Search for Leptoquarks in Electron-Proton Collisions

Frederic Benard

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Physics University of Toronto

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Search for Leptoquarks in Electron-Proton Collisions

Frederic Benard

Graduate Department of Physics

University of Toronto

P h.D . 1995

A b stract

Leptoquarks carry lepton number as well as baryon number and could provide an

explanation for the observed symmetry between the quarks and leptons. Leptoquarks

coupling to first-generation quarks and leptons were searched for in electron-proton colli

sions at HERA using the ZEUS detector. In a sample of e~p —> v X events corresponding

to an integrated luminosity of 27.5 nb-1, no leptoquark candidates were found. Limits

on leptoquark couplings are derived for leptoquark masses ranging from 50 GeV/c2 to

225GeV/c2. Scalar (vector) isosinglet leptoquarks coupling to a left-handed electron

and a tz-quark (d-quark) with electroweak coupling strength are ruled out at the 95%

confidence level for masses below 154 G eV/c2 (108 GeV/c2).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgements

I am very grateful to my supervisor, David Bailey, for his enthusiasm, his patience,

and his continuous support. I am happy to have been his first graduate student. Being

part of the ZEUS Third Level Trigger group has been an exciting and enriching adventure.

I am indebted to Robert Orr, Sampa Bhadra, Dinu Bandyopadhyay, and Gerd Hartner,

as well as the students on the project: Frank, Mike, Cortncy, and Richard. I wish

to thank the members of the ZEUS Exotics physics group, in particular Frank Sciull’-,

Steve Ritz, Bruce Straub, and Jurgen Schroeder. I also wish to thank Sacha Davidson for

answering my many qu .rations on leptoquarks. David Bailey and •onathan Labs reviewed

many drafts of the thesis and their comments and suggestions have been invaluable. In

addition, their questions prepared me well for my Ph.D. defences.

The Canadian ZEUS group at DESY, under the leadership of John Martin, provided

intellectual and social support during my stay in Hamburg. In addition to the aforemen

tioned ZEUS members, I would like to thank Milos, Burkhard, Wai, Laurel, and Larry.

I thank my friends, Sophie, Frederic, Jason, Charles. Mieke, Heather, Lysiane, Thomas,

and Robert, without the support of whom I would have had difficulty maintaining my

sanity during the last five years. The support of Charles, Heather, and Robert this last

year is especially appreciated. Un gros merci a ma soeur Isabelle, ma mere Rolande et

mon pere Raymond pour leurs encou-agements et leur amour. Finally, I would like to

thank Jonathan for his tremendous support, for his love, and for having waited for me

so long in rainy Hamburg while I finished my thesis in Toronto.

iii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Personal Contributions to the ZEUS Experiment

I joined the ZEUS Third Level Trigger group in the fall of 1989. During the following

two years I was involved with Monte Carlo trigger studies. I also set up and maintained

a network of five computer workstations used by TLT members at the University of

Toronto.

I moved to Hamburg in the spring of 1991. As a member of the TLT group, I

continued doing trigger studies and developed analysis software for the TLT processors.

In particular, I interfaced various versions of the VCTRAK track reconstruction pr^ram

to the TLT environment. I also set up a large network of computer workstations currently

used by the Canadian ZEUS group in Hamburg. In 1992, I contributed to the conception

and development of Funnel , the platform now used for almost all ZEUS Monte Carlo

event generation.

I joined the ZEUS Exotics physics group in the fall of 1991 and over the following two

years made many contributions to that group. The first collisions were provided by the

accelerator during the summer of 1992. A collective effort was made to extract a possible

leptoquark signal from the data. I worked on the decay to neutrino plus jets channel and

helped design criteria to select the deep inelastic charged current data. I also studied

the effects of trigger acceptance, je t reconstruction, and track and vertex reconstruction.

No leptoquark signals were found and lim its on leptoquark couplings were derived. The

work of '.he Exotics physics group led to the publication “Search for Leptoquarks with

the ZEUS Detector”, Phys. Lett. B 3 0 6 (1993) 173.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C ontents

Introduction 1

1 Theoretical Framework 3

1.1 The Standard M odel ...... 3

1.2 Leptoquarks Beyond the Standard M odel ...... 6

1.2.1 Grand Unification ...... 0

1.2.2 Technicolour ...... 7

1.2.3 Compositeness ...... 8

1.3 A Model Independent Approach ...... 0

1.4 Experimental Limits on Leptoquarks ...... 9

1.4.1 Searches in Electron-Positron Collisions ...... 9

1.4.2 Searches in Proton-Antiproton Collisions ...... 12

1.4.3 Leptonic Pion Decays ...... 13

1.4.4 Unitarity of the CKM M a trix ...... 15

1.4.5 Atomic Parity V iolation ...... 10

1.5 Kinematics of Electron-Proton Scattering ...... 18

1.6 Leptoquark Production and Decay at HERA ...... 20

2 Experimental Setup 27

2.1 The HERA Electron-Proton C ollider ...... 27

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.2 The ZEUS Detector ...... 30

2.2.1 O verview ...... 30

2.2.2 C a lo r im e te r ...... 34

2.2.3 Central Tracking D etector ...... 37

2.2.4 Co D e te c to r ...... 37

2.2.5 Luminosity Monitor ...... 39

2.3 The ZEUS Trigger and Data Acquisition System ...... 40

2.3.1 C o n ce p ts ...... 40

2.3.2 First Level Trigger ...... 42

2.3.3 Second Level Trigger ...... 43

2.3.4 Third Level Trigger ...... 44

2.4 The ZEU S O ffline E n v iro n m e n t ...... 48

2.4.1 Event R e co n stru ctio n ...... 4S

2.4.2 Offline Analysis ...... 49

3 Data Analysis 52

3.1 Description of the Problem ...... 52

3.2 Analysis T o o ls ...... 54

3.2.1 C5 T im e ...... 54

3.2.2 Track and Vertex Reconstruction ...... 57

3.2.3 Calorimeter Tim e ...... 59

3.2.4 Calorimeter Energy Islands ...... 60

3.2.5 M uon F i n d e r ...... 64

3.2.6 Reconstruction of Kinematic V ariables ...... 66

3.2.7 Luminosity Calculation ...... 67

3.3 Data S e le c tio n ...... 68

3.3.1 T he Level One F i l t e r ...... 6S

3.3.2 The Level Two F ilte r ...... 70

3.3.3 The Level Three F ilte r ...... 71

3.3.4 The Level Four F ilter ...... 73

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.3.5 The Level Five F ilte r ...... 7-1

3.3.6 Final Data Sam ple ...... 77

3.4 Monte Carlo Sim ulation ...... 82

3.4.1 Event Generation ...... 82

3.4.2 Trigger Acceptance and Selection Efficiency ...... 33

3.5 Kinematics of the Charged Current Candidate ...... 88

4 Limits on Leptoquarks 90

4.1 Limit Calculation ...... 90

4.2 Systematic Checks ...... 91

4.3 R e s u lts ...... 99

4.3.1 Effect of the Background Subtraction on the Lim its ...... 102

4.3.2 Effect of the Structure Functions on the Limits ...... 102

4.3.3 Effect of the Energy Scale on the L im its ...... 103

4.4 C o n c lu s io n s ...... 104

A Upper Limit Calculation 107

References 110

v ii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Tables

1.1 Scalar and vector leptoquarks and their couplings to quark-lepton pairs . 10

1.2 Limits on leptoquarks from rare processes at low-energy ...... IS

1.3 Production and decay of leptoquarks in e~p collisions ...... 22

1.4 Leptoquark cross-sections at H E R A ...... 24

2.1 HERA beam parameters ...... 31

2.2 Dimensions of the ZEUS calorimeter cells ...... 35

2.3 CAL FLT trigger tower thresholds ...... 43

3.1 Parameters used in the calorimeter time algorithm s ...... 61

3.2 Integrated luminosity used in the present analysis ...... 68

3.3 Level two calorimeter time rejection c rite ria ...... 71

3.4 Level three calorimeter time rejection criteria ...... 72

3.5 Level four calorimeter time rejection c rite ria ...... 73

3.6 Summary of the data selection c rite ria ...... 78

3.7 Properties of the five events remaining after the level five selection require

ments ...... 79

4.1 Correction to the CAL FLT trigger acceptance due to dead channels . . . 95

4.2 Estimated systematic e rro rs ...... 99

4.3 Summary of the results ...... 106

v iii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures

1.1 Diagram showing the interaction of a quark, a lcpton, and a leptoquark . (i

1.2 The decay of a leptoquark via the exchange of an extended Lechnicolour

gauge boson ...... 8

1.3 Leptoquark pair production in e+e~ collisions ...... 11

1.4 Leptoquark pair production in ppcollisions ...... 12

1.5 The decay 7r+ —► e+ uc via the exchange of an So leptoquark ...... 15

1.6 Electron-proton deep inelastic scattering ...... 19

1.7 D irect and v irtu a l production o f So leptoquarks in e~p collisions ...... 21

1.8 Leptoquark cross-sections at HERA as a function of leptoquark mass . . 25

2.1 The H E R A ac c e le ra to r ...... 28

2.2 The HERA injection system ...... 29

2.3 Integrated luminosity collected in 1992 as a function of tim e ...... 31

2.4 Section of the ZEUS detector along the beam ...... 32

2.5 Schematic view of an FCAL tower ...... 36

2.6 Wire layout in a 45° sector of the Central Tracking D etector ...... 38

2.7 Luminosity Monitor ...... 40

2.8 The ZEUS trigger and data acquisition system ...... 41

2.9 Processors, data links, and control links in one branch of the TLT .... 45

2.10 FCAL and RCAL time for physics and beam-gas events ...... 47

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.11 Data flow of ZEUS data and Monte Carlo data in the offline environment 50

3.1 Event display of a 150 GeV/c2 S'o —> v X Monte Carlo event ...... 53

3.2 C5 time distribution for Run 4272 ...... 55

3.3 Overall vertex r distribution from the C5 time information, for the runs

used in the present a n a ly s is ...... 57

3.4 Vertex fitting with and without the beam line constraint ...... 58

3.5 Calorimeter time distribution for Run 4272 ...... 62

3.6 An example of the calorimeter island algorithm ...... 63

3.7 p r distribution for Run 4272 ...... 69

3.8 Vertex distribution of the data after me level four filter criteria are applied 74

3.9 Azimuthal angle versus pseudorapidity of highest E t island, for events left

before the island p r requirement ...... 76

3.10 pr ca'culated using cells from islands with p < 3, for events entering the

level five filte r ...... 76

3.11 Time difference between the two highest E t islands, for events left prior

to :he island tim e re q u ire m e n t ...... 77

3.12 Event display of a cosmic muon event ...... 80

3.13 Event, display of the charged current candidate ...... 81

3.14 Generated and reconstructed x d istrib u tio n for 150 G e V /c 2 So leptoquarks

decaying into v X ...... 83

3.15 Trigger acceptance for LQ —» v X e v e n t s ...... S5

3.16 Selection efficiency for LQ —> v X e v e n t s ...... 86

3.17 Generated y distributions for 180 GeV/c2 scalar and vector LQ —► v X events 87

3.18 Reconstructed x distribution after data selection for the data and the

charged current DIS Monte C a rlo ...... 87

3.19 Shifts and resolutions in pr, x, y, and Q2 as a function of reconstructed y,

for ISO G eV /c2 So —► v X e v e n ts ...... 89

4.1 Mean reconstructed leptoquark mass and mass resolution as a function of

generated mass for scalar and vector leptoquarks ...... 91

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.2 Overall efficiency for LQ —► v X e v e n t s ......

4.3 Vertex efficiency versus 0mar for neutral current deep inelastic scattering

Monte Carlo and data ......

4.4 Upper lim its on the cross-sections of So, Si, V'o, and Vf leptoquarks . . .

4.5 Upper lim its on the couplings of S0. Si, Vo, and \\ leptoquarks ......

4.6 Effect of a ±5% shift in the energy scale on the coupling lim its ......

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Introduction

ZEUS is one of two large scale detectors at the HERA electron-proton collider in Ham

burg, Germany. HERA, which collides 26.7 GeV electrons with S20GeV protons, is an

ideal tool to study the structure of the proton, as well as to search for new particles.

In particular, leptoquark bosons, which carry both electric charge and colour, would

form an s-channel resonance and could be seen as a sharp peak in the x distribution of

deep inelastic scattering events at HERA. The number of leptoquark events produced

depends on the leptoquark mass and coupling to quark-lepton pairs. If their coupling is

sufficiently large, leptoquarks with masses up to the kinematic lim it (296 GeV/c2) could

be observed.

Scalar and vector leptoquarks coupling to first-generation quarks and leptons are

searched for in a sample of e~p —* u X events collected with the ZEUS detector during

1992. This sample corresponds to an integrated luminosity of 27.5 nb_1. No leptoquark

candidates are found and limits on leptoquark masses and couplings are derived.

This thesis is organized as follows. In Chapter 1, various theoretical models predicting

the existence of leptoquarks are presented, current experimental limits on leptoquark

masses and couplings are reviewed, and the production and decay of leptoquarks at

HERA are discussed. The ZEUS detector is described in Chapter 2, with emphasis on

the detector components which are used in the present analysis. Chapter 3 provides

a description of the data reconstruction and selection processes, and deals w ith issues

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. concerning the Monte Carlo programs used in the analysis. The limits on leptoquark

masses and couplings are presented in Chapter 4.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 1 Theoretical Framework

1.1 The Standard Model

All observed phenomena in elementary particle physics are described by the so-called

Standard Model [1]. According to this theory, all matter consists of pointlike spin-1/2

fcrmions: quarks and leptons. Excluding gravitation, which is of negligible strength at the

energies achievable by present-day accelerators, there are three fundamental interactions

amongst quarks and leptons: the weak force, electromagnetism, and the strong force.

These forces are described by local gauge symmetries and are mediated by vector gauge

bosons. The quarks experience all three forces while the leptons only participate in the

weak and electromagnetic interactions.

The Standard Model is the combination of the Glashow-Weinberg-Salam model [2]

with the theory of Quantum Chromodynamics [3]. It is based on the gauge group SU(3)

SU(2) ® U (l). The Glashow-Weinberg-Salam model, based on the gauge group SU(2) ®

U (l), provides the description for the weak and electromagnetic interactions. In this

model, the local gauge invariance is spontaneously broken by the Higgs mechanism [4],

which causes the weak gauge bosons W* and Z° to acquire large masses while leaving the

photon massless. Yukawa couplings to the Higgs boson generate masses for the fermions.

Quantum Chromodynamics is the field theory of the strong force, and it is based on an

exact SU(3) symmetry acting on the quark colour indices. The strong force is mediated

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4

by eight massless gluons, which are themselves coloured.

The known fermions are usually grouped into three families:

"*« \ leptons / ' I /

!lr

quarks C) C) Ur , d'R cRi s'n I n • b'n

Left-handed (right-handed) particles arc shown above as SU(2) isospin doublets (sin

glets). The weak eigenstates d! , s', and b1 mix to form the mass eigenstates d, s, and b

via the Cabibbo-Kobayashi-Maskawa (CKM ) matrix [5]:

j d ' \ ( V ud VU3 V'u6\ f d \

s' = vcd VC3 vcb s (l.l)

u > \Vtd Vta VtJ \ b j

Until recently, the i-quark had not been observed, but its existence was suggested, for

example, by the absence of flavour changing neutral currents. Recent evidence [()] suggests

the f-q u a rk exists w ith a mass o f about 175 G eV /c2.

The Standard Model has lead to a number of predictions which have since been con

firmed experimentally: weak neutral current interactions, the existence and the masses

of the weak gauge bosons. It is a theory free of mathematical inconsistencies, and it

successfully describes all known facts of elementary particle physics. Nev irtheless, many

physicists do not believe that the Standard Model is the ultimate theory because it leaves

several questions unanswered, some of which are the following:

• The theory has a large number of arbitrary parameters. There are three gauge

couplings, two CP violating 0 parameters for the SU(2) and SU(3) subgroups, two

parameters for the Higgs potential, ten parameters for the quark mass matrix (six

masses, three mixing angles, and one CP violating phase), and three charged lepton

masses. If the neutrinos are massive, one must include seven additional parameters.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5

• Some quantities, such as the ratio of the neutrino masses (if non-zero) to other

ferm ion masses, the ra tio of the ferm ion masses to the W ± and Z ° masses, the

mass scale of strong interactions ( i\ q cd) compared to the IF* mass, and the 0

parameters, are surprisingly small.

• The Higgs mechanism requires unnatural fine-tuning of parameters. For instance,

radiative corrections to the Higgs mass parameter /z2 are proportional to the square

of a large cut-ofF parameter A introduced in the process of renormalizing the theory:

/z2 —>/z2 + a A 2. (1.2)

The initial value of /z2 must therefore be chosen to cancel q A 2 to great accuracy,

otherwise the theory is expected to be no longer valid at TeV energies [7].

• The pattern of gauge groups is complicated and arbitrary. Moreover, the three fun

damental forces are not really unified since there are still three coupling constants.

• The symmetry between the quarks and leptons with respect to the electroweak

interaction is surprising, and so is the existence of three families of fermions, with

identical properties except for their masses.

• In each family, the quarks and leptons have equal and opposite contributions to

non-renormalizable divergencies associated with fermion triangle diagrams. The

contributions cancel each other because the charges of the fermions are related in

the form

Qe + Qu + 3 {Qu + Qd) = 0. (1-3)

However, this relationship between the quark and lepton charges is not a require

ment of the Standard Model.

• Gravity is absent from the theory.

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e -

d, u, ..

Figure 1.1 Diagram showing the interaction of a quark, a lepton, and a leptoquark.

1.2 Leptoquarks Beyond the Standard Model

In order to explain some of the enigmatic features of the Standard Model, many alterna

tive theories have been developed. A number of these theories predict, or allow for, the

existence of leptoquarks , spin-0 or spin-1 particles which carry both electric charge and

colour, and which couple to quark-lepton pairs, as shown in Figure 1.1. In this section,

three classes of models which include leptoquarks (grand unified theories, tcchnicolour

models, and composite models) are briefly described.

1.2.1 Grand Unification

Grand unification is a framework for the unification of the weak, electromagnetic, and

strong interactions. The idea is that the SU(3) 0 SU(2) 0 U (l) gauge group is embedded

in a single group G, whose symmetries become manifest at some very large energy scale.

At this unification scale, the three coupling constants associated with the elementary

forces becc ne equal. A t lower energies, the differences between the elementary forces

arise from the spontaneous symmetry breaking of the underlying group G.

Grand unified theories may restrict some free parameters of the Standard Model, such

as the weak m ix in g angle sin2 6w and the ratios of quark masses to lepton masses. Quarks

and leptons usually share multiplets of G, implying the quantization of the fermion

charges. It is also natural for these theories to contain gauge or Higgs bosons which

couple to both quarks and leptons, i.e., leptoquarks. These leptoquarks may violate

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. baryon number ( B ) and lepton number ( L) conservation and induce proton decay.

One attractive grand unification model is based on the gauge group SU(5) [8]. It

is the simplest grand unification model with a single coupling constant incorporating

SU(3) 0S U (2)0U (I). However, the value of sin2 0\y in this model is inconsistent with the

recent high-precision measurements at LEP [9]. The model also predicts a large proton

deca.y w id th , which is incom patible w ith the lim its on p —> e+7r° decay from IMB-3 [10].

A recent extension of this minimal SU(5) model [11] includes an additional pair of light,

D and L conserving leptoquarks and agrees with the measured value of sin2 0\y. It is also

marginally consistent with lim its on proton decay. The extra leptoquarks do not couple

to pairs of quarks, and hence do not induce proton decay. Their mass is expected to be

of the order of 100 GeV/c2.

Other grand unified theories are based on the gauge groups SU(4) [12], SU(15) [13],

and E g [14].

1.2.2 Technicolour

Technicolour models [15] do away with the Higgs sector of the Standard Model and

the associated fine-tuning problems and instead provide a dynamical explanation for

the breaking of the weak gauge symmetry. A new non-abelian gauge interaction called

technicolour is introduced, along with a new set of fermions called technifermions. A t the

electroweak scale, technicolour becomes strong and, in analogy to QCD, a technicolour

condensate forms, breaking the electroweak symmetry. This generates masses for the

W ± and Z° bosons without a fundamental Higgs boson.

In order that they be realistic, technicolour models must provide a mechanism to

generate masses for the quarks and leptons. This is achieved in extended technicolour

models. The idea is to introduce another interaction, extended technicolour, which is me

diated by heavy gauge bosons and dynamically broken (somehow) at very high energies.

The new gauge bosons convert ordinary fermions into technifermions, and vice-versa, and

they generate masses for the Standard M odel quarks and leptons.

In extended technicolour theories, leptoquarks appear as technimesons made up of a

techniquark and an anti-technilepton [16]. The leptoquarks couple to ordinary quarks

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u re 1.2 Diagram for the decay of a leptoquark ( LQ) into a positron and a it-quark, via

the exchange of an extended technicolour gauge boson (A ’e t c )- The leptoquark is originally made up o f a techniquark ( U) and an anti-technilepton ( E ).

and leptons when the leptoquark constituents exchange an extended technicolour gauge

boson and turn into a quark and a lepton, as shown in Figure 1.2.

One problem with extended technicolour theories is that they predict the existence

of some light technistates which should have been observed at LEP, and were not.

1.2.3 Compositeness

Composite models [17], in which the leptons and the quarks, and sometimes the gauge

bosons, are bound states of more fundamental particles called preons , were built in the

hope of explaining the vast fermion spectrum and reducing the number of elementary par

ticles. Leptoquarks appear naturally in such models: a composite quark and a composite

lepton can transform themselves into a lepton and a quark, respectively, by exchanging

the relevant preons, the bound state consisting of the exchanged preons being a lep

toquark. In some models [18], the leptoquarks may be considerably lighter than the

compositeness scale Ac ^ ITeV and may therefore be relevant at IIERA.

It is difficult to explain why the observed fermion masses are much smaller than the

compositeness scale. So far, no composite models account for the three generations of

quarks and leptons of the Standard Model [7].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9

1.3 A Model Independent Approach

Rather than considering each separate theory predicting the existence of leptoquarks, it is

more efficient to adopt a model independent approach. The effective Lagrangian with the

most general couplings of scalar and vector leptoquarks consistent with the symmetries

of the Standard Model has been presented in [19]. There are seven renormalizable,

SU(3) 0 SU(2) 0 U (l) invariant, B and L conserving Yukawa couplings to quark-lepton

pairs for both scalar and vector leptoquarks. They are listed in Table 1.1. Leptoquarks

may couple independently to fermions of any family. The leptoquark Yukawa couplings

are denoted A Lq, where H is the lepton helicity, LQ is the leptoquark multiplet, and i

and j are the lepton and quark generations.

This analysis focuses on leptoquark couplings to quarks and leptons of the first gen

eration. Throughout this thesis, when generation indices to leptoquark couplings are

suppressed, couplings to the first-generation fermions are implied (A h lq = A lq)- F ur

thermore, no attempts are made to differentiate between the different states of a given

leptoquark m ultiplet: isospin states are assumed to be degenerate in mass.

1.4 Experimental Limits on Leptoquarks

L im its on leptoquark masses {ttilq) and couplings (A'/j^g) have been obtained from

direct searches at e+e_ and pp collider experiments and have been calculated from rare

processes at low-energy. Those limits associated with B and L conserving couplings to

first-generation quarks and leptons are reviewed in this section.

1.4.1 Searches in Electron-Positron Collisions

Leptoquarks carry electric charge and could therefore be pair produced in e+e“ colli

sions. The lowest-order Feynman diagram for this process is shown in Figure 1.3. Scalar

leptoquarks decaying into leptons plus jets have been searched for at LEP [20], with null

results. The derived lim its depend on the leptoquark electric charge and isospin, as well

cis on the generation of the leptoquark decay products, but are near the kinematic lim it

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10

Leptoquark J t 3 Q Interaction Lagrangian

So 0 0 - 1 /3 M s . [(U iY E i - ( D i) eiV* ] + X ^ U it Y E },}5 ‘

So 0 0 - 4 /3 A V - ^ Y E t f l

S1/2 0 + 1 /2 - 2 /3 {A'/sl/3^ r A'/. - A/jSl/J

- 1 / 2 - 5 /3

Sl/2 0 +1/2 + 1/3 ^LSu^ N i S \ „

- 1 /2 - 2 /3 4 su D\.E)S\,,

Si 0 +1 + 2 /3 yfiX[sM TNisl 0 - 1 /3 -4s\{UirEi^{b[YN\\S\

- 1 - 4 /3 -sflXis^DiYEiSl

V0 1 0 - 2 /3 M vo [.Djnr E i + + A-{V,/X7'‘/•;;,}<

Vo 1 0 - 5 /3

VU2 1 + 1 /2 - 1 /3 { 4 v uM ) cr n + \ % U2{u i ) V W ' /2(I

- 1 / 2 - 4 /3 { a 2v1/3( W 7'‘ £ i + A ^ I/a( O ir 7 '‘ ^ } v.%.

Vi/2 1 + 1 /2 + 2 /3

- 1 / 2 - 1 /3 V tjftrrE ivU

Vi 1 +1 + 1/3 \/2A ‘//r, Z/jj 7'1 F/;1

0 - 2 /3 aM - ^ 7 ^ 1 +

- 1 - 5 / 3 >/2A/v, Uf{ y'1 Ey V l

Table 1.1 Scalar (S) and vector (F ) leptoquarks, their spin (./), their electric charge (Q), the third component of their weak isospin (T3), and their couplings to quark-lepton pairs. N' and E' are the charge 0 and charge —1 leptons of the z-th generation; Ui and Dj are the charge +2/3 and charge - 1 /3 quarks o f the j- th generation. The superscript c denotes charge conjugation.

The leptoquark Yukawa couplings are denoted A '/{L q , where H is the lepton helicity and LQ is the leptoquark multiplet.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11

LQ / /

\ LQ

Figure 1.3 Feynman diagram for the production of leptoquarks in e+e“ collisions,

of half the centre of mass energy:

rnLQ > 41 -46GeV/c2 (1.4)

at the 95% confidence level (C.L.). Similar limits are expected for vector leptoquarks [16].

In the LEP analyses, the leptoquarks were assumed to decay within a few centimetres

of the primary vertex. Since the decay width of a leptoquark is related to its Yukawa

coupling (cf. Equations 1.48 and 1.49, Section 1.6), the vertex assumption implies that

the mass lim its are applicable only if \ l ,r ~ 10“ '.

The DELPHI collaboration has also searched for the single production of leptoquarks

[21]. The Feynman diagram for this process is identical to that for pair production,

except that only one of the leptoquarks is produced on-shell. No leptoquark candidates

were found and lower mass lim its—from 55 to 80 GeV/c2— as a function of Yukawa

coupling—0.1 to 0.5— were obtained. For a Yukawa coupling equal in strength to that of

the clectrowcak coupling, i.e.,

A L,R = \/4TTCiEW (1-5)

~ 0.31, (1.6)

the mass lim it for scalar leptoquarks coupling to first-generation fermions is

m LQ > 65 GeV/c2 (1.7)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12

9 LQ , LQ / / /

\ <7 \ LQ

g JLQJL2JLQJI 9 ------LQ

9 JUULJLQJLfil______l q

Figure 1.4 Lowest-order Feynman diagrams contritmling to the processes

at the 95% confidence level.

1.4.2 Searches in Proton-Antiproton Collisions

Since leptoquarks are coloured objects, they can be pair produced in quark-anfiqnark

annihilation and in gluon-gluon fusion. The lowest-order Feynman diagrams contributing

to these processes [22] are shown in Figure 1.4. The cross-sections for these processes

do not depend on the leptoquark Yukawa coupling and can be calculated using standard

QCD methods.

The CDF and DO collaborations have searched for scalar leptoquarks pair produced in

pp collisions at the Fermilab Tevatron [23]. Because of the large background associated

with events in which both leptoquarks decay into a neutrino and a quark, one of the

leptoquarks was required to decay into an electron and a jet in the DO analysis while

both leptoquarks were required to decay into an electron and a jet in the CDF analysis.

No events were observed. The derived lim its depend on B , the leptoquark branching

fraction into electron plus jets. The 95% confidence level limits on scalar leptoquarks

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13

from CDF are

m LQ > 113GeV/c2 (5=1). (1.8)

m L Q > 80 GeV/c2 (5 = 0.5), (1.9)

and from DO are

m i# > 133 G eV /c2 ( 5 = 1), (1.10)

> 120 G eV /c2 ( 5 = 0.5). (1.11)

In both the CDF and DO analyses, the leptoquarks were assumed to decay within a few

millimetres of the primary vertex. Therefore, the mass lim its are applicable as long as

the leptoquark Yukawa coupling is greater than 10“ '.

The CDF limits on scalar leptoquarks have been translated into limits on vector

leptoquarks [24]. The cross-sections for vector leptoquarks are substantially larger than

the ones for scalar leptoquarks but depend on a model dependent parameter k . The

weakest lim its are obtained in the case k = 0:

m LQ > ISO GeV/c2 (5 = 1), (1.12)

m LQ > 120 G eV /c2 ( 5 = 0.5), (1.13)

at the 95% confidence level.

1.4.3 Leptonic Pion Decays

Charged pions decay weakly mostly into because the decay into euc is helicity sup

pressed. The ratio R = T(7r+ —»• e+i/c)/r(7r+ —> has recently been measured to

great accuracy at TM U M F [25] and PSI [26]:

R = (1.2265 ± 0.0034 ± 0.0044) • 10“4 (TRIUMF), (1.14)

R = (1.2346 ± 0.0035 ± 0.0036) • 10"4 (PSI), (1.15)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14

where the second errors are theoretical. Averaging the results of the two experiments

yields:

R exp = (1.231 ±0.004) • 10~‘. (1.16)

This quantity is in very good agreement with the latest Standard Model calculation [27]:

R» = i + (1.17)

= (1.2352 ± 0.0005) • 10-', (I.IS)

where A is a radiative correction.

Leptoquarks coupling to both left-handed and right-handed leptons would contribute

to the decay of charged pions. For example, the decay 7r+ —> c+ i/e can proceed via the

exchange of an So leptoquark, as shown in Figure 1.5. Note that this decay is not helicity

suppressed. So, £1/ 2 , K>, and V \/2 leptoquarks would contribute an amount A R to the

ra tio R [16]:

1M ~ _ 7At‘A«' m A x / 1 for 5° a,,d 5,/'2’ ( 1 1()) Rlh \j2G FmlQme ^G FmlQm^j \ 2 for l/0 and Vl/2 .

If one assumes that there are no cancellations between the leptoquark contributions to

7r+ —j- c+ue and 7r+ —>■ and requires |A/?| to be less than the sum of the errors on

R.exp and R th added in quadrature, the following 95% confidence level lim its result:

> 135TeV/c2 (S0 and Sl/2), (1.20)

> 190 T e V /c 2 (Vo and V ,,2). (1.21)

These are very strong limits. However, they are only applicable if the leptoquarks couple

to both left-handed and right-handed leptons. If = 0 or \ r = 0, the leptoquark cou

plings to quarks and leptons are said to be c h ira l and the lim its are no longer applicable.

Hereafter, only leptoquarks with chiral couplings are considered.

Leptoquarks coupling to left-handed electrons and neutrinos would also contribute to

the decay of charged pions. For example, a 7r+ could decay into a right-handed positron

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 1.5 Feynman diagram for the decay ir+ —- e+ uc via the exchange o f an S0 leptoquark. This decay is not helicity suppressed.

and a left-handed neutrino via the exchange of an S0, an Si, a Vo, or a Vi leptoquark.

Note that this decay is suppressed by helicity conservation. So, Si, V0, and Vi leptoquarks

would contribute an amount A R! to R [16, 28]:

\AR'\ _ V2Xj f 1 ^ So and S i, R th 4.GFm2LQ \ 2 for Vo and Vi,

where is the leptoquark Yukawa coupling to first-generation quarks and leptons. If

|A/2'| is required to be less than the sum of the errors on R exp and R th, the following

limits result:

m LQ/Ai, >2.2TeV/c2 (S0 and SO, (1.23)

m LQ/ \ L > 3.1 T e V /c 2 (Vo and V i). (1.24)

1.4.4 Unitarity of the CKM Matrix

The weak coupling constant measured in nuclear beta decay ( Gp )is slig h tly sm aller than

the one measured in muon decay (G f ) because the charged current couples Cabibbo-

Kobayashi-Maskawa (CKM) rotated quarks. The magnitude of the CKM m atrix element

Vuu is in fact obtained by comparing Gp and G f [29]:

\Vud\ = G 0 /G f , (1.25)

= 0.9744 ± 0.0010. (1.26)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16

So and Si leptoquarks would contribute an amount A Gp to Gp [16]:

|AC„| = ^1. (1.27) o m LQ

Vo and V] leptoquarks would contribute twice that amount. The contribution of these

leptoquarks, via box diagrams, to G f would be much smaller and can be neglected.

Assuming unitarity of the CKM matrix, Vud is related to and V„i, as follows:

\vud\2 = l-\vu3\2-\vub\2. ( 1.28 )

Equation 1.28, along with the experimentally measured quantities [29]

IK*! = 0.2205 ±0.0018, (1.29)

|Kfc| = 0.0032 ± 0.0009, (1.30)

constrain Vud to bewithin 0.2% of its measured value at the 95% confidence level. If the

absolute value of each leptoquark contribution to Gp is required to be less than 0.2%,

the following lim its result:

m LQ/X L > 2.8TeV/c2 (S0 and S i), (1.31)

m LQ/ \ L > 3.9TeV/c2 (VQ and Vt ). (1.32)

In the absence of unitarity, these lim its would no longer be applicable.

1.4.5 Atomic Parity Violation

Experiments have demonstrated cases of parity violation in atoms during the absorption

of light [30]. These results are consistent with the exchange of Z ° bosons between the

electrons and the nucleus of the atoms. The measured parity-violating amplitude is

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17

proportional to the weak charge of the atom

Qw = —2[Ciu(2Z + N) + CU{Z + 2iV)], (1.33)

where C Ui = -/3+2Q em sin2 Ow at first-order, and Z and N are the number of protons and

neutrons in the nucleus. For Cesium atoms (Z = 55, N — 77.9), the latest measurements

yield [29]

Q l? = -7 1 .0 4 ± 1.81, (1.34)

consistent with the Standard Model calculation [29]

Q% = -72.92 ±0.10. (1.35)

In the presence of leptoquarks, there would be the following additional contributions

to G'iu *-.nd C u [16, 28]:

' +1 for RS0 and LS1/ 2,

— 1 for LSq, R S l/2^ and LS\ , v/2A? n + 2 for RV\/2, (1.36) AC,U " 8G Fm lQ X —2 for RV0 and LV\/2 ,

. + 4 for LVi,

and +1 for

2l r - 1 for A C U = x (1.37) 8 G Fm lQ + 2 for

_ 22 for LS1, RV q, and LVi / 2.

In the above two equations, the leptoquark states are preceded by the helicity of their

Yukawa couplings (L or R). If the absolute value of each leptoquark contribution to Q w

is required to be less than the sum of the errors on Q w P and Q w , limits on the ratio

ik l q / ^ h l q , ranging from 1.3 to 3.2TeV/c2, are obtained. The specific lim its are listed

in Table 1.2. Note that in the presence of two or more leptoquark multiplets, individual

contributions to C \u and C u could cancel each other, and these lim its would no longer

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IS

Lower limit on m Lq lX u Lq (TeV /e2) Leptoquark Coupling Helicity 7T decays CKM m atrix P violation

So L •2.2 2.8 1.3 R — — 1.3 So R — — 1.3 Sl/2 L —— 1.3 R —— 1.8 Sl/2 L —— 1.3 Si L •2.2 •2.8 •2.3 Vo L 3.1 3.9 1.9 R —— 1.9 Vo R — — 1.8 Vi/a L — — 1.9 R — — 2.6

V1/3 L — — 1.8 V! L 3.1 3.9 3.2

T a b le 1.2 95% confidence level lower lim its on the ratio m ^q /Xji cq, in TeV/c2. for leptoquarks with chiral couplings to the first-generation fermions, from lcptonic 7r decays, unitarity of the CKM matrix, and parity violation in Cesium.

be applicable.

The limits on the ratio lq calculated from low-encrgy measurements, for

leptoquarks with chiral couplings to the first-generation fermions, are summarized in

Table 1.2. These lim its would be weakened if one considered the possible cancellations

between different leptoquark contributions to a particular process.

1.5 Kinematics of Electron-Proton Scattering

Before discussing the production and decay of leptoquarks at HERA, the kinematics of

electron-proton scattering must first be introduced. The lowest-order Feynman diagram

fo r e~p deep inelastic scattering (DIS) is shown in Figure 1.6. The electron and the quark

(a u or d valence quark, or a sea quark or antiquark of any flavour) exchange a photon,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19

P Pp

Figure 1.6 Feynman diagram for electron-proton deep inelastic scattering. The incoming electron (with four-momentum pe) and the quark (with four-momentum xpp) exchange a photon, a Z ° ,o r a W ± boson. The four-momentum transfer at the hard scattering vertex is denoted q.

a Z °, or a W ± boson. The outgoing lepton is an electron in the case of neutral currents

(photon or Z ° exchange) and a neutrino in the case of charged currents { W ^ exchange).

The four-momentum transfer squared at the electron-lepton-boson vertex is

q2 = {pe-pi)2, (1-38)

where pe and pi are the four-momenta1 of the incoming electron and outgoing lepton,

respectively. The total ep centre of mass energy squared is

s = (Pc + Pp)2, (1-39)

where pp is the proton four-momentum. If the incoming electron and proton energies, E e

and E p, are much larger than the electron and proton masses, one can write

s = 4 E eE p, (1-40)

Momentum four-vectors are defined as p — (E,p), where E is the energy and p is the momentum vector (and the speed of light is c = 1). The product p2 = E2 — |p|2 is spacelike (e.g., a scattering process) if p2 < 0 and it is timelike (e.g., the mass squared of a free particle) if p2 > 0.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20

A t H E R A in 1992, E e = 26.7 G eV, E p = S20 GeV, and thus = 296 GeV.

It is convenient to use the positive variable

Q2 = -<72. (l.-H)

as well as the dimensionlesr variables

Q 7 x = ( 1, 12) 2 PP • q' Pp-q Pp'Pe

The variable y is called the inelasticity parameter and is proportional to the energy loss

of the incoming electron in the proton rest frame. The variable x, in the context of the

P arton Model [31] where the proton is considered to be made ofpartons (i.e., quarks

and gluons), is the fraction of the proton momentum carried by the struck quark. The

variables x, y , and Q 2 are related in the form

*»*-«•( i+ = i± = £ ).

1.6 Leptoquark Production and Decay at HERA

HERA provides a unique environment for the direct production of leptoquarks. In

collisions, leptoquarks could be singly produced as an s-channel resonance, as shown

in Figure 1.7. This process, the fusion of an electron and a quark or antiquark, would

dominate for leptoquark masses up to m^Q ~ y/s. For higher masses, one could search

for effects arising from the virtual exchange of leptoquarks.

The leptoquark production cross-sections have been calculated in [19] for each lepto

quark multiplet. The s-channel differential cross-section averaged over the quark spin,

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u (d)

u (d )

Figure 1.7 Feynman diagrams for the direct (s-channel) and virtual (u-channel) production o f S0 leptoquarks in e~p collisions.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Leptoquark s-Channel Coupling Leptoquark s-Channel Coupling s 0 e luL el uL Ac Vo c[. dR — c; dR A/.

eRuR eRuR A R cr<1l c7;(h. A R e~LuL — vedL —A L (' l (ht — veiiR A/. So ertdR e~kdR A R Vo c Ttu /. — CjtUl. An Sl/2 —* eRdR — A R V./2 cRllL ' An

e lu L — e lu L A L ec dR — ejdn A/, eRUR —*• eRuR A R Cndi. —* ( i{d[. An

Sl/2 eldL e~LdL A L F i/2 e L “ n —* < 7. ILn Ac

S, elttL — e lu L —A L Vt €i.dn —• f'7 dn —A/.

e~LuL ■— v>'dL —A C c-7.dii — "<• un A i. e~LdL — eldL — y/2XL r-7 hn — c7 11 it \/2 A/.

Table 1.3 .s-channel production and decay o f leptoquarks in c~p collisions, with corresponding Yukawa couplings.

for leptoquarks with chiral couplings, is

, (*.

for scalar leptoquarks and

do- _ 1 v- , n2v ______Q 2 ~ xs t , 17 \ d x d Q 2 Sir “ ’ (x s - m„ ,2 \Q)2 \2 + l rn2LQY2LQ p2 „ x 2 2s2 ,.2 ( ' )

for vector leptoquarks, where q(x,Q2) is the parton distribution function and the sum

is over all possible incoming quark or antiquark flavours. The relevant production and

decay channels are listed in Table 1.3.

The leptoquark partial decay widths F l q can be calculated from the effective La-

grangian (cf. Table 1.1):

T l q = (scalars), (1.48) 107T

Tlq = — ' f p — (vectors), (1.49) Z47T

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23

where A/,,/* denotes the leptoquark coupling to a particular final state, as given in Ta

ble 1.3. For example, a scalar leptoquark with a mass of 100 GeV/c2 and a Yukawa

coupling of 0.31 would have a partial decay width of 200 MeV. The total decay width is

obtained by summing over all possible final states.

At HERA, leptoquarks would appear as narrow Breit-Wigner resonances in the in

variant mass distribution of the decay products. Since the incoming quark momentum

is equal to xp p (in the Parton Model), leptoquarks would appear as narrow resonances

in the x distribution, peaked at

(1.50) = iPc + *Pp)2 -

th a t is at

* - ™2lq / s - (1.51)

In the lim it of very narrow leptoquark widths (T l q / ttilq —> 0), the cross-section for

a specific final state can be approximated by [19]

for scalars, (1.52) for vectors,

where q{x,Q2) is evaluated at x = ra^/s and Q 2 = m \ Q, and B lq is the branching

ratio into the final state. The leptoquark cross-sections in this approximation are listed

in Table 1.4. The cross-sections over Yukawa coupling squared as a function of leptoquark

mass are shown in Figure 1.8. Scalar leptoquarks have a smaller cross-section than vector

leptoquarks, and leptoquarks coupling to antiquarks (£ti/ 2 i •S'i/2, K>> Km and Vi) have a

smaller cross-section than leptoquarks coupling to quarks, as expected. As an example,

consider a 100 G e V /c 2 So leptoquark with — 0.31 and = 0. After collecting data

corresponding to an integrated luminosity of 27.5 nb-1, one would expect about fifty

leptoquark events.

The final state of a leptoquark event consists of a lepton (an electron or a neutrino)

balanced by a jet in transverse momentum, along with the so-called spectator jet from

the proton remnant. The signatures of leptoquark decays are therefore identical to that

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. s-Channel Cross-Section

Leptoquark Decay to e X Decay to vX

So ^(X2BSou + X2ru) 37AL(1 ~ b s0)u So —

S\/2 ^•[A | u 4- X%(u + d)] —

Sl/2 t M d —

Si f;\2L(Bs:U + 2d) ^ 1 ( 1 - D Sl)u

Vo ^{XlByJ+Xld) f-Xl(l ~ B Vn)d

Vo —

Vl/2 ^■[A id + X 2n(d + u)] — — 10

Vi % \i(B Vtd + 2u) £A£(1 - B Vt)d

Table 1.4 5-channel leptoquark cross-sections at HERA, in the narrow width approximation. B lq denotes here the branching fraction ofleptoquark LQ into e^A'; u, d, u, and d denote the parton distribution functions u(x,Q2), d(x,Q2), u(x,Q2), and d(x,Q-’) evaluated at x =

and Q2 = i t i 2Lq.

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10 -oc Scalar. LQ —> e'X Vector. LQ —» e~X

■RS, 10 10

■IS, I RS. LV, I I 10 10

10 10 LV,

■3 ■3 10 10 100 200 100 200 Leptoquark mass (GeV/c ) Leptoquark mass (GeV/c )

10 ■Q 10 t Scalar LQ —> vX Vector L Q —> vX 'k 10* 102

10 10

1 1

I I 10 10

.2 10 10

3 ■3 10 10 100 200 100 200 Leptoquark mass (GeV/c") Leptoquark mass (GeV/c )

F ig u re 1.8 Cross-section over Yukawa coupling squared as a function o f leptoquark mass for leptoquarks with chiral couplings produced at HERA. The cross-sections are calculated using the narrow width approximation and the MT B1 parton distribution functions [32]. The branching fractions of the So, Si, V0, and Vi leptoquarks (coupling to left-handed electrons) into e~A' are set to 0.5.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26

of neutral and charged current deep inelastic scattering events. Generally, the leptoquark

amplitudes for e~p —> e ~ X and e~p —> v X interfere with the Standard Model amplitudes

for photon, Z °, and \\r± exchange. Both classes of events can only be separated using

statistical methods.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 2 Experimental Setup

2.1 The HERA Electron-Proton Collider

HERA1 [33] is the world’s first electron-proton collider which has been constructed at the

DESY2 laboratory in Hamburg, Germany. It consists of tw’o independent accelerators,

6.3 km in circumference, designed to store 30 GeV electrons and 820 GeV protons, respec

tively. The two accelerators are located in a common tunnel 10 to 25 m below ground

level. The counter-rotating beams arc brought into head-on collision at two points along

the ring, Hall South and Hall North, thereby providing electron-proton interactions to tw’o

experiments, ZEUS and III (see Figure 2.1). The electron-proton centre of mass energy

at HERA (296GeV during 1992) is one order of magnitude larger than that previously

available at fixed target experiments.

A layout of the HERA pre-accelerators is shown in Figure 2.2. Protons are initially

accelerated as negatively-charged hydrogen ions in the 50MeV H“ LINAC [34]. The

ions are stripped of their electrons in a thin foil, and the resulting protons are injected

into the DESY' III synchrotron, wfhere they are accelerated to 7.5 GeV. The protons are

then transferred to PETRA II, where they are accelerated to 40 GeV. Finally, they are

transferred to HERA and accelerated to 820 GeV.

1 Hadron-Elektron Ring Anlage. 2Deutsches Elektronen-Synchrotron.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2S

H all N orth

H all East

HERA

H all 4 0 GeV W est { protons

PETRA

14 GeV H all electrons S o u th

Figure 2.1 The HERA accelerator.

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UHERA AM n P-820 GeV 30G«Vm«'^aGeV

,PETRA PETRA Hj IINE Hall NW

CrYO-. 1 Technic LlnacJl Hal

PETRA Hall W ,r.a* PlA^W 1

PETRA

Hill SW HERA

Proton bypass

Figure 2.2 The HERA injection system.

Electrons are liberated from a high voltage cathode and first accelerated to 500 MeV

with the LIN AC II linear accelerator. They are then accumulated into a single bunch

in the PIA storage ring and transferred to the DESY II synchrotron. There they are

accelerated to T GeV and then transferred to the PETRA II storage ring. This whole

procedure is repeated until PETRA II ha.s been filled. Once PETRA II is full, the

electrons are accelerated to 14 GeV, transferred to HERA, and finally accelerated to

26.7 GeV.

The particles in the beams are grouped in bunches. HERA is designed to store and

collide 210 bunches of protons and 210 bunches of electrons. Consecutive bunches are

separated by 28.8 m (96 ns in time, since the particles essentially travel at the speed of

light). The HERA proton energy is lim ited by the magnetic field of the superconducting

dipole magnets needed to keep the protons in orbit, while the electron energy is lim ited by

the radio frequency power necessary to replace the energy lost by synchrotron radiation.

Luminosity, £, is an important parameter of colliding beam facilities because it relates

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30

the cross-section of a particular process, a, with the rate of observed events, R:

R = C • a. (2.1)

In terms of the beam parameters, luminosity is defined as

c - , W (2 .2) Zxy/vL+vlpy/rfc + tfr

where / is the revolution frequency (47.3kHz at HERA), k is the num ber o f co llid in g

bunches, N e and N p are the number of electrons and protons per bunch, and

axpi and ayp are the horizontal and vertical RMS dimensions of the electron and proton

beams. Design and 1992 values of HERA beam parameters are listed in Table 2.1.

Nineteen ninety-two was the first year HERA delivered luminosity to ZEUS and HI.

During that year, the accelerator was operated with nine colliding bunches, one addi

tional unpaired electron bunch and one additional unpaired proton bunch. The unpaired

bunches, called pilot bunches, were used for estimating beam-related backgrounds. The

highest luminosity recorded by the ZEUS experiment in 1992 was 1.5 x 1029 cm-2s-1

(1033cm-2 = ln b -1) while the typical luminosity was 0.5 x 1029 ernes'1. These num

bers are two orders of magnitude smaller than the design luminosity of 1.(5 x 1031 cm ' V .

The integrated luminosity recorded by ZEUS in 1992 was over 30 nb-1; the inte

grated luminosity used in the present analysis totals 27.5 nb-1. A plot of the integrated

luminosity as a function of time :s shown in Figure 2.3.

2.2 The ZEUS Detector

2.2.1 Overview

The ZEUS detector is a multi-component detector designed to measure a large number

of physics processes at HERA [36]. Like many recent high-energy detectors, it consists

o f

• tracking chambers, for measuring the trajectories and momenta of charged particles,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31

Proton Beam Electron Beam Parameter 1992 Design 1992 Design Energy (GeV) 820 820 26.7 30 Circulating current (mA) 1.2 160 2.0 60 Particles per bunch (10IQ) 1.6 10 2.6 3.8 Number of bunches 10° 210 10° 210 Horizontal size (mm) 0.32 0.29 0.30 0.26 Vertical size (mm) 0.10 0.07 0.07 0.07 Longitudinal size (cm) 25 11 0.8 0.8 Filling time (hr) 5 0.3 1 0.25 Lifetime (hr) 40 30 > 4 > 4 “Nine of the ten bunches collided with bunches from the other beam.

T a ble 2.1 Typical 1992 values and design values of various HERA beam parameters. The beam sizes are RMS values at the electron-proton interaction point are are taken from [35].

•SSt 25 8

20 tu 5 ec 15 50

0 30 35 40 45 Week

Figure 2.3 Integrated luminosity collected in 1992 as a function of time. Only the luminosity from the runs used in the present analysis are included.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Overview of the ZEUS D e te c t o r ( longitudinal cut )

uuurg g o J w jB»oumoo» pr^-0** °7m tiU U O CRYO- BOX IK

FCALiFDET CTD

W A L l M

-H I- 10 m 0 -5 m

Figure 2.4 Section of the ZEUS detector along the beam. The 2-axis points in the direction of the incoming proton beam, the y -axis points upwards, and the x-axis points towards the centre of the HERA ring (i.e., out of the page).

• calorimeters, for measuring energy deposits, and

• muon chambers, for detecting muons and measuring their momenta.

The asymmetry between the electron and proton beam energies at IIERA lead to the

design of an asymmetric detector, as seen in Figure 2.4. The coordinate system used

throughout this analysis is as follows: the z-axis points in the direction of the incoming

proton beam, the t/-axis points upwards, and the x-axis points towards the centre of the

HERA ring. The nominal crossing of the beams is at z = 0.

The main tracking detectors are the Vertex Detector (VXD), a small cylindrical drift

chamber immediately surrounding the beam pipe, and the Central Tracking Detector

(CTD), a large jet-type drift chamber. Additional tracking in the rear and forward

regions is provided by the Rear and Forward Tracking Detectors (RTD and FTD), con

sisting of one and three planar drift chambers, respectively. A superconducting solenoid

magnet outside the CTD provides a magnetic field of up to 1.8 T. A smaller solenoid

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33

magnet is located in the rear region to provide a 5T magnetic field which compensates

the influence of the detector solenoid on the beams. The Transition Radiation Detector

(TRD), which consists of two radiator modules and two drift chamber modules, is in

terleaved between the FTD chambers and helps to discriminate between electrons and

hadrons in the forward region.

The main calorimeter for ZEUS is a uranium-scintillator calorimeter (CAL), which

surrounds the central solenoid magnet and tracking detectors. It is finely segmented,

has very good electromagnetic and hadronic energy resolution, and provides nearly full

angular coverage. The Hadron Electron Separator (HES) consists of narrow layers of

silicon diodes inserted in gaps within the calorimeter at depths of three radiation lengths

in the rear region. The HES helps to discriminate between electromagnetic and hadronic

energy deposits. An iron yoke surrounding the calorimeter returns the flux of the central

solenoid and also serves as the absorber material for the Backing Calorimeter (BAG).

The BAG uses aluminum proportional tubes inserted into the yoke as the active material

and provides a measurement of energy leakage through the CAL.

Muons are detected in the central and rear regions with the Barrel and Rear Muon

chambers located on both the inner and outer sides of the yoke (BM UI, BMUO, RMUI,

and RMUO). The chambers consist of two double layers of limited streamer tubes

(LST’s). Coils surrounding the yoke provide a toroidal field of 1.6 T, allowing for momen

tum measurement, in the forward region is a Forward Muon Spectrometer (FMUON),

comprising two magnetized iron toroids interleaved with drift chambers and LST’s; there

are also drift chambers and LST’s inside the iron yoke (FM UI).

The C5 detector (C5)—four scintillator counters surrounding the beam pipe—and

the Veto Wall— a large iron wall with scintillator hodoscopes on both sides—are located

in the rear region to provide rejection of beam-related background events. The Veto Wall

also provides shielding against particles from the beam halo.

The luminosity at ZEUS is measured by detecting bremsstrahlung events in two

small electromagnetic calorimeters located at 2 = —35 m and 2 = —108 m (L U M I).

The calorimeter at 2 = —35 m is also used to detect electrons from photoproduction

events.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The Leading Proton Spectrometer uses the proton beam line magnets and six small

silicon strip detectors installed very close to the beam at c values of 24, 41, 44. 63, 81,

and 90 m. Its purpose is the detection of protons scattered at very forward angles.

Many ZEUS components were not fully installed or instrumented during the 1992

running period. The present analysis uses the information from the CAL, CTD, 05, and

LUM I, which are described in more detail below.

2.2.2 Calorimeter

Physical Structure

The calorimeter is constructed from stainless steel clad depleted uranium plates inter

leaved with SCSN-38 scintillator tiles [37, 38]. The thickness of the uranium plates and

scintillator tiles, 3.3 mm and 2.6 mm, were chosen such that each layer is one radiation

length (Xo) thick and the response of the calorimeter to the electromagnetic component

of a shower (e) is the same as the response to the hadronic component ( h). i.e., c/li = 1.

The calorimeter is divided into three main mechanical parts: the forward calorimeter

(FCAL) in the polar angle region 2.2° < 0 < 39.9°, the barrel calorimeter (BCAL) in

the region 36.7° < 0 < 129.1°, and the rear calorimeter (RCAL) in the region 128.1° <

6 < 176.5°. The coverage is 99.8% in the forward hemisphere and 99.5% in the rear

hemisphere.

The FCAL and RCAL are each composed of twenty-three modules which are further

divided in to 20 x 20 cm 2 towers. Each tower is segmented lo ngitudinally in to an ele ctro

magnetic cell (EMC) with a depth of about 2oX 0 (one absorption length A), and two

(one in the RCAL) hadronic cells (IIA C l, HAC2) of depth 3A each. The EMC cells are

further segmented transversely to 5 x 20 cm2 in the FCAL and 10 x 20 cm2 in the RCAL.

A list of the different calorimeter cell dimensions is given in Table 2.2.

The BCAL consists of thirty-two trapezoidal modules, each spanning 11.25° in az

imuth. The modules are divided longitudinally into an EMC, a HACl, and a IIAC2

section. The EMC cells are projective in polar angle (0) and azimuthal angle (<£), with

front face dimensions 5 x 23 cm2 and thickness corresponding to 21X 0. The HACl and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35

Calorimeter Cell Transverse Dimensions Depth (cm2) (cm) (A) FCAL EMC 5 x 20 24 1.0 H A C l 20 x 20 64 3.1 HAC2 20 x 20 64 3 .1 BCAL EMC 5 x 23" 21 0.9 H A C l 24 x 27" 42 2.0 HAC2 24 x 35“ 42 2.0 RCAL EMC 10 x 20 23 1.0 HACl 20 x 20 64 3.1 "Dimension of first layer.

Table 2.2 Transverse dimension and depth at normal incidence of the different ZEUS calorime ter cells.

IIAC2 cells are only projective in and are 2A thick each. The transverse dimensions of

the first 11 AC 1 layer are 24 x 27 cm2.

There arc a total of 5918 EMC and MAC cells, and each is read out on both sides by

wavelength shifter bars, light guides, and photomultiplier tubes (PM T’s). The optical

readout system of one FCAL tower is shown in Figure 2.5.

Readout Electronics

The signal from each PMT is sent to electronic cards, called Analog Cards, mounted

on the detector [39], The signal is split into low gain and high gain. The low gain and

high gain signals are then shaped and sampled, and the results are stored in an analog

pipeline fifty-eight cycles long, the duration of one cycle being 96 ns. After a positive

First Level Trigger decision (see Section 2.3.2), the pipeline data are sent to digitizing

electronics (Digital Cards) sitting in VM E crates in the electronics area of the experiment.

The digitizing cards have built-in analog to digital converters (AD C ’s) and digital signal

processors (DSP’s). The output of the DSP’s is PMT energy and time with respect to

the HERA clock.

A two-transputer module (2TP) sits in the VME crate: one transputer performs

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36

Depleted Uranium Scintillator Material

Rotlector Stainless Steel

Wavelength Shlltor

Rolloctor

HES Photomultiplier Tube Slots ^ HAC1 EMC Section Section

Light W a v e le n g th Guide Shiltor

Figure 2.5 Schematic view of an FCAL tower.

calorimeter Second Level Trigger tasks, the other performs readout tasks. After a positive

Second Level Trigger (see Section 2.3.3), the output of the DSP is read out and sent, to

the Event Builder.

Calibration and Resolution

The natural radioactivity of the t/238 provides a very stable calibration signal. During

special calibration runs, the PMT signals are integrated for 20 ms and the results are

compared to nominal values obtained in beam tests and cosmic tests [38, 40, 41]. This

procedure is repeated at eight hour intervals. The PMT energy measurement can be

calibrated to better than 1% in this fashion. The electronics are calibrated with a charge

injection system built into the Analog Cards.

The calorimeter energy resolution has been measured in beam tests [38, 40]. The elec

tromagnetic energy resolution is 18 % /\/~E for FCAL and RCAL modules, and W)%f\/~E

(20% / \ f E with the coil) for BCAL modules, where E is expressed in GeV. The hadronic

energy resolution is 35 % / \ f E for RCAL, FCAL, and BCAL modules ('1 8 % /y/E for B C A L

modules with the coil). The linearity of the response to electrons is within 1% for ener

gies between 15 GeV and 110 GeV in the FCAL and RCAL, and within 1% for energies

between 6 GeV and 90 GeV in the BCAL. The linearity for hadrons is within 1% for

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37

energies between '20 GeV and 110 GeV in the BCAL. The absolute energy scale was also

measured in beam tests, where precise knowledge of the beam momentum was available.

A laser and LED light injection system is used to calibrate the PMT time measure

ment. The PMT time resolution is about 1 ns for PMT energies above 1 GeV [42].

2.2.3 Central Tracking Detector

The Central Tracking Detector (CTD) is a cylindrical drift chamber surrounding the

Vertex Detector. It is active in the radial region 18 cm < r < 79 cm and over a length

o f 205 cm. Charged track position and dE/dx energy losses are measured in nine super

layers, each consisting of eight layers of sense wires. The wire layout in a 45° sector is

shown in Figure 2.6. Five of the superlayers, labelled 1, 3, 5, 7, and 9 in Figure 2.6,

have wires parallel to the beam line. The other four superlayers have wires at a stereo

angle of approximately ±5°. The total number of sense wires is 4608. The chamber

is read out with a system of flash analog to digital converters (FADC’s). The wires in

superlayer one and half of the wires in superlayers three and five are also instrumented

with z-by-timing readout. The Lorentz angle is expected to be 45° in a magnetic field of

1.8 T. Since the planes of wires are oriented at 45° to a radial line from the beam axis,

ionization electrons should drift tangentially to the chamber azimuth. This allows the

left-right hit ambiguities to be easily resolved.

During 1992, only z-by-timing information was available, providing coarse track posi

tion measurement in three superlayers. The ionizing gas was a mixture of argon, carbon

dioxide, ethane, and ethanol in the proportions S8%, 9%, 2%, and 1%; the d rift field was

1.2kV/cm; and the magnetic field was 1.43 T [43]. Under these conditions, the Lorentz

angle was 39° and the drift velocity was 49 /zm/ns. The hit resolution was 4 cm in z and

0.1 cm in r.

2.2.4 C5 Detector

The C5 detector, located near the beam pipe at z = —314 cm, consists of two pairs of

scintillator counters, one above and one below the beam pipe, separated by 5 mm of lead.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38

3. SUPERLAYER

Figure 2.6 Wire layout in a 45° sector of the Central Tracking Detector. The sense wires are indicated by solid dots.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 9

The counters measure the arrival times and rates of particles in the electron and proton

beam halos, as well as particles created in the interaction of the beam or beam halos with

gas molecules in the beam pipe, with the beam pipe itself, or with the C5 collimator [44].

The C5 time information is used at the trigger and offline levels to identify and reject

background events. C5 information is also used online to monitor the background rates

and the quality of the beams.

2.2.5 Luminosity Monitor

The purpose of the Luminosity Monitor (LUMI) is to measure the luminosity delivered

by HERA during data taking. In order to do so, the LUM I monitors the rate of the

bremsstrahlung process ep —► ep 7 , which has a distinct experimental signature and a

large cross-section given by the Bethe-Heitler formula [45]

da _ 2 E' (E E' 2 \ /. iE p E E y l \ dk Qr' k E \ E ' E 3 ) V n m pm ek 2 ) ’ )

where k is the photon energy, E and E' are the initial and final electron energies, E p is

the proton energy, m p and m e are the proton and electron masses, a is the fine structure

constant, and r e is the classical radius of the electron. There is a large background to the

bremsstrahlung process from electrons interacting with gas molecules in the beam pipe,

but it can be determined and subtracted using the electron pilot bunch.

The layout of the LUMI is shown in Figure 2.7. A calorimeter located at z = —35 m

detects the final state electron and a calorimeter located at 2 = —108 m detects the final

state photon. Both calorimeters are made of 5.7 cm thick lead plates interleaved with

2.8 mm thick SCSN-3S scintillator tiles. The photon calorimeter has a depth of 22X 0

and a transverse size of 18 x 18 cm2; the electron calorimeter has a depth of 24X0 and a

transverse size of 25 x 25 cm2. Both detectors have an electromagnetic energy resolution

o f 1 8 % /V E , where E is expressed in GeV. For Bethe-Heitler events, the final electron

and photon energies should add up to the initial electron energy.

The LUM I is also useful in detecting electrons from photoproduction events and initial

state radiative photons from neutral and charged current deep inelastic scattering events.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. •10

LUMIG

-0.4

LUMIE

i i i i i i i. i i i i i 0 50 100 -z (m)

Figure 2.7 Luminosity Monitor. The electron and photon calorimeters are labelled LUMIF and LU M IG .

2.3 The ZEUS Trigger and Data Acquisition System

2.3.1 Concepts

In order to cope with the large HERA bunch crossing rate (10 MHz), the large back

grounds from beam-gas interactions (10 to 50 kHz at design luminosity), and large event

sizes (up to 200kBytes per event), ZEUS has adopted a multi-level trigger system. A

First Level Trigger (FLT) has the task of reducing the data rate to 1 kHz, a Second Level

Trigger (SLT) must reduce that rate to 100 Hz, and in turn, a Third Level Trigger (TLT)

must reduce that rate to a manageable rate of 5 Hz.

A layout of the ZEUS trigger and data acquisition system is shown is Figure 2.8.

Each component has its own pipelined readout and local FLT system. The length of the

pipeline is fifty-eight clock cycles of 96 ns. The local FLT systems must evaluate the data

and send their results to the Global First Level Trigger (GFLT) within twenty-six clock

cycles. The GFLT must make a trigger decision within another twenty clock cycles. After

a positive GFLT decision, the pipelines are read out and any remaining analog signal is

digitized. The data are then written to dual port memories, which serve as SLT pipelines.

The Local SLT processors have access to more complete data and can use more

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41

Front/End Front/End

CAL CTD

10 GBytes/s

Local Local FLT m u FLT

GFLT

100 MBytes/s

Equipment Local Local Computer SLT SLT WLU Digitizer Buffer GSLT Equipment Computer

10 MBytes/s

Equipment EVB Computer CTD data CAL data

Equipment Computer TLT

Branchbus Switch

VAX IBM Link

1 M Byte/s

Storage on IBM

Figure 2.8 The ZEUS trigger and data acquisition system.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. elaborate algorithms than the Local FLT processors. The Local SLT results arc sent to

the Global Second Level Trigger (GSLT), which then makes a trigger decision. After a

positive trigger decision, the data from the different components are assembled by the

Event Builder in one of six memory buffers [46]. The EVB writes the data in ADAMO

structure [47]. A 64 x 64 crossbar switch provides the connection from the components

to the TLT.

The TLT is a farm of thirty analysis processors, arranged into six brandies. Eadi

processor has access to a complete event and has enough time to perform sophisticated

algorithms, such as track reconstruction. Triggered events are written to a disk on the

DESY IBM 3090 via the process called IBM Link. The events are then archived to

cartridges. At the moment, the trigger output rate is limited by the speed at which

events can be written to that disk. Some of the events are also sent to a VAX mainframe

for monitoring and online event display purposes.

Because of the importance of the trigger system in understanding efficiencies, the

First, Second, and Third Level Triggers are described in further detail in Sections ‘2.3/'

to 2.3.4. The trigger algorithms especially are discussed.

2.3.2 First Level Trigger

During the 1992 running period, the GFLT trigger was based on calorimeter activity, as

reported by the CAL FLT, along with a non-veto by the Co detector. A C5 veto is issued

if the signals from the PMT’s reading out the two C5 scintillator counters, either above

or below the beam pipe, are in coincidence.

W ithin the CAL FLT, EMC and HAC calorimeter cells are grouped into trigger

towers about 20 x 40cm2 in size [48]. In 1992, the calorimeter was divided into the

following calorimeter regions [49]: Beam Pipe, comprising the first ring of cells around

the FCAL beam pipe; FCAL Inner, comprising the next three rings of cells; FCAL Outer,

comprising the remaining FCAL cells; RCAL Beam Pipe, comprising the first ring of cells

around the RCAL beam pipe; RCAL Non Beam Pipe, comprising the remaining RCAL

cells; and BCAL, comprising all BCAL cells. A positive CAL FLT trigger was issued

whenever a trigger tower in a specific calorimeter region was above the threshold for that

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43

Threshold (GeV) Trigger Type Region DAY1 LOW-REMC LOW-BEMC EMC FCAL Beam Pipe 50 50 50 FCAL Inner 20 20 20 FCAL Outer 10 10 10 RCAL Beam Pipe 10 10 10 RCAL Non Beam Pipe 2.5 1 1 BCAL 2.5 2.5 1 IIAC FCAL Beam Pipe 70 70 70 FCAL Inner 25 25 25 FCAL Outer 10 10 10

Table 2.3 JAL FLT trigger tower thresholds for the DAY1, LOW-REMC, and LOW-BEMC configurations.

region. Three CAL FLT trigger configurations were used in 1992: DAY1, from June to

mid-September, LOW -REM C, from mid-September to early October, and LOW -BEMC,

from early-October to early-November. About 10%, 60%, and 30% of the luminosity was

collected with the first, second, and third configurations, respectively. The trigger tower

thresholds for each configuration are listed in Table 2.3.

In addition to these thresholds, a lower RCAL EMC threshold was used to increase the

acceptance of photoproduction events, but only in coincidence with a positive trigger from

the LUMI electron calorimeter. Additional prescaled triggers were used for monitoring

purposes. The average GFLT rate during the 1992 running period was about 20 Hz.

2.3.3 Second Level Trigger

The SLT processors, many of which consist of programmable transputers, have about

five milliseconds of processing time to arrive at a trigger decision. The processors can

perform some iterative tasks, such as finding track segments in the CTD (CTD SLT), or

energy clusters in the calorimeter (CAL SLT).

At the beginning of the 1992 running period, the GSLT did not reject events. After

trigger selection algoriturns had been implemented and tested at the TLT, people gained

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. confidence in the algorithms and implemented them at the SLT. For instance, an SLT

version of the TLT spark and calorimeter time algorithms, described in Section 2.3.4, was

eventually run at the SLT. The GSLT also rejected cosmic rays satisfying the following

conditions: a positive Barrel Muon trigger in coincidence with calorimeter activity and

less tha n two track segments in the C T D .

2.3.4 Third Level Trigger

System Architecture

The Third Level Trigger (TLT) consists of thirty Silicon Graphics 4D/35S processors

used for event reconstruction and trigger decision. The processors use the R3000/R3100

RISC chip set, operating at 36 MHz, and provide a UNIX environment to the user. The

total processing power of the system is over 1000 MIPS3.

The reconstruction processors are organized into six branches. Each branch is man

aged by a 4D/25S processor. A schematic diagram of the processors, data links, and

control links in one branch of the TLT is shown in Figure 2.9. Events are written into

a 512kByte memory buffer on the VME module labelled 2TP, which also comprises two

INMOS T800 transputers. The 2TP module sits in the Event Builder crate, a VME crate

separate from the TLT. The Fermilab Branchbus [50] is used as the data link between

the Event Builder crate and the TLT processors. Branchbus VMEbus Interface (BVI)

modules [51] sitting in the Event Builder crate provide an interface to the Branchbus. For

increased bandwidth, two B V I’s serve two sub-branches of reconstruction processors and

a third serves the manager processor. The TLT processors are linked to the Branchbus

via VMEbus Branchbus Controller (VBBC) modules [52] sitting in the VME adaptor of

the processors.

The manager processor controls data input and output and communicates with the

TLT equipment computer. Control messages are sent between the manager processor,

the reconstruction processors, and the TLT equipment computer via Ethernet. The

reconstruction processors read events from the Event Builder buffer, reconstruct them,

3M illion instructions per second.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45

Event Builder Crate

2 B B B F ro m T VVV Event Builder P 1 1 1

Manager Processor

V B 2SS B C V V B B 3SS 3 5 S B B C C

V V Five Reconstruction B B 3 5 S 3 5 S P ro c e s s o rs B B C C

V B 3 5 S B C

E th e rn e t

Branchbus Switch

¥ ¥ T o V A X T o IB M

Figure 2.9 Schematic diagram of the processors, data links, and control links in one branch o f the T hird Level Trigger.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. •16

and make a trigger decision. Triggered events are transferred to a number of destinations

(IBM, VAX) via a Branchbus Switch.

Control Software

The data input, output, and analysis tasks are divided into separate processes, which

were written using the Cooperative Process Software package [53] developed at Fermi-

lab. The reconstruction and trigger process, which runs on each reconstruction pro

cessor, is called Analyze_Event. This program, written mostly in FORTRAN, incor

porates software developed offline. Processes called Manage_.Job, Manage_Input, Man-

age_Output, and Monitor_Event run on the manager processors: Manage_.Job allocates

hardware resources and communicates with the TLT supervisor process, Control_TLT.

Manage_Input and Manage_Output coordinate the event input (from the EVB buffer)

and output (to the VAX and IBM ). Monitor_Event monitors the software and hardware

performance and sends its results to Monitor_Level_3, a process running on the TLT

equipment computer.

Trigger Algorithms

The T L T processors have access to the com plete event data and can use, on average,

300 ms of processing time per event. They can therefore perform sophisticated algorithms,

such as track and vertex reconstruction.

The trigger selection is done in two stages. First, all events must satisfy general

criteria aimed at rejecting backgrounds. Second, physics events of particular interest

are selected with specific filters. Events which do not satisfy any filter requirement are

rejected. It is also possible to prescale individual filters, for example, those associated

with large event rates. A great advantage of the TLT system is its flexibility: a new

algorithm can be designed, tested, and implemented within a few days.

An unexpected background in 1992 was due to random electrical discharges from the

calorimeter PM T’s. A calorimeter EMC or HAC cell was defined as a spark candidate if

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47

pl 111 Ml i ! | tF~o tF~o tR ~ -12 ns

F ig u re 2.10 Schematic diagram of the FCAL and RCAL time for physics and beam-gas events.

there was a large energy imbalance between its two PM T’s:

E l ~ E r E l + E r > 1.5 GeV AND > 0.9, (2.4) e l + e r

where E l and ER are the left and right PMT energies. Events were rejected if they

contained a single spark candidate and little other calorimeter energy (less than 2 GeV),

and if the CAL FLT bit corresponding to the appropriate calorimeter region was set.

A second algorithm, based on calorimeter tim e information, was used to reject beam-

gas events. Particles originating in beam-gas interactions reach the RCAL about 12 ns

earlier than particles from electron-proton interactions since they do not go through the

nominal interaction point, as illustrated in Figure 2.10. PM T’s with energy greater than

I GeV in a 3 x 3 array of cells around the beam pipe in the RCAL and in a 5 x 5 array

of cells around the beam pipe in the FCAL were used to calculated a mean RCAL time,

tR, and a mean FCAL time, tF. Events with two or more PM T’s above 1 GeV in the

RCAL and in the FCAL were rejected if:

+ 10.5ns| < 4.5ns A N D \tR — tR — 10.5ns| < 4.5ns. (2.5)

The spark and calorimeter time algorithms provided sufficient rejection power to

reduce the TLT event input rate to an appropriate level. However, additional algorithms

were used. Full CTD and VXD track reconstruction was performed using the VCTRAK

global track reconstruction program [54], and a number of algorithms were used to classify

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. •18

events:

• a muon finder based on calorimeter time and energy, to identify cosmic and beam

muons [55];

• a high track m ultiplicity filter, to identify physics events;

e the requirement of an isolated electromagnetic energy cluster in the calorimeter

with a matched CTD track, to identity neutral current deep inelastic scattering

events;

• the requirement of large missing transverse energy in the calorimeter, to identify

charged current events.

These algorithms were used to flag events as possible physics candidates. This scheme

was expanded and reorganized in 1993 as the filtering scheme described earlier.

2.4 The ZEUS Offline Environment

2.4.1 Event Reconstruction

In 1992, ZEUS data were retrieved from IBM cartridges and reconstructed using a farm of

three Silicon Graphics multiprocessors (SGI 480 UNIX stations), each equipped with six

processors. Events were reconstructed with the ZEPHYR4 program [36], which performs

track and vertex reconstruction, calorimeter clustering, and global track and cluster

matching, and the results were appended to the data. W ithin ZEPHYR, calorimeter

data are corrected by using offline calibration information and by taking into account

bad PM T’s. EMC cells with less than 60MeV of energy and HAC cells with less than

110 MeV of energy are removed (“zero-suppression” ). In 1992, two independent packages

were used to reconstruct CTD tracks: TCRECON [56] and VCTRAK. This analysis uses

the results from VCTRAK.

4ZEUS Physics Reconstruction.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49

A filter program selects events according to the specifications of the different ZEUS

physics groups. Events which satisfy the requirements of a particular group are flagged

by setting a specific bit in a filter word which is added to the data. Reconstructed events

which satisfy the requirements of at least one group are kept, copied to the DESY IBM ,

and archived on cartridges. The filter algorithms used for this analysis are described in

Section 3.3.

2.4.2 Offline Analysis

Monte Carlo events arc produced using a variety of generator programs. The generators

chosen for this analysis are discussed in Section 3.4.1. To ensure a standard data format,

the generators are interfaced to a common shell called ZDIS. The ZEUS detector is

simulated with MOZART5, which uses the GEANT framework [57] for describing the

detector geometry and tracking particles through the detector media. Shower terminators

have been added to speed up the simulation of energy deposits in the central calorimeter,

and the calorimeter response in the Monte Carlo has been tuned to reproduce results

from beam tests [58].

The format of the Monte Carlo data is identical to that of the ZEUS data and one

uses a common reconstruction and analysis chain for both the Monte Carlo and the ZEUS

data, as shown in Figure 2.11. The ZGANA program provides a detailed simulation of the

First, Second, and Third Level Triggers. The trigger results are appended to the Monte

Carlo data and are available for trigger acceptance studies. Monte Carlo data are then

reconstructed using ZEPHYR. During the reconstruction, electronic noise and uranium

noise arc added to the simulated calorimeter PM T energies, before the zero-suppression

process.

The detector simulation, trigger simulation, and reconstruction of large numbers of

Monte Carlo events necessitates considerable computing power. The Funnel environ

ment [59] has been developed for this purpose. It makes use of over fifty personal com

puters (DECstations from Digital Equipment Corporation) used by ZEUS collaborators

5Monte Carlo for ZEUS Analysis, Reconstruction, and Trigger.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50

ZDIS Physics Generator

MOZART Detector Simulation

ZGANA ZEUS DAQ

Trigger Simulation

Reconstruction ZEPHYR

FILTER

D S T Filter

EAZE Event Analysis

Event Display LAZE

Figure 2.11 Data flow of ZEUS data and Monte Carlo data in the offline environment.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51

at DESY. ZDIS events are distributed to individual nodes via Ethernet. The nodes run

the same versions of MOZART, ZGANA, and ZEPHYR, and return fully reconstructed

events to the Funnel computer.

Physics analysis is performed using the EAZE6 shell. Users write their own analysis

code in this shell and the same EAZE program can be used to analyze ZEUS data and

Monte Carlo data. A two-dimensional event display (LAZE) and a three-dimensional

event display (GAZE) are available to display Monte Carlo and ZEUS data.

6Easy Analysis of ZEUS Events.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3 Data Analysis

3.1 Description of the Problem

The aim of this thesis is the extraction of a possible leptoquark signal from the ZEUS

data collected in 1992. In the present analysis, leptoquarks arc searched for in the channel

LQ —> vX . The signature of these events is identical to that of charged current deep

inelastic scattering events and is quite striking. The neutrino, which carries a large

fraction of thecentre of mass energy, goes undetected and, in consequence, there is

missing energy in the event. The display of a Monte Carlo leptoquark event is shown in

Figure 3.1.

Because the ZEUS calorimeter does not detect particles escaping through the beam

pipe, it does not provide a good measure of total missing energy. However, it does

provide a good measure of missing transverse energy, also called transverse momentum

o r p r • Transverse momentum is defined as the magnitude of the vectorial sum of the

transverse momentum vectors, px{X + p yiy, associated with each calorimeter cell i:

Pri = Ei s>n 0{ cos (3.1)

p y i = E{ sin O i sin (/>,-, (3.2)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53

UCAL transverse energy

Figure 3.1 Event display of a 150GeV/c2 S0 -*• v X Monte Carlo event. Calorimeter energy and reconstructed CTD tracks are shown in a z r projection on the left; a lego plot o f calorimeter transverse energy in rjcj) space is shown on the right.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where 0 ,-, and 4>i are the energy, polar angle, and azimuthal angle of cell i.

After apx requirement of 10 GeV, the dominant electron-proton background to lepto

quark events decaying into neutrino plus jets is charged current deep inelastic scattering,

which has a cross-section of 0.07 nb. However, there are a number of other backgrounds:

• Incoming protons interacting with gas molecules inside the beam pipe can deposit

a lot of energy in the calorimeter and lead to p r > 10 GeV.

• Proton beam halo particles interacting with material upstream of the detector can

lead to large pr-

• Cosmic muons, cosmic showers, and muons from the proton beam halo can emit a

high-energy photon and also lead to large pr-

In order to identify and reject these backgrounds, a number of tools are used: calorime

ter time algorithms, a track and vertex reconstruction program, a calorimeter clustering

algorithm, and a muon finder algorithm. These and other relevant analysis tools are

described in Section 3.2. The data selection procedure used in this analysis is presented

in Section 3.3. The Monte Carlo generation of charged current DIS, and scalar and vec

tor leptoquark events, necessary for estimating the trigger acceptance and data selection

efficiency, is described in Section 3.4.

3.2 Analysis Tools

3.2.1 C5 Time

The C5 time information is used at the trigger and offline levels to reject background

events. In addition, C5 time distributions are very useful in monitoring the quality of

the beams and estimating the z position of ep collisions. During each run, the C5 time

distribution is histogrammed, combining information from all bunches. A typical time

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protons

satellite electrons

electrons

20 30 50 6040 C5 time (ns)

F ig u re 3.2 C5 time distribution for Run 4272. The larger peak corresponds to the passage of proton bunches, while the smaller peaks correspond to the passage o f primary electron bunches

and satellite electron bunches 8 ns later. Note that C5 time runs backwards: it decreases as time progresses. The two spikes and the inverted parabola correspond to the fitted and unsmeared satellite electron, electron, and proton time distributions.

d is trib u tio n is shown in Figure 3.2. The larger peak corresponds to the passage o f proton

bunches, while the smaller peaks correspond to the passage of primary electron bunches

and satellite electron bunches Sns later. The unwanted satellite electron bunches are

created early in the accelerator chain in the PIA storage ring, which has an RF frequency

of 125 MHz (1/125MHz = Sns).

The C5 electron and proton times, te and tp, are related to the 2 position of the

interaction vertex:

c = {tp — tc)~ + zcs, (3.4)

where c is the speed o f lig h t and zc5 is the r position of the C5 counters (zcs = —314 cm ).

The RMS width of the electron bunches, typically a few centimetres, is small compared

to the C5 time resolution of about 0.5 ns. The electron time distribution is therefore a

measure of the C5 time resolution. The proton time distribution is broader than the C5

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resolution and can therefore be used to obtain the length of the proton bunches. For each

run, fits to the primary electron and satelhte electron time distributions are performed

using a Gaussian function coupled to an exponential tail1, as described in [-hi]. The

unsmeared proton time distribution, f ( t p), is assumed to be a quadratic function of

f ( ‘ p) = h ( l - T (t, - [„)■) .

where h, tp, and ZP± A are the height, mean, and zeros of the function. A fit to the proton

time distribution is performed using f { t p) coupled to a Gaussian and an exponential tail.

The unsmeared tim e distributions for the primary and satellite electron bunches (spikes),

and for the proton bunches (inverted parabola) for Run 4272 are shown in Figure 2.2.

The mean primary electron time and mean proton time are used to refine the calorimeter

tim e rejection criteria, as described in Section 3.2.3.

Substituting Equation 3.4 into Equation 3.5, one obtains the vertex distribution for

the run. The average vertex z distribution for the entire running period, /'’(-), b obtained

by summing the individual vertex distributions over all runs, weighting with the run

integrated luminosity X,-:

F (z) = {[(.- + =cs) \ + („] - ipi}^ .

During the fall 1992 running period, the r-vcrtex mean and RMS width varied up to

20 cm from run to run. The average vertex z distribution for the runs used in the present

analysis is shown in Figure 3.3 [60]. It has a mean of —6 cm and an RMS width of 22 cm,

in agreement with the vertex distribution determined from photoproduction events, for

which the detector acceptance does not depend much on 2 [61]. Also shown in Figure 3.3

is the vertex distribution used ir *he Monte Carlo simulation: a Gaussian function, G(z),

centred around z = 0 with RMS width of 25 cm. In order to simulate the z distribution

of the data in the Monte Carlo, one can weight the Monte Carlo data with the function

F (z )/G (z ).

1 According to [44], the exponential tail is an effect of the C5 detector itself.

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-100 0 50-50 100 Vertex z (cm)

Figure 3.3 Overall vertex z distribution from the C5 time information, for the runs used in the present analysis (solid curve); vertex z distribution used in the Monte Carlo simulation (dashed curve).

Finally, the C5 time distributions are used to correct the effect of the satellite electron

bunches on the measured luminosity. Electrons from satellite bunches interact with

protons at z ~ 1.2 m, close to the FCAL. Such events are rejected at the trigger or

offline level with calorimeter time algorithms, as described in Section 3.2.3. They do,

however, contribute to the measurement of the luminosity. The integrated luminosity

must therefore be appropriately corrected on a run by run basis, according to the size

of the satellite electron bunches. During the fall 1992 running period, the size of the

satellite electron bunches relative to the primary electron bunches varied from 0 to 23%;

the correction to the integrated luminosity for the entire running period is 6% [44].

3.2.2 Track and Vertex Reconstruction

CTD track and vertex reconstruction is performed with version 5.0 of the VCTRAK

program [54]. VCTRAK first performs two-dimensional pattern recognition in r

starting with hits in the outermost superlayer and searching for tracks pointing towards

x = y — 0. The tracks are then reconstructed in three-dimensions using the z-by-timing

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Track 1

Track 2

Figure 3.4 Vertex fitting with and without the beam line constraint. In this example, two reconstructed tracks are shown as arrows and their errors are shown in grey. These tracks are consistent with x = y = 0 but lead to a vertex away from a: = y = 0 if the beam line constraint is not used.

information. Tracks are required to have a minimum number of hits in each superlayer:

• for tracks extending to superlayer live, three hits out of a possible eight in superlayer

one, and two hits out of four in both superlayers three and five, are required;

• for tracks extending to superlayer three only, three hits in superlayer one and two

hits in superlayer three are required;

• for tracks with hits in superlayer one only, four hits are required.

The track candidates are fitted to a five-parameter helix. For each track the number of

degrees of freedom is N y = n — 5, where n is the number of hits.

The tracks are then fitted to one or more vertices using the full fit techniques described

in [62]. A diffuse beam line (x = 0, y = 0, and crx = cry = 0.7cm) is added to the list of

tracks before the vertex fit. This helps the vertex reconstruction efficiency in the case of

imprecise track trajectories. Consider, for example, the two tracks shown in Figure 3.4.

W ithout the beam line constraint, one would reconstruct a vertex away from x = y = 0,

even though both tracks are consistent with x = y = 0. The beam line constraint

introduces no bias in z.

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W ith the poorer resolution of the 2 -by-timing system, some vertices are not well

reconstructed when all tracks are assumed to belong to the same vertex. An option to

reconstruct multiple vertices helps to reduce this problem and was used for this analysis.

3.2.3 Calorimeter Time

Calorimeter time is a powerful tool to reject beam-gas and cosmic muon backgrounds. In

1992, simple rejection algorithms based on out-of-time calorimeter energy deposits were

used at the SLT and TLT. In addition, a number of rejection criteria were used offline

either as part of the filter algorithm running on the ZEUS reconstruction processors or

at higher levels of data selection.

The general concepts are as follows. An average time is calculated for a particular

calorimeter region (RCAL, RCAL Beam Pipe, FCAL, etc.) using PM T’s above a certain

threshold. The average can be a simple average or a weighted average. In the case of a

weighted average, the error on the time of each PMT, cr,-, is parameterized as a function

of the PMT energy,

<7,- = 1.157 + 1 .6 9 5 /y ii, (3.7)

where 0 7 is expressed in nanoseconds and Ei is expressed in GeV. This function was

obtained by fitting the time resolution of single PM T’s asa function of PMT energy for

beam-gas events. The weighted average time is given by

‘ = TER)' (3's) i

where the sum is over PM T’s above threshold in the appropriate calorimeter region. The

error on t is given by - 1 /2 St = (3.9)

Eighteen different calorimeter time rejection criteria, based on different PM T thresh

old, or different requirements on the number of PM T’s or total energy sum in a particular

calorimeter region, were used in the selection of the present data. They are described

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in Section 3.3 and relevant parameters are listed in Table 3.1. Here is an example of a

rejection algorithm:

A weighted average RCAL time, tp , is calculated using RCAL PM T’s above

200 M e V ( E min = 200 MeV). A minimum of two PMT’s above threshold

is required (N p m t > 2), the energy sum of PMT’s above threshold must

be greater than 1 GeV (£ jum > lG eV), and the \ 2 per degree of freedom

associated with tp must be less than three (x 2/N

tp < m in( —4.5ns, — 3 6tn) O R In > max(6ns,3 6//*), (3.10)

then the event is rejected. Similarly, a weighted average FCAL time,

calculated using PMT’s in the FCAL region, with similar requirements on

Emin, N p m t , E ,um, and x 2/A rdf. Events are rejected if

\tp\ > m ax(6 ns, 3 8tp). (3.11)

Events which satisfy the Em{„, N p m t , E^um, and X2f^d / requirements for

both tp and tp are also rejected if

\If ~ £r| > max(6ns,3 \JS t2F + 5l2R). (3.12)

A plot o f If — tp versus tn for Run 4272, calculated as described above, is shown in

Figure 3.5. A clear distinction between proton-gas events, satellite clcctron-gas events,

and electron-proton events can be observed.

3.2.4 Calorimeter Energy Islands

An algorithm is used to group calorimeter cells into energy clusters. The algorithm,

which is depicted in Figure 3.6, operates on calorimeter towers: an FCAL tower consists

of four EMC, one HAC1, and one HAC2 cell; an RCAL tower consists of two EMC

and one HAC1 cell; a BCAL tower consists of one HAC1, one HAC2, and four EMC

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Parameter Description

Region Designated calorimeter region, for example, RCAL, R C AL Beam Pipe, FCAL, etc.

Emin Per PM T energy requirement

N PMT Number of PMT’s in the designated region with energy greater than Emin p Energy sum of all P M T ’s in the designated region

E',um Energy sum of all PM T’s in the designated region with energy greater than Emin t Average time computed as a simple average and using P M T ’s with energy greater than Em,„

t Average time computed as a weighted average and using P M T ’s w ith energy greater than £ m,n. The weight for each PMT is 1/of

St Error on the weighted average time, given by E (l/o f)]-1^2

X2/N « X2 per degree of freedom for the weighted average time, defined as

U ( ‘< - N PM T ~ 1

Table 3.1 Parameters used in the calorimeter time algorithms.

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300 p-gas

200

ep physics 100 - satellite e-gas

-10 -10 -20

Figure 3.5 Weighted FCAL and RCAL time (tp — tR versus l R) for Run 4272. A PMT threshold o f 200 MeV is used. Only events satisfying the following requirements for both the RCAL and FCAL are included in the plot: NPMT > 2, E ’um > 1 GeV, and x2/N

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Figure 3.6 An example of the calorimeter island algorithm. A 9 x 9 array of calorimeter towers is shown, w ith circles corresponding to the tower energies. Arrows point from each energetic tower to its highest energy neighbour. The trails of pointers lead to three different peaks, corresponding to three islands.

cells. The forward (rear) BCAL MAC tower is smaller and only encompasses two (three)

EMC cells. Each calorimeter tower is assigned neighbouring towers. Those are adjacent

or diagonally adjacent towers in the same calorimeter volume, or adjacent towers in a

different calorimeter volume. The algorithm is as follows:

• One loops over all towers and, for each tower, sets a pointer to the tower’s highest

energy neighbour. A tower with a pointer to itself is called a peak.

• One loops again over all towers and follows the trails of pointers. Each trail leads

to one and only one peak. The towers with pointers leading to the same peak form

an island.

One can calculate the total energy, Eisiand, and the energy-weighted position, Xisiand ,

of each island by summing over contributing calorimeter cells:

Eittand = (3‘13) t

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'island

where £,■ is the centre of cell z. One can also calculate a weighted island time:

w ith error - 1 - 1 /2

aland — ^ ]( 1/) (3.16)

The sums in Equations 3.15 and 3.16 are over all contributing PMT’s. The error on the

tim e o f each P M T , cr,-, is given by E quation 3.7.

3.2.5 Muon Finder

A muon finder called ISITAMU [63] is used to identify cosmic and beam halo muon

events. The algorithm is based on the following facts:

1. Cosmic muons can leave a trail of calorimeter cells above threshold in the FCAL

or RCAL aligned in a straight line.

2. Beam halo muons can leave a trail of calorimeter cells above threshold in the BCAL

aligned in a straight line.

The algorithm operates on the ( x ,y ,z ) position of calorimeter cells above 100 MeV and

searches for cells aligned in the xy plane (FCAL and RCAL) or xz plane (BCAL). The

Pearson coefficient, r, and the circularity, c, are calculated in different planes and, de

pending on the results, a flag is returned with value 2 (muon candidate), 1 (probable

muon candidate), 0 (unclear object), or —1 (not a muon).

Consider an event with n cells above threshold in the RCAL. The Pearson correlation

coefficient between the X{ and i/,- positions of the cells is

£(*» - g)(y»y) - r = (3 . 17 )

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where

x = a;,-, (3 .IS) n

y = (3-19)

Before calculating the circularity, the coordinate system is first modified, as follows. The

centre o f the cell cluster is defined as (x 0,2/o), where

xq = (smallest of all X i’s + largest of all x,’s)/2, (3.20)

j/o = ( smallest of all y i ’s + largest of all y i ’s)/2. (3.21)

The coefficients x,- and y, are fitted to a straight line x = a + by. The coordinate system

is then moved to the centre of the cell cluster and rotated through an angle 0, where

cos, = (3.22)

sin, = jJ&p (3.23)

In the new coordinate system, the centre of the cell cluster is

(*o» Vo) = (a + by0, y0). (3.24)

and the new cell positions are

x'i = [Xi - Xq) cos 0 - ( yi - y'0) sin 6 , (3.25)

y'i = {yi - y'o) cos 6 + (x,- - Xo) sin 6. (3.26)

The circularity in the new coordinate system is

, ,/E *f-E s -i2)J+4(i>;!/;)2

C = 1 ------e x ? + e j ? ------• ( 3 ' 2 7 )

An event with |r| > 0.7 and c < 0.1, for example, is classified as a muon candidate.

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3.2.6 Reconstruction of Kinematic Variables

K in e m a tic x is an important variable since it is related to the leptoquark mass. (Recall

th a t x ~ m ^q/s.) The kinematic variables :r, y, and Q2 of leptoquark events decaying

into neutrino plus jets, and of charged current DIS events, can only be reconstructed from

the jet particles since the outgoing lepton is a neutrino. In this case, the Jacquet-Blondel

method [64] must be used. The outgoing hadrons can be described by the four-momentum

w: / lk \

Pxh v, = £ h. Pyh

\Pzh/

where the sum is over all hadrons. Consequently, the four-momentum transfer q can be

expressed as

([.f('ZEk)-Ep\ h ' r . Pxh. q = w -p p = h (3.29) y,Pyh. h (y,pSh)-Ep) x h j where E p is the incom ing proton energy. Using Equations 1.41 and 1.43, one obtains:

EiEk-p*) _h______V = (3.30) 2 E e

f e p r O v h ' v h ' Q2 = (3.31) i - y

where E e is the incoming electron energy.

For LQ —> v X events and charged current events, Equations 3.30 and 3.31 become:

E -P z y - (3.32) 2 Ee

Pt Q2 = (3.33) i - y ’

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where E is the total energy, p . is the to ta l energy in the z direction, and px is the

transverse momentum. The kinematic x variable is then simply

O 2 x = 2 - . (3.34) sy

Note that the kinematic variables reconstructed with the Jacquet-Blondel method

are not largely affected by undetected particles escaping through the beam pipe because

those particles give a small contribution to E — pz and px-

3.2.7 Luminosity Calculation

Integrated luminosity is given by the rate of ep bremsstrahlung photons detected in the

LUM I photon calorimeter, Rep, divided by the ep bremsstrahlung cross-section corrected

for detector acceptance, cr°£\ The rate of ep bremsstrahlung can be estimated using the

following formula:

R ep = (R tot - Rcgas ~ (3.35)

where R loi is the total rate of events in the photon calorimeter, R egas is the rate of

elcctron-gas background events, and R se*tell,ic is the rate o f ep bremsstrahlung events

from satellite electron bunches. The rate of electron-gas events is estimated using the

electron pilot bunch: J t o t

Regas — .pilot Rpiloti (3.36) 1e

where I* ot and I^ ,loi are the total electron and pilot electron currents, and R pu0t is the rate

of events for the electron pilot bunch. The contribution from satellite electron bunches

is estimated using the C5 time distributions (cf. Section 3.2.1).

During 1992, the integrated luminosity measured by ZEUS was over 30 nb-1. The

integrated luminosity used in this analysis is listed in Table 3.2 for the three CAL FLT

trigger configurations of 1992.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Trigger Configuration Integrated Luminosity (n b -‘ ) D A Y l 2.20 ± 14% LOW_REMC 17.15 ± 5% LOW _B EMC 8.16 ± 5% Total 27.5 ± 6%

Table 3.2 Integrated luminosity used in the present analysis, shown for the three CAL I’ 1/1' trigger configurations of 1992. The uncertainty on the luminosity is M% for data collected with the D A Y l configuration [65] and 5% for data collected w ith the LO W —REMC and LOW _H KMC configurations [35],

3.3 Data Selection

The selection of the data is broken down into five levels of filters. The level one and level

two filters are run on the offline reconstruction processors as part of the selection process

for the ZEUS Exotics physics working group. The level three filter is used by the Exotics

group as a first step in the data analysis. The level four and level five filters are used in

the last stage of data selection. These last two filters utilize selection criteria developed

by the Exotics group and algorithms designed specifically for the present analysis. Events

remaining after the filter selection are visually scanned with the LAZE event display and

form the final event sample.

3.3.1 The Level One Filter

The first selection criterion used at the level one filter is aimed at identifying LQ — > v X

events and charged current DIS events. It is based on the total calorimeter transverse

m om entum :

p r > 10 GeV. (3.37)

The p t sum is over all good calorimeter cells. A cell is considered bad if the following

three conditions are satisfied:

1. The energy of the cell is greater than 200 MeV.

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4 10

0 20 40 60 80 100 pT(GeV)

Figure 3.7 pT distribution for Run 4272.

2. The energy imbalance between the cell’s left and right PM T’s, |(£x — E r )/(E l +

E r ) |, is greater than 0.7.

3. Both PMT’s are good channels, according to the list of bad channels for the run.

Bad cells arc usually cells with undetected sparks, cells with bad PM T’s which have not

yet been included in the bad channel list, or cells adjacent to the beam pipe and with

energy deposits from particles entering only into the wavelength shifter. The p r d is trib u

tion for Run 4272 is shown in Figure 3.7. Out of a total of 2391S events (corresponding

to an integrated luminosity of 0.9 nb-1), only 321 events (1.3%) are left after the px

requirement.

The subsequent selection criteria are aimed at rejecting standard backgrounds:

• Beam pipe PMT’s with energy greater than 1 GeV are used to calculate simple

average FCAL and RCAL times. Events with two or more beam pipe PMT’s

above 1 GeV in both the FCAL and RCAL are rejected if

|f/? + 14 ns| < 6 ns A N D \tp — tn — 14ns| < 6ns. (3.38)

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The above was an early implementation of the TLT calorimeter time algorithm. Al

though it is less restrictive than the updated TLT algorithm, it rejects background

events which were kept at the TLT for monitoring purposes.

• Events are rejected if they were flagged as a spark candidate at the TLT. (For

monitoring purposes, some spark events were not rejected at the TLT.)

o Events w ith the Co trigger bit set, indicating a veto by the C’5 detector, are rejected.

A ll events remaining after the level one filter criteria are passed to the level two filter.

3.3.2 The Level Two Filter

The level two filter criteria are aimed at rejecting cosmic and beam muons, spark events

with a bad channel, and general out-of-time backgrounds:

• Events are rejected if flagged as a muon candidate by the ISITAMIJ muon finder.

• Events are rejected if the highest energy cell in the calorimeter has a bad PMT and

if the energy sum of all other calorimeter cells is less then 2 GeV.

• Events are rejected based on calorimeter time, as described below.

There are five calorimeter time rejection criteria used at the level two filter, each one

dealing with a different calorimeter region. The regions are FCAL Extended Beam Pipe

(comprising the 5x5 array of cells surrounding the beam pipe in the FCAL), RCAL Beam

Pipe (comprising the 3x3 array of cells surrounding the beam pipe in the RCAL), RCAL,

FCAL, and Entire CAL (the entire calorimeter). A weighted average time is calculated

for each region using PM T’s above a specific threshold F min, as described in Section 3.2.3.

Only PM T’s from good calorimeter cells are considered. There are requirements on the

number of P M T’s above threshold, N pmt, the energy sum of PM T’s in the region, E „ im ,

and the x2 Per degree of freedom associated with the average time. The time criteria

and associated parameters are listed in Table 3.3. For an event to be rejected based on

a particular time criterion, all associated requirements must be satisfied.

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p Region Aprnt F ■ ^ sum X '/N d f Rejection Criterion (GeV) (GeV) FCAL Extended Beam Pipe 4 0.20 1 3 |£f| > max(6 ns, 3 Stp) FCAL 6 0.08 1 3 Iffl > max(6 ns, 3 St?) RCAL Beam Pipe 4 0.20 1 3 |/h| > max(6 ns, 3 8tR) RCAL 6 0.08 1 3 |ffi| > max(6 ns, 3 <5 max(8 ns,4 6t)

Table 3.3 Level two calorimeter time rejection criteria. For a description of the parameters, see Table 3.1. Events are rejected only if the requirements on Npmt, Em{n, E aum, and x 2/A Tdj are satisfied. An entry with “—” indicates no requirements.

Out of the 4 x 106 events triggered in 1992, 1S989 events are left after the selection

criteria of the level one and level two filters and are passed to the level three filter.

3.3.3 The Level Three Filter

The level three filter criteria are as follows:

• Events are rejected if flagged as a probable muon candidate by the ISITAM U finder.

• Events are rejected if the CAL data stayed in the analog pipelines longer than one

thousand beam crossings. This criterion targets a very smail number of events for

which the CAL data stayed in the pipeline for an extended period of tim e and, as

a result, were degraded.

• Events are rejected with the calorimeter time criteria described below.

The level three calorimeter time rejection criteria and relevant parameters are listed

in Table 3.4. Weighted average times are calculated using good cells in three calorimeter

regions: FCAL, RCAL, and Entire CAL. Individual PMT energy thresholds of 80 MeV,

200 MeV, and 1 GeV are used, along with requirements on the number of P M T ’s above

threshold, N pmt, the energy sum of PM T’s above threshold in the region, ££um, and the

X2 per degree of freedom associated with the average time.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. —i —i t o r ) 61 StR) ,3 %) 6t%) 6t + + max(6ns,3<5f/i) > > > max(6ns 6tF) StF ) 6t)

> max(6ns,3 r r \/6t% +\/6 6t%) t2F \J6t% I r I I OR OR

) r 6tR) 6 1 Rejection Criterion |f| > max(6 ns,4 | | > max(6ns,3 |/f| > max(6ns,3 6if) jtfl > max(6ns, 3 i H - *«| > max(6 3 ns, — — - ini > max(Gns,3 m in(—■4.5 ns, -ns, 3 m in(—■4.5 < < m in (-4.53 ns, — < min(—4.5ns, 6ffl) —3 OR r tR i n i jj 3 3 — 3, 3 3, 3 3, 3 X'/N 1 sum — 1, 1, 1 1,1 1, 1, 1 pm (GeV)

1.00 1 3 0.08 1 3 |ij,| > max(6 3 ns, 0.08 0.08 1 3 F ■ 0.20 1 0.20 and \ 2/Ard/ are satisfied. An entry with u—” indicates no requirements. (GeV) 8 0.08 4 4 2 2 ,2 1.00 4 ,4 N pmt m £‘um, Npmt, Npmt, E FCAL RCAL Region(s) FCAL 2 Entire CAL FCAL, RCAL FCAL, RCALFCAL, RCAL 2 ,2FCAL 0.20 RCAL 2 1.00 2 1 3 RCAL Table 3.4 if Level the threerequirements calorimeter on time rejection criteria. For a description of the parameters, Tablesee 3.1. Events are rejected only

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Region Npml F. F'sum Rejection Criterion (GeV) (GeV) FCAL 2 0.20 0.75 \tF\ < m in (-6 ns, — 36tF) RCAL 2 0.20 0.75 |/r| < m in(—6 ns, — 3 6tn )

Table 3.5 Level four calorimeter time rejection criteria. For a description of the parameters, see Table 3.1. The calorimeter times are corrected with the mean C5 time for the run. Events are rejected only if the requirements on Npmt, E min, and E ’um are satisfied.

The level three muon algorithm reduces the event sample from 18989 to 10909 events.

The requirement that the CAL data should not sit in the analog pipelines longer than one

thousand beam crossings rejects an additional 206 events. The level three calorimeter

time rejection criteria reduce the sample to 5595 events, which are passed to the level

four filter.

3.3.4 The Level Four Filter

In the first three filter levels, there are no requirements of an event vertex. The level four

filter consists of general background rejection algorithms plus the requirement of a CTD

vertex with |r| < 75 cm:

• Events are rejected if the CTD was not on for that event.

• Events are rejected if there is more than 5 GeV of energy in the electron calorimeter

of the luminosity monitor. This criterion targets photoproduction background.

• Events are required to occur in one of the nine colliding electron and proton bunches

(i.e., not in a pilot electron or proton bunch).

• Events are rejected with the calorimeter time criteria listed in Table 3.5.

• Finally, events are required to have a reconstructed vertex, as described below.

Tracks and vertices are reconstructed using the VCTRAK program, with the beam

line constraint and multiple vertices options. The highest m ultiplicity vertex is taken as

the event vertex and must satisfy the following requirements:

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a 60

REJECT REJECT

-200 -100 100 200 Vertex z - Z nm (cm)

Figure 3.8 Vertex z — zrun distribution of the data after the level four filter criteria (excluding the vertex requirement) are applied.

1. X'2 Per degree of freedom less than ten.

2. |z — zTun | < 75 cm, where zrun is the mean vertex c for the run, as calculated from

the C5 electron and proton times (cf. Section 3.2.1).

Since VCTRAK is run with the beam line constraint option, there are no requirements

on the x and y positions of the reconstructed vertex. The vertex distribution of the

data, after the level four filter criteria (excluding the vertex requirement), is shown in

Figure 3.8. Only vertices with x 2/^ d f < 10 are included in the plot.

The number of events remaining after each level four rejection criterion is listed in

Table 3.6. O ut of the 5595 events entering the level four filter, 836 events remain after the

level four filter criteria, with most of the rejection being due to the vertex requirement.

3.3.5 The Level Five Filter

The level five filter criteria are:

• Require p r > 10 GeV, where p r is now corrected for the event vertex.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75

• Require p r > 10 GeV, excluding cells from islands with pseudorapidity2 p > 3. The

motivation of this requirement is given below.

• Require y, reconstructed with the Jacquet-Blondel method and corrected for the

event vertex, to be less than one.

• Require the calorimeter island times to be consistent with cp events, as described

below.

It was discovered that there was a class of beam halo background events with asym

metric energy deposits in the FCAL, leading to large p r- These events might be due

to collimators which were positioned asymmetrically. The fraction of those background

events changed from run to run, suggesting that this effect is related to the quality of the

beams. The events have between 150 GeV and 300 GeV of energy in the FCAL and very

little RCAL or BCAL energy. Furthermore, 95% of the calorimeter energy is located in

one island centred around 7/ ~ 3.5 (0 ~ 3.5°) and ~ 7r, i.e., centred on the FCAL cell

on the right of the beam pipe (negative x value). This is shown in Figure 3.9. The island

consists, on average, of a hundred calorimeter cells. To reject this class of events, but

keep a large efficiency for LQ —► u X and charged current events, p r is recalculated using

only cells from islands with p < 3 (0 > 5.73°) and is required to be greater than 10 GeV.

The p r distribution calculated in this manner, for events entering the level five filter, is

shown in Figure 3.10.

The Jacquet-Blondel y criterion targets background events which have somehow sur

vived the previous selection criteria. Out of the thirteen events rejected with this last

criterion, eleven have over 80 GeV of energy in the RCAL, which clearly indicates a

non-cp in teractio n [66].

The purpose of the island time requirement is to reject cosmic muons and events with

hardware problems. For each event:

Consider the two highest E r islands in the event. If they both have more

than 500 MeV of energy, then require the time difference between the two

2Pseudorapidity is related to polar angle as follows: p = — In[tan(0/2)].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76

6 2_ -Si ■». Q 5 “5 4

•g 3

0 ■4 ■2 0 2 4 Island pseudorapidity

Figure 3.9 Azimuthal angle versus pseudorapidity of highest E r island, for events left before the island p r requirement. A cluster of events have their highest E r island centred at // ~ .'{.5

and (j) ~ 7 i\

•5 10' -S

CO fN a. a 10 ■ 3 63

, I , M 0 20 40 60 80 100 pT excluding forward islands (GeV)

Figure 3.10 pT, calculated using cells from islands with tj < 3, for events entering the level five filter.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77

1.5

0.5

Figure 3.11 Time difference between the two highest E t islands, for events left prior to the island time requirement. Only events in which the two highest ET islands have more than 0.5 GeV of energy are included in the plot.

islands to be less 6 ns or 5 \fStJ3landl + Stfsland2, whichever is larger.

The island time difference, for events left prior to the island time requirement, is shown

in Figure 3.11. There is a cluster of events at \tisiandi ~ tisiand 2\ — 10 ns, characteristic of

cosmic muons.

The level three, level four, and level five filter selection criteria are listed in Table 3.6,

along with the number of events left after each criterion. The island pj- requirement

rejects 95% of the events entering the level five filter, reducing the sample to thirty-eight

events. The Jacquet-Blondel y requirement and the island time requirement reduce that

number to five events.

3.3.6 Final Data Sample

Five events remain after the filter procedure. Their properties are summarized in

Table 3.7. Upon scanning the events with the LAZE event display, four are found to be

cosmic muon or cosmic shower events, and one is a charged current candidate. During

the scan, an event is classified as a cosmic muon or cosmic shower event based on the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78

Selection Criterion Events Remaining Preselection (level one and level two) I.SOSO Level three Reject muon candidates 10900 Reject if CAL busy for long time 10703 Level three time rejection criteria 5595 Level four Require CTD on •18-17

Require LUMI E e < 5 GeV •1801

Require ep bunch crossing •1237 Level four time rejection criteria •I 1*13

Require vertex with \z - rPU„| < 75 cm 090 Level five Require pr > 10 GeV (vertex corrected) 011

Require pr > 10 GeV (excluding forward islands) 35

Require yjB < 1 (vertex corrected) 22 Island time rejection criterion 5 Visual scan 1

T ab le 3.6 Summary of the data selection criteria, along with the number of events remaining after each criterion.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79

Run Event % Zrun r / N df N tr Pt X y Q2 \At\ 5 a (cm) (cm) (GeV) (GeV2) (ns) (ns) 3444 5927 -74.1 -72.6 0.3 2 22.0 0.02 0.58 1100 3.6 5.8 4211 12649 -36.4 -33.4 0.6 7 81.5 0.31 0.41 11000 1.5 1.7 4077 11845 -60.6 -60.6 1.3 2 10.7 0.01 0.17 140 7.5 12.9 4077 38831 17.9 17.9 2.0 2 31.4 0.06 0.72 3500 7.4 8.2 4651 6354 -78.0 -72.3 1.1 2 16.4 0.01 0.31 390 _a _ a “The island time difference is not calculated because the energy of the second highest E r island is below 0.5 GeV.

T able 3.7 Properties of the five events remaining after the level five selection requirements, c is the 2 coordinate of the event vertex; zrun is the z coordinate of the mean vertex for the run, as calculated from the C5 electron and proton times; x~/Ndf is the x 2 Per degree of freedom of the vertex fit; N tr is the number of tracks associated with the event vertex; p r is the transverse momentum, corrected for the event vertex; x, y, and Q2 are the kinematic variables reconstructed with the Jacquet-Blondel method and using the event vertex; A t is the time difference between the two highest E r islands; 5a is five times the error on the island time difference. The charged current candidate is Event 12649 from Run 4211.

following criteria: the event has energy clusters in the top and bottom halves of the

calorimeter; the energy clusters are out of time; and CTD tracks align with the clusters

in a straight line. It was found that the cosmic muon events go through the interface of

two calorimeter regions (see Figure 3.12) and fail the island time rejection criteria. The

cosmic shower events have energy clusters in the top and bottom sections of the BCAL

but the time difference between the two highest E t islands is w ith in 5a.

The charged current candidate has a distinctly different topologv than the cosmic

muon and cosmic shower events. It consists of two high-pr jets into the FCAL; the jets

are clearly identified by two calorimeter clusters with associated CTD tracks. The event

vertex is at z = —36 cm and the reconstructed p r , after vertex correction, is 81.5 GeV.

The kinematic variables reconstructed using the Jacquet-Blondel method and corrected

for the event vertex, are x = 0.31, y = 0.41, and Q 2 = 11000 GeV2. The event is shown

in Figure 3.13.

The efficiency of the scan for leptoquark events is difficult to estimate. As a check,

one can replace the scan with the following algorithm:

If the event vertex consists of two tracks and if the highest E t island in the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. so

ZEUS

Figure 3.12 Event display of a cosmic muon event remaining after the filter procedure. A z r projection of the detector is shown on the left and an xy projection is shown on the right.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81

[TA PH 75444585

Figure 3.13 Event display of the charged current candidate. A lego plot of calorimeter transverse energy in t]4> space is shown in the upper-left window; calorimeter energy and CTD hits and tracks are shown in a zr projection in the lower-left vvindow; CTD hits and tracks are shown in xy and zy projections in the upper-right and lower-right windows (the event vertex is shown as a cross in the lower-right window).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S»\

event has —0.5 < r/ < 0.1 then reject the event.

This algorithm rejects all four cosmic events and would lower the elliciency of scalar and

vector leptoquark events by less than 0.2%.

3.4 Monte Carlo Simulation

3.4.1 Event Generation

Scalar leptoquark events ( e~p —► 5'o —> v X ) are generated with a modified version of the

general-purpose Monte Carlo event generator P Y T IIIA 3 [07]. Vector leptoquark events

(e~p —*■ Vo —> v X ) are generated with the LQUARK generator [68]. Both generators

include leptonic initial state radiation and use the Lund parton shower model for Q ('l)

fragmentation (via JETSET [69]).

Samples of scalar leptoquarks, a thousand events each, were generated at the following

leptoquark mass points: 50, SO, 100, 120, 150, 180, 220, and 280 GeV/c2. Samples of

vector leptoquarks, also a thousand events each, were generated at the following mass

points: 50, 80, 120, 150, 180, 220, and 250GcV/c2. The leptoquark Yukawa coupling was

set to 0.31 (electroweak coupling strength) and the structure function parameteri/.ation

used was MT B l.

The interference between the leptoquark and the charged current DIS contributions

to e~p —► v X is expected to be small. According to LQUARK the ratio of the in

terference cross-section to the leptoquark cross-section is less than 4% for leptoquark

masses between 30 G e V /c2 and 150 G eV /c2. For higher masses the effect is larger: +37%)

for 225 GeV/c2 So —► v X and —32% for 225 GeV/c2 Vo —> v X . In this analysis, the

interference term is neglected.

The differential cross-sections for the processes c~p —► So —> u X and c~p —> .S'| —> u X

are identical. Similarly, the differential cross-sections for the processes c~p —* Vn —* v X

■’The only leptoquark production and decay channel simulated within PYTMA is r,~u — .% —* n~u. In order to generate So — v X events, e- u — So — e~u were generated and the final electron was changed to a neutrino prior to the detector simulation.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. u— l- iCL~Uci:,Lj i I l _ j i I i i i I i i i___ 0 0.2 0.4 0.6 0.8 I x

Figure 3.14 Generated (solid curve) and reconstructed (dashed curve) x distribution for 150 G eV/c2 Sq leptoquarks decaying into i/X.

and e~p —> V\ —► v X are the same. Hereafter, any result given for Sq (Vq) leptoquarks

also applies to Si (Vi) leptoquarks.

Charged current deep inelastic scattering events are generated with the HERACLES

generator [70] coupled to ARIADNE [71]. ARIADNE simulates QCD cascades based

on the colour dipole model. QCD radiation is described as radiation from the colour

dipole formed between the struck quark and the proton remnant, an approach which

has been shown to agree well with the neutral current DIS data [72]. A total of 5000

charged current events were generated, with MT B i structure functions and including

leptonic initial state radiation. The total charged current cross-section, as calculated

with HERACLES, is 0.07 nb.

3.4.2 Trigger Acceptance and Selection Efficiency

The Monte Carlo simulation of the detector is done with MOZART, the trigger acceptance

is calculated with ZGANA, and the same filter program used for the data is used for the

Monte Carlo samples. The effect cf the detector simulation on the x distribution of

150 GeV/c2 scalar leptoquark events is shown in Figure 3.14.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84

The trigger acceptance as a function of leptoquark mass, for scalar and vector lepto

quarks, is shown in Figure 3.15. The acceptance is 70% to 90% for le p to q ua rk masses

between 50 G o V /c2 and 100 G eV /c2. For higher masses the acceptance is close to 100%.

The selection efficiency is shown in Figure 3.16. The efficiency ranges from 70% to 90%

for scalar leptoquarks with masses between 50GeV/c2 and 250GeV/c2. The efficiency

for vector leptoquarks is lower, ranging from 65% to S5%, with most of the inefficiency

being due to the vertex requirement.

The difference in efficiency between scalar and vector leptoquarks is explained by the

different kinematic y distributions of scalar and vector events. Scalar leptoquarks have a

fiat y dependence, while vector leptoquarks have a y distribution proportional to (1 — y)2,

as shown in Figure 3.17. The hadrons in low-y events tend to go in the forward direction

and, as a result, it is difficult to reconstruct tracks and vertices in those events. Consider

the case of 180 GeV/c2 vector leptoquarks. Out of 991 events left after the level three

filter requirements:

• 94 events (9%) have no tracks;

• 26 events (3%) have one or more tracks but no vertices;

• 79 events (8%) have a vertex but x 2/N d j > 10;

• 56 events (6%) have a vertex, and x 2/ ^ d f < 10, but \z\ > 75cm;

• 736 events (74%) have a vertex, x 2/N df < 10, and \z\ > 75 cm.

The trigger acceptance and selection efficiency for charged current DIS events is esti

mated to be 68%. The estimated background contribution from charged current events

to the data sample is therefore:

0.07 nb • 27.5 nb-1 • 68% = 1.3 events. (3.39)

The reconstructed x distribution of charged current DIS Monte Carlo data, after trigger

acceptance and selection efficiency, is consistent w ith the reconstructed x of the charged

current candidate, as shown in Figure 3.18.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S5

& 'j S? 0.75

0.5 6 P > S q > VX

o D A Yl □ LOW_REMC 0.25 a LOW_BEMC • Luminosity-Weighted Average

i i t i i i t . I 50 100 150 200 250 •> Leptoquark mass (GeV/c )

& u S£j 0.75

0.5 1 e p —> V0 -> V X

o D A Y l □ LOW_REMC 0.25 a LOW_BEMC • Luminosity-Weighted Average

i i i i I i ' ' ' I i i i i I ' i i i I 50 100 150 200 250 2 Leptoquark mass (GeV/c )

Figure 3.15 Trigger acceptance for S0 and V0 leptoquarks decaying into u X . (The statistical errors are smaller than the data points.)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S6

0.75 T

0.5 _ 6 p —> S q —* v X

" o Trigger □ pT > 10 G eV 0.25 ~ a Vertex a pT > 10 G eV (excl. islands)

0 1 1 1 1 1 ! ! 1 i 1 . 1 1 1 1 1 1 1 1 1 50 100 150 200 250 Leptoquark mass (GeV/c~)

I - ■2i T is, 0.75

0.5 1 e p - > V0 -¥ vX

o Trigger □ pT > 10 G eV 0.25 ~ a Vertex • pT> 10 GeV(excl. islands)

i i i i I l 1 I I I t t l r I I I I I 50 100 150 200 250 Leptoquark mass (GeV/c )

F ig u re 3.16 Selection efficiency for So and V0 Ieptoquarks decaying into u X . (The statistical errors are smaller than the data points.)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.17 Generated y distributions for 180GeV/c‘ scalar and vector LQ — uX events. The dashed curves are the functions f(y) = 1 and f(y) — (1 — y)2 normalized to the Monte Carlo data.

I 10 ■3 ■2 l 10 10 10

Figure 3.18 Reconstructed x distribution after data selection for the data (solid circle) and charged current DIS Monte Carlo (dashed histogram). The Monte Carlo has been normalized to the integrated luminosity of the data.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ss

3.5 Kinematics of the Charged Current Candidate

The reconstructed kinematic variables of the charged current candidate are

pT = 31..5 GeV, (3.40)

x = 0.31, (3.41)

y = 0.41, (3.42)

Q 2 = 11000 G eV2. (3.43)

One can estimate the true kinematic variables using the scalar leptoquark Monte Carlo

samples, which have an approximately flat generated y distribution, and a narrow gen

erated x distribution centred around x = tti2Lq / s . The event sample generated with

iu lq = 180 GeV/c2 is best suited here since it corresponds to a generated x of 0.37 and

a reconstructed x of about 0.21 to 0.31. The shifts and resolutions in px, x, y , and

Q 2 as a function of reconstructed y, after data selection, are shown in Figure 3.19. For

1UB — 0.41, one obtains:

[T T tru e ~ PT)) / PT true = 15% ± 10% (3-44)

(x iruc — x JB ) / x truc. = 30% ± 19% (3.45)

(ytrue-yjB)lytrue = -3% ± 34% (3.46)

( Q L e - Q j B ) / Q l u e = 29% ± 18% (3.47)

Hence, the estimated true values for the charged current candidate are

pT = 96 ±10 GeV, (3.48)

x = 0.44 ±0.08, (3.49)

y = 0.40 ±0.14, (3.50)

Q2 = 16000 ±3000 GeV2. (3.51)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. erdcdwt priso o h cprgt we. ute erdcin rhbtd ihu permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced iue 3.19 Figure 8 e/2 6 180GeV/c2

Q2 shift (%) y shift (%) x shift (%) pTshift (%) ’n —► -50 -25 -50 -25 -25 -50 25 50 25 50 50 25 hfs n rsltos in resolutions and Shifts 0 0 0 02 . 06 . 1 0.8 0.6 0.4 0.2 0 02 . 06 . 1 0.8 0.6 0.4 0.2 0 02 . 06 . 1 0.8 0.6 0.4 0.2 0 02 . 06 . 1 0.8 0.6 0.4 0.2 0 X v events. ■ ' 1 i! ; i l n i ! 111 ■r ' i ' y t.t >' T x y, x, pT, >' b j b j yJB | ,Q ^ ? • .5 Si "5 ,5 S. "5 si Cl § c ^ £ 5 K 40 30 50 20 40 50 50 30 30 40 20 10 40 50 20 30 20 10 10 10 0 0 0 and and 0

02 . 06 . I 0.8 0.6 0.4 0.2 0 02 . 06 . I 0.8 0.6 0.4 0.2 0 02 . 06 . I 0.8 0.6 0.4 0.2 0 02 . 06 . I 0.8 0.6 0.4 0.2 0 2 Q as a function o f reconstructed reconstructed f o function a as I ! 1 ! 1 1 ! 1 I I I I I ' ' I I 'I I ' y'jn y , for for , 89 Chapter 4 Limits on Leptoquarks

4.1 Limit Calculation

One event remains aftei the data selection process described in Chapter 3, which is

consistent with the estimeted 1.3 events expected from charged current deep inelastic

scattering. Since there are no leptoquark signals, lim its on scalar and vector leptoquark

cross-sections and couplings have been calculated. They are presented in this chapter.

Firstly, the reconstructed leptoquark mass distribution, m rcc, is plotted and fitted to

a Gaussian distribution for each separate leptoquark Monte Carlo sample. Note that

m rcc = \ A JB' where x j b is kinem atic x reconstructed with the Jacquet-Blondel

method and corrected for the event vertex. The means (ft) and standard deviations

(a ) of the Gaussian distributions, as a function of generated leptoquark mass, are shown

in Figure 4.1.

Secondly, the means are fitted to first-order polynomials in m,LQ and the standard

deviations are fitted to second-order polynomials in t t i l q . The results of the fits are:

f i( m LQ ) = -4 .1 -(- 0.876 • m L Q , (4.1)

v(m LQ ) = 5.3 + 0.042 • + 0.000096 • m ^Q, (4.2)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91

250 30 § % o 200

■a 150 Siu

100 10

0 0 0 100 200 0 100 200 Leptoquark mass (G eV/c) Leptoquark mass (CeV/c~)

250 30 § o 200 53 ,3 5 20 "s3 150 "3

U 100 schJ ,0

0 0 100 200 0 100 200 Leptoquark mass (GeV/c ) Leptoquark mass (GeV/c")

Figure 4.1 Mean reconstructed leptoquark mass and mass resolution as a function of gen erated mass for scalar (top plots) and vector (bottom plots) leptoquarks. The curves show the parameterized fits to the Monte Carlo data points. The statistical errors on the mean reconstructed mass are smaller than the data points.

for scalars, and

K m LQ) = —3.8 + 0.933 • mLQ, (4.3)

for vectors. In the above four equations, /z, cr, and are expressed in GeV/c2. The fits

are shown as curves in Figure 4.1. The reconstructed masses of scalar (vector) leptoquarks

are 12% (7%) smaller than the generated masses.

Thirdly, a search region as a function of leptoquark mass is defined as ±

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92

%cr(mLQ). This search region is chosen such that if there was a leptoquark signal to

observe at it would be visible within this window. The overall efficiency, after trigger

acceptance, filter selection, and the requirement that the reconstructed leptoquark mass

is w ith in 3<7 of /r, is calculated for each leptoquark Monte Carlo sample. The overall

efficiencies as a function of leptoquark mass are shown in Figure 4.2. For leptoquark

masses between 50 G eV /c2 and 225 G e V /c 2, the overall efficiency is 70% to 80% for

% —»■ v X , and 60% to 85% for Vo —> u X . The efficiencies are fitted to a fourth-order

polynomial in ttilq. Those are shown as curves in Figure 4.2.

Upper lim its on the leptoquark cross-sections, as a function of leptoquark mass, are

calculated using the lim it expression for Poisson statistics in the presence of background

given in Appendix A. For ttilq ranging from 50GeV/c2 to 225GeV/c2, the number of

observed data events and the number of expected charged current DIS background events

inside the search region, i.e., with

u{m LQ) - Za-{miQ) < m TCC < n{m LQ) + 3c r ( m L Q ) , (4.5)

are counted. The 95% confidence level (C.L.) upper lim its on the leptoquark contribution

are then calculated using Equation A .15. The parameterized efficiencies, along with

the integrated luminosity of the data, are then used to calculate an upper lim it on the

leptoquark cross-sections: $lim it Glimit — 7 “ e • L

The theoretical So (Vo) leptoquark cross-section, as a function of leptoquark mass, is

calculated using the PYTHIA (COMPOS [73]) Monte Carlo program. The cross-section

calculation includes leptonic initial state radiative corrections, ignores the leptoquark-DlS

interference term, assumes an LQ - * v X branching fraction of 1/2, assumes a coupling

Af, = 0.31 (the electroweak coupling strength), and uses the MT B l parton distribution

functions. The cross-section is calculated for different ttilq values (in steps of about

25 GeV/c2). For masses between these values, the cross-section is interpolated assuming

an exponential behaviour for the cross-section.

Finally, upper lim its on the leptoquark couplings, as a function of ttilq, are calculated

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o Trigger- 0.25 ~~ • Trigger and filter ■ Trigger, filter, and mass requirement

_] I I I I I I I I I I I L. 50 100 150 200 250 Leptoquark mass (GeV/c‘ )

0.75

0.5 - _ e p — > V q — > vX

o Trigger 0.25 - • Trigger and filter m Trigger, filter, and mass requirement

100 150 200 250 Leptoquark mass (GeV/c. f 2,)

Figure 4.2 Overall efficiency for So and V0 leptoquarks decaying into u X . (The statist errors are smaller than the data points.)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94

using

A,,w,=0.31.p^. (4.7) Y crAi =0.31

Before showing the limits, the question of systematic errors is addressed in the following

section.

4.2 Systematic Checks

In the present analysis, systematic uncertainties are due to the integrated luminosity,

the theoretical leptoquark and charged current cross-sections, and the leptoquark effi

ciency. The error on the integrated luminosity is 6% (see Section 3.2.7). Comparisons of

the leptoquark cross-sections calculated with COMPOS, LQUARK, and PYTHIA, show

variations of 6% [74]. The interpolation of the cross-sections to different m iQ values

introduces an additional error of 4%. The overall uncertainty on the leptoquark cross-

sections is therefore estimated to be 7%. The uncertainty on the charged current DIS

cross-section is due to the choice of the structure function parameterization. Comparing

different parameterizations (e.g., MRS DO, MRS SO [75], M T B l, MT Si [32], and GRV

HO [76]) gives an estimated uncertainty of 6%.

The uncertainty on the leptoquark efficiency can be divided into uncertainties on

the trigger acceptance, the efficiency of the background rejection criteria (calorimeter

time, etc.), the vertex efficiency, and the fit of the overall efficiency. The uncertainty

on the calorimeter energy scale can affect the overall efficiency, via the p r > 10 G eV

and ij j b < 1 requirements, but it can also affect the reconstructed leptoquark masses

and consequently, the limits on leptoquark couplings and masses. This uncertainty is

considered in Section 4.3.

Trigger Acceptance

The SLT and TLT are expected to be close to 100% efficient for physics events collected

in 1992. The main trigger inefficiency (and uncertainty) comes from the CAL FLT. The

CAL FLT simulation within ZGANA does not take into account trigger towers which were

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95

niLQ (G eV /c2) Correction 50 -4.8% too -3.2%

120 -1.5%

150 - 1.2 %

180 - 0 .8 %

220 -0.4% 280 -0.4%

Table 4.1 Correction to the CAL FLT trigger acceptance clue to dead channels, for — v X events.

dead at some point during the running period. These dead channel effects arc*, however,

simulated with a standalone program. Samples of scalar leptoquark events have been

processed with this program [77] and the results are listed in Table 4.1. The correction

to the trigger acceptance ranges from —4.8% for 50GeV/c2 leptoquarks to —0.4% for

2S0 GeV/c2 leptoquarks.

Background Rejection Criteria

The calorimeter time rejection algorithms are not performed in the selection of the Monte

Carlo data, but are expected to be over 99.5% efficient [Go]. The other background

rejection criteria, such as spark rejection and cosmic rejection, are applied to the Monte

Carlo data.

Vertex Efficiency

A study of the efficiency of the vertex requirement was performed with a neutral current

DIS data sample in which the scattered electron is emitted very close to the RCAL beam

pipe (and hence is not expected to produce a track in the CTD). The data sample was

obtained by filtering a fourth of the 1992 data (7 nb-1) using the following requirements:

• Same requirements as in the level one, level two, and level three charged current

filters (cf. Sections 3.3.1 to 3.3.3), with the exception of the p r > 10 GeV require-

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96

ment.

• Require CTD on.

• Require less than 5 GeV of energy in the electron calorimeter of the luminosity

monitor (to reject photoproduction events).

• Require the events to occur in one of the nine buckets with colliding bunches.

• Events must not be rejected with the calorimeter time criteria of the level four

charged current filter (cf. Section 3.3.4).

• The quantity 8 = C — pz, where E and pz are the total calorimeter energy and total

calorimeter energy in the ^ direction, respectively, must be between 35 GeV and

60 GeV. This criterion selects neutral current events, for which 8 should be about

twice the initial electron energy (2 x 26.7 GeV), and it rejects photoproduction and

other backgrounds.

• Events are required to have an electron found with the EEXOTIC electron finder

[61]. with energy greater than 5 GeV and with measured position at least 6 cm away

from the beam pipe, i.e.,

|ar| > 16 cm OR |t/|>16cm. (4.S)

The last requirement is to ensure that the electron energy and position are well-

measured and are not affected by energy leakage into the beam pipe.

• In order for the vertex efficiency to be due solely to the jet particles, the electron

is required 1 0 be in the RCAL, with position

|a:|<25cm AND |yl<25cm. (4.9)

The above criteria lead to a data sample of 566 events. The backgrounds in the sample

are expected to be small: about 2% e-gas, very little photoproduction, and negligible

p-gas [61].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97

Neutral current Monte Carlo events were generated with the HERACLES Monte Carlo

program coupled to ARIADNE. The sample includes radiative corrections and uses the

M T B1 structure functions. The Monte Carlo events were weighted according to the

vertex distribution of the data sample (as calculated from the C5 electron and proton

times for the appropriate runs). A total of 11531 Monte Carlo events were processed

through the ZGANA simulation and through the data selection requirements described

earlier, after which 2970 events remained.

The efficiency of the vertex requirement

X 2/ N df < 10 A N D |s| < 75cm (4.10)

for the neutral current data was compared with the efficiency of the same requirement,

for neutral current Monte Carlo events. The vertex efficiency is plotted as a function as

Qman where 6max is the polar angle of the calorimeter island with largest polar angle1.

The variable 0max indicates where there is activity in the calorimeter and therefore where

there should be CTD tracks. One expects the vertex efficiency to be large for large 0mnx

values and small for small 6max. The results are shown in Figure 4.3. For 0max > 80°,

the vertex efficiency is lower for the data than for the Monte Carlo by about 5%. This

is consistent with the vertex efficiency study performed in [78]. For 0max < 60°, the

efficiency is higher for the data by 5% to 20%. This last result is not well understood

but can conservatively be ignored.

Fit Procedure

The overall efficiencies for each leptoquark Monte Carlo sample (solid squares in Fig

ure 4.2) are all within 2% of the fitted efficiencies (curves in Figure 4.2). The uncertainty

due to the efficiency fit is estimated to be 2%.

1Only islands with energy greater than 1 GeV and with polar angle less than 167° are considered. The latter criterion is to exclude islands associated with the scattered electron.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98

0.8

0.6

0.4

0.2

0 50 100 150

0 mnt (degrees)

F ig u re 4.3 Vertex efficiency versus 6max for neutral current DIS Monte Carlo (dashed his togram) and data (solid circles).

Overall Uncertainty on Efficiency

The uncertainties on the trigger acceptance, on the efficiency of the background rejection

criteria, and on the efficiency of the vertex requirement are added linearly. They are then

added in quadrature with the uncertainty on the efficiency fit. This leads to an overall

uncertainty of +2% /—10% on the efficiency. For a breakdown of the uncertainties, see

Table 4.2.

The uncertainty on the efficiency, the uncertainty on the luminosity, and the uncer

tainty on the leptoquark cross-sections are added in quadrature and lead to an overall

uncertainty of +9% /—14%. The overall uncertainty on the efficiency of the charged

current DIS background is estimated to be +6% /—13%.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99

Description Systematic Error

Leptoquark efficiency + 2 %/- 10% Trigger acceptance -4% Background rejection -0.5% Vertex requirement -5%

F it ± 2 %

Luminosity measurement ± 6 % Leptoquark cross-section ±7% + 9 % /-14 %

Table 4.2 Estimated systematic errors.

4.3 Results

The 95% confidence level upper lim its on the cross-sections and on the couplings of the

So and Vo leptoquarks, and of course S i and V j, are calculated as described in Section 4.1.

The limits are then recalculated taking into account systematic errors:

• The estimated number of charged current DIS background events is reduced by

13%.

• Since the lim its on the leptoquark cross-sections depend on the product L • c, the

overall leptoquark efficiencies entering the calculation of those lim its are reduced

by 12%.

• Since the lim its on the leptoquark couplings depend on the product a • L • c, the

overall leptoquark efficiencies entering the calculation of those lim its are reduced

by 14%.

The limits on the cross-sections, with and without systematic errors, are shown in Fig

ure 4.4. The kinks in the lim it curves are due to the charged current candidate entering

the search region. The lim its on the couplings are shown in Figure 4.5. For a coupling

\ L = 0.31, the 95% C.L. lower lim it on the leptoquark mass is 154 GcV/c2 for scalars

(So and Si) and 108GeV/c2 for vectors (Vo and Vi).

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0.5

o•*» •5 0.4

i -

0.2

0.1

100 150 200 *» Leptoquark mass (GeV/c')

0.5

0.2

0.1

100 150 200 2 Leptoquark mass (GeV/c )

Figure 4.4 95% confidence level upper limits on the cross-sections times branching fraction of So and 5 1 (top plot), and Vn and V\ (bottom plot) leptoquarks. The dashed curves do not include systematic errors; the solid curves do.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 101

I e~p -» S0 -» v X 0.8

0.6

0.4

0.2

100 150 200 Leptoquark mass (G eV/c2)mass

0.8

0.6

0.4

0.2

0 50 100 150 200 2 Leptoquark mass (G eV/c )

F ig u re 4.5 95% confidence level upper lim its on the couplings XL o f S0 and Si (top plot), and V0 and (bottom plot) leptoquarks. The dashed curves do not include systematic errors; the solid curves do. For a branching fraction B = B r(LQ -* e ~ X) other than 1/2, the ordinate of the curves should be multiplied by [4B(1 — B )]~ ^ 2.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102

4.3.1 Effect of the Background Subtraction on the Limits

The dominant electron-proton background to LQ —► u X events is charged current deep

inelastic scattering and only this process was taken into account in the calculation of

the icptoquark limits. The number of neutral current DIS events expected after the

requirements p r > 10GeV, vertex with \z\ < 75cm, and p j > 10GeV after vertex

correction, as estimated using Monte Carlo events generated with HERACLES, is 0.3

where the error is statistical. Minimum bias resolved photoproduction events have been

simulated with PYTHIA. No events are left after the requirement p? > 10 GeV, which

leads to an upper lim it of 2.9 events at the 90% C.L.

Not including neutral current DIS and photoproduction backgrounds leads to a more

conservative lim it. The effect of not doing any background subtraction is to raise the

coupling limits by less than 5% for scalar leptoquarks, and less than 2% for vector

leptoquarks.

4.3.2 Effect of the Structure Functions on the Limits

The structure functions used throughout this analysis are M T B l. Using the PDFLIB

package [79], one can reweight the lim its for a different set of structure functions using

the approximation I n P D F \PDF \MTB1 9______n \ /'/imx'£ — ” limit y q M T B l'

where q is the u-quark (for scalars) or d-quark (for vectors) parton distribution function

evaluated at x = m ^g /s and Q 2 = m 2Lq. For example, with the GRV HO structure

functions, compatible with the latest structure function measurements at HERA [80],

the coupling lim its would change by —3% to +8% over the range of masses 50 GeV/c2

to 215 G eV/c2 for scalars, and by —S% to —4% over the range of masses 50 GeV/c2 to

150 G e V /c 2 for vectors.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103

4.3.3 Effect of the Energy Scale on the Limits

Comparison of the calibration of the calorimeter energy using halo muons and using

cosmic muons shows differences of at most 4%[Si]. These differences are attributable

to the higher momentum of the halo muons. Comparison of the electron energy in

neutral current DIS data and Monte Carlo shows a discrepancy of about 5% [61]. This

discrepancy is believed to be due to inactive material not being properly modeled in the

Monte Carlo.

The effect of a ±5% miscalibration of the Monte Carlo calorimeter energy scale on

the coupling lim its was studied. A shift in the energy scale would affect variables such

as reconstructed p r and yjBi which are used in the selection of the Monte Carlo data. It

would also modify, via shifts in x j b , the parameterized means and standard deviations

for the reconstructed leptoquark masses. The effects of a shift E —» E(l + 8) in the

energy scale on the variables pr, t/jg, xjb, and Q2B are

PT -> pr(l + <$), (4.12)

V j b yjB{l + °), (4.13)

xjb xjb 1 + (4.14) 1 -V j b ( 1 + < $ )

2 < 5 (1 + *) Qj 2 b Q JB 1 +<5 + (4.15)

The analysis of the leptoquark and charged current DIS Monte Carlo data was redone

with a —5% shift ir. the Monte Carlo energy scale:

• The calorimeter energies were shifted by —5% in the Monte Carlo data.

• The new reconstructed leptoquark masses, after trigger acceptance and data selec

tion, v/ere fitted to Gaussian distributions.

• The means and standard deviations were in turn fitted to first- and second-order

polynomials.

• The overall efficiencies, after trigger acceptance, data selection, and 3

quirement, were calculated and parameterized.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104

• The number of background events in each search region was recalculated.

• Limits on the couplings were recalculated (taking into account systematic errors).

The above procedure was repeated for a shift in the energy scale of +5%.

The limits on the leptoquark couplings calculated in this manner are shown in Fig

ure 4.6. The effect of a ±5% shift in the Monte Carlo energy scale is a :p5% shift in the

position of the kink in the lim it curve for scalars. The coupling lim it for scalars, away

from the kink, is shifted by less than ±3%. For vectors, the effect on the lim it is less

than ±2% .

4.4 Conclusions

In this thesis, So, Si, Vo, and V) leptoquarks decaying into v X have been searched for

in a sample of events collected with the ZEUS detector in 1992 and corresponding to an

integrated luminosity of 27.5 nb-1. One event is left after the filter selection and scan

procedure, consistent with the 1.3 events expected from charged current DIS background.

The overall efficiency for scalar leptoquarks, after trigger acceptance, data selection, and

3it leptoquark mass requirem ent, is 70% to 80% for le ptoquark masses in the range

50 GeV/c2 to 225 GeV/c2. The overall efficiency for vector leptoquarks is 60% to S5% for

the same mass range.

The upper limits on leptoquark Yukawa couplings versus leptoquark mass shown in

Figure 4.5 extend the region already excluded by collider experiments. Assuming an

electroweak coupling (A^, = 0.31) and a leptoquark branching fraction into electron plus

jets, £?, of 0.5, the 95% C.L. lower lim it on the leptoquark mass is 154 GeV/c2 for 5’o

and Si leptoquarks and 108 GeV/c2 for Vo and Vi leptoquarks. The limits calculated in

this thesis are compared with other lim its from collider experiments in Table 4.3. These

results complement the lim its calculated from rare processes at low-energy.

Scalar and vector leptoquarks have also been searched for in a sample of e~p —> e ~ X

events collected in 1992 with the ZEUS detector via the LQ —» e ~ X channel [82, 74].

This channel enables one to probe all possible leptoquark species. No leptoquark signals

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0.8

0.6 Energy scale *0.95 Energy scale * 1.00 Energy scale *1.05 0.4

0.2

50 100 150 200 Leptoquark mass (GeV/c )

0.8

0.6

0.4 — Energy scale * 0.95 Energy scale * 1.00 0.2 Energy scale * 1.05

50 100 150 200 Leptoquark mass (GeV/c )

Figure 4.6 Effect of a ±5% shift in the energy scale on the coupling limits \L of Sa and ,S'| (top plot), and VQ and Vi (bottom plot) leptoquarks.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106

95% C.L. Lower Lim it on the Leptoquark Mass Leptoquark B Other Experiments This Analysis So, St 0.05 44 GeV/c- (LEP) 98 GeV/c2, for XL = 0.31 Soi -Si 0.5 120 GeV/c2 (DO) 154 GeV/c2, for XL = 0.31 Vo, v, 0.5 120 GeV/c2 (CDF) 108 G eV/c2, for XL = 0.31

Table 4.3 Summary of the results.

were found and limits on leptoquark masses and couplings were presented. The HI

collaboration has also searched for leptoquarks decaying into e~ X and v X in a sample of

‘24 nb-1 collected in 1992 [S3], and their results are comparable to the results from ZEUS.

Since 1992, which was the first year of data taking at HERA, there has been a large

increase in luminosity and the quality of the beams and performance of the detectors have

improved. This will lead to more stringent limits on leptoquark masses and couplings,

which will be published in the very near future [84], Furthermore, the HERA experiments

will eventually be able to probe leptoquark masses well above the kinematic lim it of

y/s = 296 GeV by looking for effects from the virtual exchange of leptoquarks [85].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix A Upper Limit Calculation

When a search for a particular signal is inconclusive, for instance when the data collected

are consistent with estimated backgrounds, an upper lim it on the signal cross-section can

be calculated using Poisson statistics [29]. If the signal and background cross-sections, <7 ,

and (7ft, were known, then the number of observed events would be expected to follow a

Poisson distribution with mean s + b, where s and b are the mean signal and background

contributions:

s = cr, • cs • L, (A . I)

b = (Xb-Cb-L. (A .2)

es and e& are the signal and background efficiency, and L is the integrated luminosity.

The probability of observing N events would therefore be given by

P(s + b,N) = ^ e -^ +bHs + b f. (A .3)

In practice, one counts the number of events in a sample, estimates the background

contribution to that sample, and calculates an upper lim it on the signal contribution.

Assuming a uniform probability density function for s before the experiment, the proba

bility density function for s after the experiment, g{s), is proportional to P{s + b, iV ) [86].

107

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Hence,

(A .4)

where A is a normalization factor such that

/•oo / <7(s) ds 1. (A .5) Jo

The probability that s is less than an upper lim it s0 is called the confidence level and is

given by

r^Q C = I g{s)ds, (A .6)

(A .7) r h c~t'*t>{s+bfds

The integral

(A.S)

can be solved as follows [87]:

3 0 + 6 1 e~l tN dt , (A .9 ) I m

— [ e~l l N (A .10) Nl I r-r--"w-4 (A .11)

3 0 + 6 1 Y' g -« ^ - n ) (A .12) 6 N = E "7 (e"66n-e-^+6)(5o + 6)n) ( A .13)

n = 0 71 •

In the lim it s —> oo: N (A .14) 7 ^ E r? e" ‘ i,n- n±Tn = 0 n\

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The confidence level C can therefore be written as

£ ie-^+6>(*0 + &r c = . (A. 15) ;V i V - i e - 6 bn t u «!

The 95% confidence level upper lim it on the signal contribution is obtained by sub

s titu tin g C = 0.95 in Equation A. 15 and solving numerically for .su. This lim it on s can

be converted into a lim it on the signal cross-section using Equation A .I.

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