 where the energy of the scattered positron becomes

approximately independent of the kinematics of the event and is roughly equal to the

beam energy. In the case of ISR, the sum of positron and photon energies becomes

~27.5 GeV.

Kinematic peak events are selected for DIS01 events by performing the boxcut and

electron probability cut along with a cut of 0.005 < yJB < 0.04. Histograms of electron

energy + photon energy are made in bins of electron energy with gaussians fitted to the

kinematic peak.

The results of the gaussian fits for 1996 are shown in figure 8.2.

134

Figure 8.2: Kinematic peak study for 1996.

The left-hand plot shows the fitted energy of the peak. The dashed lines indicate 1%

error on the data, which corresponds to the error on the electron energy measurement.

As can be seen, there is a good agreement between data and Monte Carlo.

For 1997 the rate for the DIS01 trigger became too high and it was prescaled to 100.

Therefore, in order to gain enough statistics for this study, a new trigger, DIS29, was

introduced. This trigger is the same as the DIS10 trigger with the y cut removed. The

results for 1997 are shown in figure 8.3.

Figure 8.3: Kinematic peak study for 1997.

Again, the energy and resolution are well simulated by the Monte Carlo. This indicates

the validity of the offline simulation of the LUMI- calorimeter described in Chapter 5.

8.2.4 The FL Bin

135

Due to limited statistics, the measurement of FL is only performed in one bin. A large

aim of the bin selection is to maximise the accessible y range. The available range

depends on the measured positron and photon energies as well as the cut on yHERA for

the bin boundaries.

Considering first the scattered positron energy, this is related to y by:

(8.7)

The maximum value of y obtainable for several values of is shown in figure 8.4. The

accessible values of y lie below the lines. It is clear that in order to maximise the y

range the scattered electron should be measured to as low values as possible.

Figure 8.4: The maximum values of y obtainable for different minimum values of the

scattered positron energy.

As the bin is measured in terms of yHERA, the true kinematic y range is a function of z,

i.e. the photon energy. The effect of the yHERA bin boundaries is shown in Figure 8.5.

136

Overlaid on the previous plot are lines showing the range in y available due to the

choice in bin of 0.1 < yHERA < 0.23. The upper cut is placed to limit the amount of

background, which is predominantly at high yHERA. This can be seen for the F2 case in

figure 7.8. The lower cut on yHERA is limited by the cut on y introduced in the trigger.

Only the y range between these two lines is accessible for the measurement.

The vertical line indicates the cut on the ISR photon of 6 GeV. The shaded region

indicates where measurements of y can be made. Therefore, the maximum range in y

that can be measured ranges from approximately 0.11 < y < 0.42 although statistics are

limited at the extremities.

Figure 8.5: The effect of the upper and lower cut of yHERA on the accessible region of y.

The Q2 range of the bin was chosen to be 1 GeV2 < Q2 < 30 GeV2 in order to achieve as

high statistics as possible. The final bin chosen is shown in figure 8.6 and is defined as:

1 GeV2 < Q2 < 30 GeV2

0.1 < yHERA < 0.23

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Figure 8.6: The bin used for the FL measurement shown on the x, Q2 plane with the F2

bins superimposed for comparison.

As with the previous measurements a comparison of data and Monte Carlo is shown in

Figure 8.7 (1996) and Figure 8.8 (1997). In both cases, the plot of the y distribution,

used for the fit, is highlighted. In order to gain sufficient statistics for the fit, especially

at high and low y, the y distribution is limited to 5 bins. The distributions show only the

events found within the y and Q2 bin.

138

Figure 8.7: Data v MC + BGD comparison for the 1996 FL measurement. The y

distribution, used for the fit, is shown at the bottom.

139

Figure 8.8: Data v MC + BGD comparison for the 1997 FL measurement. The

y distribution, used for the fit, is shown at the bottom.

The agreement between data and Monte Carlo for these distributions is reasonable.

For the extraction of R, the 1996 and 1997 y distributions are combined.

140

8.3 Measuring FL

8.3.1 y scaling factor

The extraction of F2 uses the bin-by-bin unfolding method, which uses Monte Carlo to

take into account the effect of migration and acceptance. The extraction of R, described

in section 8.1 however, requires a ‘raw‘ measurement of the kinematic variable y and

therefore any resolution and migration effects on this must be taken into account before

a fit can be made to the shape of the y distribution.

The resolution of y in the region covered in this analysis is shown in figure 8.9. As with

the corresponding plot for the F2 measurement, shown in the previous chapter, there is a

migration of approximately 10% towards lower values of y over most of the kinematic

region covered by this measurement. Only at the lowest values of y does this effect

disappear.

Figure 8.9: The migration and resolution of y in the range used for the extraction of R.

The use of other reconstruction methods in this kinematic range gives worse resolution

with a stronger y-dependence. Therefore, in order to take this effect into account a

scaling factor, Sy, is introduced into the formula for , resulting in:

141

(8.8)

One way of determining Sy would be to make a straight-line fit to the points in figure

8.9 this would result in a value of ~1.10. This however, corresponds to the whole region

in y, whereas the fit is affected by the range in y over which the fit is performed i.e. by

size of the bin. This is shown in figure 8.10. As can be seen, changing the range in y

covered by the bin would, for the same Sy, result in a different fitted value of R.

Figure 8.10: The effect caused by fitting different ranges of y (left). The plot shows the

MC distribution for MC weighted to R = 1.4. Two fits have been made, one curve

covering the range up to y = 0.6 and the other up to y = 0.45 (corresponding

approximately to the accessible range in this analysis). As can be seen, the shape of the

curves are different, giving different fitted values of R. The plot to the right shows the

fit made with Sy set to 1.149. This fit yields the weighted value of R=1.4.

The value of Sy is therefore determined within the bin used for this analysis. This is

achieved by weighting the Monte Carlo to R=1.4 and varying Sy to find a minimum 2.

The value R=1.4 was chosen for consistency with previous attempts to determine Sy

[87]. This results in a value of Sy of 1.149 0.03. Also shown in figure 8.10 is the

result of a fit made using this value of Sy. As can be seen, the fit yields the correct result

for R.

142

8.3.2 Extraction of R

R can now be extracted using by using the corrected form of equation (8.6):

(8.9)

This fit is performed for the ‘96 and ‘97 data with the result shown in figure 8.11.

Figure 8.11: Fit of ratio of data and MC y distributions for combined 1996 and 1997

data.

The value of R obtained from this fit is:

F2 is measured in the FL bin using the method outlined in chapter 7 and is found to be

143

The ALLM97 value of F2 in this bin is 0.912 which is ~2% lower than the measured

value. This is consistent with the normalisation offset found with the measurement of F2

described in chapter 7.

8.3.3 Systematic Errors

The estimate of systematic uncertainties includes many of the same variations in

quantities as the F2 measurement. These are:

1. Decrease the electron energy cut by 1 GeV.

2. Increase the electron energy cut by 1 GeV.

3. Decrease the photon energy cut by 0.5 GeV.

4. Increase the photon energy cut by 0.5 GeV.

5. Change the Total E-PZ cut to 46 – 61 GeV.

6. Change the Total E-PZ cut to 47 – 59 GeV.

7. Raise the calorimeter E-Pz cut by 1 GeV.

8. Reduce the calorimeter E-Pz cut by 1 GeV.

9. Increase the Boxcut by 0.5cm.

10. Decrease the Boxcut by 0.5cm.

11. Change the cut on the Z vertex to 60cm.

12. Remove the veto on the 44m Tagger.

In addition to varying the cuts, changes to the reconstruction are also performed.

13. Normalise the Background in the E-PZ region > 64GeV.

14. In the LUMI- simulation, increase the energy scale of the LUMI- calorimeter by

0.1 GeV and the resolution by 1%.

15. Change the diffractive fraction to 11%.

16. Change the diffractive fraction to 19%.

17. Scale the hadronic energy by 1.03.

18. Scale the hadronic energy by 0.97.

144

19. Scale the measured electron energy by 1.005.

20. Scale the measured electron energy by 0.995.

21. Use the ‘offline’ cut for the trigger.

22. Remove the backsplash correction.

23. Scale the SRTD and presampler corrections by 10%.

Finally, the size of the bin is varied in order to take into account the uncertainty in the

scaling parameter, Sy.

24. Decrease the y bin boundaries to 0.11 – 0.22.

25. Increase the y bin boundaries to 0.09 – 0.24.

The effect of these checks on the measured value of R is shown in figure 8.12.

Removing the backsplash correction (22) affects the ratio for the low y bins causing a

reduction in the overall fitted R.

The reduction of the bin size (24) also affects the fit at low y and leads to a negative

value for R. Another large downward shift is caused by the reduction of the electron

energy cut. This is probably caused by the change in the relative SINISTRA95

efficiency for finding scattered positrons for data and Monte Carlo.

The largest positive shift is caused decreasing the photon energy cut (3). Also there is a

large positive effect caused by changing the simulation (14) demonstrating the

sensitivity of this measurement to accurate simulation of the LUMI- calorimeter.

145

Figure 8.12: The effect of the systematic checks on the value of R. Shown for each test

is the fitted value of R together with the errors on the fit. The dashed lines indicate the

nominal value together with its error.

In the calculation of the error, correlations between systematic errors have not been

taken into account and the total systematic error is therefore an overestimate.

8.4 Results

Including systematic errors, the measurement of R is

The above systematic checks are also applied to the F2 measurement and the effect on

the measurement is shown in figure 8.13. In this case, decreasing the photon energy cut

(3) and changing the energy scale of the LUMI- simulation (14) again causes the

biggest effect.

146

Figure 8.13: The fractional effect of the systematic checks on the value of F2.

Including systematic errors, the measured value of F2 is

Given R and F2, FL can be extracted using:

(8.10)

The measured value of FL is found to be

This is measured at Q2 = 5.5 GeV2 and x = 4.4 10-4 and is shown in figure 8.14. Also

included on the figure are the limits on the value of FL of FL = 0 and FL = F2. As can be

seen the measured value of FL falls within these limits although the errors are large. The

147

large asymmetry in the systematic error in particular is the result of converting R to FL

using equation 8.10.

Figure 8.14: The measured value of FL plotted at Q2 = 5.5 GeV2 and x = 4.4 10-4.

This result can be compared with the values obtained by the H1 experiment [22], which

are shown in Figure 8.15. The scale of the x-axis in both plots is the same although for

the H1 plot the points are given at different values of Q2.

Although this result is consistent with the H1 measurement, the large error here

prevents a statement on the implications of this measurement. Indeed, given the size of

the error, the result is also consistent with a value of zero. Taking into account only the

statistical error, FL=0 can be rejected at the 10% significance level. This analysis

however, demonstrates the viability of using Initial State Radiative events for future,

more accurate measurements of FL.

148

In order to improve this measurement it is clear that a large improvement in statistics is

required. The above result uses ~35pb-1 of data from the 1996 and 1997 running

periods. Up to the shutdown for the HERA upgrade in September 2000 ZEUS collected

a further 68pb-1 of e+p data and 16.7pb-1 of e-p data. Even if the e-p data is not taken into

account this represents a doubling of the available statistics.

Figure 8.15: FL measured by H1 over a similar range in x to the ISR measurement. The

yellow band shows the expectation from pQCD with the dashed lines giving the limits

of FL = 0 and FL = F2. The points are given for different values of Q2 with the FL = F2 line

also covering a range in Q2. This explains the fall with decreasing x.

A further increase in statistics could be obtained by lowering the cut on the scattered

positron energy to 5 GeV. More importantly however, this would extend the range in y

available for the fit as demonstrated in figure 8.5. The statistics in the bins of y in the

high y region would be improved. This is also the region where the ratio R shows the

greatest deviation from 1 for non-zero values of FL and therefore it would be of benefit

to gain as much data here as possible.

149

However, reducing this cut would introduce new uncertainties into the measurement as

shown by the systematic error in figure 8.11. The electron finders are tuned to find

positrons at energies greater than 8 GeV and lose efficiency dramatically as the energy

is lowered below this value. Furthermore, the reduction in efficiency is different for

data and Monte Carlo, necessitating the introduction of a new correction factor. Also,

the hadronic reconstruction routines eliminate the positron by taking the number of

positron cells directly from the electron finder. Any problems from the electron finder

may also affect the hadronic reconstruction. This is illustrated in figure 8.16. Finally,

cutting on lower energy positrons may also allow more photoproduction background

into the sample.

It is clear that background plays a significant role in improving the measurement of both

F2 and FL. The next step should be to utilise photoproduction Monte Carlo in order to

estimate the background rather than use the DIS02 trigger with overlay bremsstrahlung

events. This may also aid investigation into the problems involved with lowering the

positron energy cut.

Figure 8.16: The hadronic E-Pz distributions using positron energy cut > 8 GeV (left)

and > 5 GeV (right). As can be seen there is a deficit of Monte Carlo between 5 and 15

GeV for the lower energy cut. This may be due to more background or problems with

the reconstruction.

150

Chapter 9

Conclusions

In this analysis, Initial State Radiative events have been used to measure the F 2 and FL

structure functions of the proton. These measurements require a very good

understanding of both the main ZEUS detector and the ZEUS luminosity monitor, as

ISR events are subject to contamination from both bremsstrahlung and photoproduction

backgrounds.

Using a subset of data from 1996, taken with a low Q2 trigger and having an integrated

luminosity of 3.78pb-1, the proton structure function F2 has been measured as a function

of x and Q2. The kinematic region used covers the Q2 range of 0.3 GeV2 < Q2 < 40 GeV2

and the range in x of 7.6 10-6 < x < 4.8 10-2. In general, there is good agreement

with the standard ZEUS F2 measurement. There is also agreement with a Regge based

parameterisation, which uses previous measurements of F2 including very low Q2 ZEUS

results.

These data cover a region on the kinematic plane that spans the gap between the very

low Q2 ZEUS results and the medium and high Q2 ZEUS results. They also overlap with

fixed target data at higher values of x. Measurements of F2 at ZEUS now cover

continuously the Q2 range 0.045 GeV2 < Q2 < 30000 GeV2 and values in x ranging from

6 10-7 at very low Q2 to 0.65 at high Q2.

Also, using a special trigger for radiative events applied during 1996 and 1997 data

taking, the longitudinal proton structure function, FL has been measured. This data, with

an integrated luminosity of 35.9pb-1, covers the kinematic region 1 GeV2 < Q2 < 30

151

GeV2 and 2.6 10-4 < x < 6.1 10-4. Due to low statistics FL is measured in one bin

with central values of Q2 and x of 5.5 GeV2 and 4.4 10-4 respectively.

The ratio, R, of the cross sections for longitudinal and transverse polarised photons has

been found to be while F2 is measured as

.

These two quantities are related to FL by and give

.

This is the first direct measurement of FL at HERA and is consistent with the prediction

from perturbative QCD and with indirect QCD based extrapolations.

The measurement of FL should be further improved by using data taken up to the HERA

shutdown in September 2000.

152

Appendix A

F2 Measurement

Bin Q2 (GeV2) x # Data events # BGD events F2 stat sys

123456

0.3 7.483E-61.363E-52.217E-53.88E-57.76E-33.954E-4

11.1732.1760.16134.7122.0177.1

3.304.920.822.450.810.83

0.252 0.133 0.3580.203 0.053 0.6100.337 0.065 0.2170.266 0.033 0.0800.259 0.034 0.1370.194 0.021 0.085

789101112

0.6 1.602E-52.915E-54.731E-58.315E-51.663E-48.837E-4

92.42301.7243.6459.8383.0588.5

72.3170.6718.0614.024.903.28

0.240 0.120 0.6410.472 0.047 0.1280.441 0.042 0.0710.440 0.030 0.0680.413 0.031 0.0880.270 0.016 0.065

131415161718

1.3 3.204E-55.83E-59.463E-51.663E-43.326E-41.767E-3

186.7469.2374.1701.4583.11051

96.16134.268.4747.7415.5728.66

1.247 0.252 0.3130.703 0.060 0.0850.498 0.041 0.1030.552 0.031 0.0550.494 0.029 0.0820.382 0.017 0.045

192021222324

2.5 6.408E-51.166E-41.892E-43.326E-46.652E-43.534E-3

232.6616.3405.0736.9615.4922.2

143.81186.3158.3328.7513.1413.17

1.029 0.209 0.2590.939 0.072 0.1210.698 0.054 0.0740.740 0.040 0.0340.655 0.039 0.0570.451 0.021 0.048

252627282930

5 1.282E-42.332E-43.785E-46.652E-41.33E-37.069E-3

196.4502.6376.5627.7494.6758.0

117.74164.6159.9231.289.8012.31

1.096 0.230 0.1420.988 0.084 0.1390.920 0.077 0.0680.865 0.052 0.0520.740 0.049 0.0400.524 0.028 0.046

313233343536

10 2.563E-44.664E-47.57E-41.33E-32.661E-31.414E-2

138.8318.4211.9395.4295.5426.0

69.2080.5319.8121.356.579.80

1.679 0.366 0.2191.403 0.147 0.1581.073 0.114 0.1041.036 0.081 0.0460.793 0.068 0.0490.534 0.038 0.035

373839404142

20 5.127E-49.328E-41.514E-32.661E-35.321E-32.827E-2

64.54172.3144.3192.3161.4240.4

26.4716.479.149.061.634.08

1.963 0.565 0.3231.693 0.218 0.0541.460 0.199 0.0741.024 0.113 0.0470.843 0.098 0.0650.513 0.048 0.048

434445464748

40 1.025E-31.866E-33.028E-35.322E-31.064E-25.655E-2

27.9577.0358.8268.7367.36161.3

8.2010.765.802.482.450.82

2.186 0.860 0.4581.588 0.313 0.0511.090 0.223 0.1570.722 0.122 0.1430.669 0.118 0.1300.592 0.071 0.054

Table A.1:Values of F2 measurements and bins with number of events found and errors.

153

Bibliography

[1] S.Weinberg, Phys. Rev. Lett. 19 (1967) 1264

A.Salam, “Elementary Particle Theory”, Ed. N. Svartholm, Almquist & Wiksells,

Stockholm (1969) 367

S.L.Glashow, J.Iliopoulos, L.Maiani, Phys. Rev. D2 (1970) 1285

[2] R.G. Roberts, “The Structure of the Proton”, CUP (1990)

[3] E.D. Bloom et al., Proceedings of the XVth International conference on High

Energy Physics, Kiev (1970)

[4] J.D. Bjorken, Phys. Rev. 179 (1969) 1547

[5] R.P. Feynman, Phys. Rev. Lett. 23 (1969) 1415

[6] C.G. Callan & D. Gross, Phys. Rev. Lett. 22 (1969) 156

[7] TASSO Collaboration, Phys. Lett. B86 (1979) 243

[8] ZEUS Collaboration, “Measurement of the Proton Structure Function F2 in e+p

collisions at HERA”, Abstract 1048, ICHEP00, Osaka

[9] J.C.Collins, Nucl. Phys. B261 (1985) 104

[10] G. Altarelli & G. Parisi, Nucl. Phys. B126 (1977) 298

[11] G. Altarelli, Nucl. Phys. B91 (1981) 1

[12] V.N. Gribov & L.N. Lipatov, Sov. J. Nucl. Phys. 15 (1972) 438

[13] L.N. Lipatov, Sov. J. Nucl. Phys. 20 (1975) 96

[14] Y.L. Dokshitzer, Sov. Phys. JETP 46 (1977) 641

[15] H.Plotow-Besch, Comp.Phys.Commun. 75 (1993) 396, Version 7.05, CERN-PPE

1996.11.06

[16] A.D.Martin, W.J.Stirling, R.G.Roberts, Phys. Rev. D51 (1995) 4756

[17] CTEQ Collaboration, “Improved Parton Distributions from Global Analysis of

Recent Deep Inelastic Scattering and Inclusive Jet Data”, hep-ph/9606399, Phys. Rev.

D55 (1997) 1280

[18] A.M. Cooper-Sarker et al., Proc. of the HERA workshop, Hamburg 1987, ed. R.D.

Peccei, Vol.1, p.231

154

[19] A.M. Cooper-Sarker et al., Proc. of the HERA workshop, Hamburg 1991, eds. W.

Buchmuller and G. Ingelman, Vol.1, p.155

[20] M.W Krasny et al., Z. Phys. C53 (1992) 687

[21] L. Favart et al., Z. Phys. C72 (1996) 425

[22] H1 Collaboration, Phys. Lett. B393 (1997) 452

[23] BCDMS Collaboration, A.C. Benvennuti et al., Phys. Lett. B195 (1987) 91

[24] BCDMS Collaboration, A.C. Benvennuti et al., Phys. Lett. B233 (1989) 485

[25] BCDMS Collaboration, A.C. Benvennuti et al., Phys. Lett. B237 (1990) 592

[26] CDHSW Collaboration, P. Berge et al., Z. Phys. C49 (1991) 187

[27] E143 Collaboration, K.Abe et al., Report SLAC-PUB-7927, SLAC (1998), hep-

ex/9808028

[28] E140 Collaboration, S.Dasu et al., Phys. Rev. Lett. 61 (1988) 1061

[29] E140 Collaboration, S.Dasu et al., Phys. Rev. D49 (1994) 5641

[30] L.W.Whitlow et al., Phys. Lett. B250 (1990) 193

[31] NMC Collaboration, M.Arneodo et al., Nucl. Phys. B483 (1997) 3

[32] CCFR/NuTeV Collaboration, U.K.Yang et al., “Measurements of the Longitudinal

Structure Function and |Vcs| in the CCFR experiment”, Proc. 6th International Workshop

on Deep Inelastic Scattering and QCD (DIS98), ed. G.Coremans,R.Roosen,Singapore,

World Scientific (1998) 131

[33] P.Higgs, Phys. Rev. Lett. 12 (1964) 132

[34] P.Higgs, Phys. Rev. 145 (1966) 1156

[35] P.G.O.Freund, “Introduction to Supersymmetry” ; CUP (1986)

[36] C.Seez & T.S. Virdee, “Detection of an intermediate mass Higgs Boson at LHC

via its two photon decay mode”, CMS TN/92-56 (1992)

[37] W. van Loo, Phys. Stat. Sol. 28 (1975) 227

[38] P.Lecoq et al., “Lead Tungstate Scintillators for LHC e.m. Calorimetry”, CMS

TN/94-308 (1994)

[39] S.Dazu et al., “The Level-1 Calorimeter Trigger Performance Studies”, CMS

TN/94-285 (1994)

[40] U Schäfer, Private Communication

[41] P.J. Ashenden, “The Designer’s Guide to VHDL”, Morgen Kaufmann (1996)

155

[42] A. Rushton, “VHDL for Logic Synthesis”, Second Edition, John Wiley & Sons

(1998)

[43] G.A. Voss & B.H. Wiik ; “The Electron-Proton Collider HERA” ; Ann. Rev.

Nucl. Part. Sci. 44 (1994) 413

[44] ZEUS Collaboration, Eur. Phys. J. C7 (1999) 609

[45] ZEUS Collaboration, Phys. Lett. B487 (2000) 53

[46] P.A. Mauchiz et al., Phys. Lett. B295 (1992) 159

[47] A.C. Benvenuti et al., Phys. Lett. B237 (1990) 592

[48] S.R.Mishra & F.Sciulli, Ann. Rev. Nucl. Part. Sci. 39 (1989) 259

[49] Phys. Rev. D54 (1996) 3006

[50] L.W. Whitlow et al., Phys. Lett. B250 (1990) 193

[51] ZEUS Collaboration, “A detector for HERA”, PRC 87-02

[52] ZEUS Collaboration, “The ZEUS Detector”, Status Report (1993)

[53] E.Hilger, “ZEUS coordinate System”, ZEUS Note-86-17

[54] B.Foster et al., NIM A315 (1992) 397-403

B.Foster et al., NIM A338 (1994) 254-283

[55] B.Foster, “Whisker Growth in Test Cells”, Preprint 29054 (1986)

[56] A.Bamberger et al., “The Small Angle Rear Tracking Detector at ZEUS”, NIM

A401 (1997), 63-80

[57] A.Caldwell et al., NIM A321 (1992) 356

[58] H.Brueckmann, “A Precision Calibration Method (DU) for the ZEUS Hadron

Calorimeter”, ZN-86-36

[59] J.F.Zhou & D.Krakauer, “Calorimeter calibration triggers in the ZEUS luminosity

run”, ZN-94-130

[60] J.Michell & D.Hanna, “Status of the FCAL/BCAL Laser Calibration”, ZN-90-104

[61] A.Bamberger et al., “The Presampler for the Forward and Rear Calorimeter in the

ZEUS Detector”, DESY-96-139, Proc. ICCHEP96 Frascati, Italy 6 209-218

[62] K.Piotrzkowski & M.Zachara, “Determination of the ZEUS Luminosity in 1994”,

ZEUS Note-95-138

[63] G.Hartner et al., “VCTRAK (3.07/04) Offline Output Information”, ZEUS Note 97-

064

156

[64] H.Abramowicz, A.Caldwell and R.Sinkus, “Neural Network Based Electron

Identification in the ZEUS Calorimeter”, N.I.M. A365 (1995) 508-517

[65] U. Bassler & G. Bernardi, DESY H1-03/93-274 (1993)

[66] A. Courau et al., “Quasi-Real QED Compton Monte Carlo for HERA”,

Proceedings of the Workshop Physics at HERA 2 (1991) 902

[67] H.Spiesberger, “DJANGO6 version 2.4 – A montecarlo generator for Deep

Inelastic lepton proton scattering including QED and QCD radiative effects”, 1996.

[68] A. Kwiatkowski, H Spiesberger, H.J.Mohring, Comp. Phys. Commun 69 (1992),

155

[69] H.Spiesberger, “HERACLES. An event generator for ep interactions at HERA

includingRadiative processes (Version 4.6)”, 1996

[70] L.Lonnblad, Nucl. Phys. B306 (1988) 746

[71] L.Lonnblad, Z.Phys. C43 (1989) 625

[72] L.Lonnblad, Nucl. Phys. B339 (1990) 393

[73] T. Sjöstrand, Comp. Phys. Commun. 39 (1986) 347

[74] T.Sjöstrand, Comp. Phys. Commun. 82 (1994) 74

[75] H, Jung, “RAPGAP. The RAPGAP montecarlo for Deep Inelastic Scattering”,

1997,

[76] H.U.Bengtsson, T.Sjöstrand ; Comp.Phys.Commun 46 (1987) 43

[77] G.Ingleman,A.Edin,J.Rathsman, DESY 96-057, DESY (1996), hep-ph/9605286

[78] H. Abramowicz, A. Levy, DESY 97-251, DESY (1997), hep-ph/9712415

[79] CERN, CH-1211 Geneva 23, Switzerland, “GEANT Detector Description and

Simulation Tool”, October 1994

[80] E. De Wolf et al., ZGANA, ZEUS Trigger Simulation Library

[81] K. Olkiewicz & A. Eskreys, “Off-line Luminosity Calculation in the ZEUS

Experiment in 1997, 1998 and 1999”, ZEUS Note 99-044 (1999)

[82] J. Adamczyk et al.,“Proposal for upgraded Lumi monitor for ZEUS Experiment”

ZEUS Note 99-078.

[83] A. Caldwell et al., “A Luminosity Spectrometer for ZEUS”, HERA-ZEUS

Document 22/10/99

[84] R. Graciani, “A New Electron Tagger for ZEUS”, ZEUS Note 99-067

157

[85] D.Roff, “Luminosity Measurements from Virtual Compton Scattering”, ZEUS

Note 97-026

[86] N. Wulff, “Radiative Corrections for ep-interactions in Leading Log

Approximation”, ZEUS Note 95-143

[87] A. Bornheim, Private Communication

[88] R.Deffner, “Measurement of the Proton Structure Function F2 at HERA using the

1996 and 1997 ZEUS Data”, Thesis, Bonn (1999)

[89] N. Tuning, Private Communication

[90] ZEUS Collaboration, Zeit. f. Phys. C72 (1996) 399

[91] A.M. Cooper-Sarker, R.C.E. Devenish, A. De Roeck, “Structure Functions of the

Nucleon and their Interpretation”, DESY 97-226, DESY (1997), hep-ph/9712301

[92] A. Bornheim, “Messung der Protonstrukturfunktionen F2 und FL in radiativer ep-

Streuung mit dem ZEUS-Detektor”, Thesis, Bonn (1999)

158