Search for Leptoquarks in Electron-Proton Collisions · 2016. 11. 24. · 1.6 Electron-proton deep...

Search for Leptoquarks

in E lectron-Proton C ollisions

by

Frederic Benard

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Graduate Department of Physics University of Toronto

Copyright © 1995 by Frederic Benard

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

Search for Leptoquarks in Electron-Proton Collisions

by

Frederic Benard Graduate D epartm ent o f Physics

U n ive rs ity o f Toronto

Ph.D . 1995

A b stract

Leptoquarks carry lepton num ber as w e ll as baryon num ber and could provide an

explanation fo r the observed sym m etry between the quarks and leptons. Leptoquarks

coupling to first-generation quarks and leptons were searched for in e lectron-pro ton co lli

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

to an in tegra ted lum inos ity of 27.5 nb-1 , no leptoquark candidates were found. L im its

on leptoquark couplings are derived for lep toqua rk masses ranging from 50 G eV /c2 to

225G eV /c2. Scalar (vector) isosinglet lep toquarks coupling to a le ft-handed electron

and a tz-quark (d-quark) w ith electroweak coup ling strength are ru led out a t the 95%

confidence level for masses below 154 G e V /c 2 (108 G eV /c2).

i i


Acknowledgem ents

I am very grate fu l to m y supervisor, David Bailey, for his enthusiasm, his patience,

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

part o f the ZEUS T h ird Level Trigger group has been an exc iting and enriching adventure.

I am indebted to Robert O rr, Sampa Bhadra, D inu Bandyopadhyay, and Gerd H artner,

as well as the students on the pro ject: Frank, M ike , Cortncy, and Richard. I wish

to thank the members o f the ZEUS Exotics physics group, in pa rticu la r Frank S c iu ll’-,

Steve R itz , Bruce S traub, and Jurgen Schroeder. I also wish to thank Sacha Davidson for

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

many drafts o f the thesis and th e ir comments and suggestions have been invaluable. In

add ition , the ir questions prepared me well for my P h.D . defences.

The Canadian ZEUS group a t DESY, under the leadership o f John M a rtin , provided

in te llec tua l and social support du ring m y stay in H am burg. In add ition to the aforemen

tioned ZEUS members, I would like to thank M ilos, B u rkha rd , Wai, Laurel, and Larry.

I thank my friends, Sophie, Frederic, Jason, Charles. M ieke, Heather, Lysiane, Thom as,

and Robert, w ith o u t the support o f whom I would have had d iffic u lty m a in ta in ing my

san ity during the last five years. The support o f Charles, Heather, and Robert th is last

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

mon pere Raymond pou r leurs encou-agements et leu r am our. F ina lly , I would like to

thank Jonathan for his trem endous support, for his love, and for having waited for me

so long in ra iny H am burg w hile I finished m y thesis in Toronto.

ii i


P e rso n a l C o n tr ib u t io n s to th e Z E U S E x p e r im e n t

I jo ined the ZEUS T h ird Level Trigger group in the fall o f 1989. D uring the fo llow ing

two years I was involved w ith M on te Carlo trigger studies. I also set up and m aintained

a netw ork o f five com puter workstations used by T L T members at the U n ivers ity o f

Toronto.

I moved to Hamburg in the spring o f 1991. As a m em ber o f the T L T group, I

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

In pa rticu la r, I interfaced various versions o f the V C T R A K tra ck reconstruction p r ^ ra m

to the T L T environm ent. I also set up a large network o f com puter workstations cu rren tly

used by the Canadian ZEUS group in Hamburg. In 1992, I con tribu ted to the conception

and development of Funnel, the p la tfo rm now used for a lm ost a ll ZEUS M onte Carlo

event generation.

I jo ined the ZEUS Exotics physics group in the fa ll of 1991 and over the fo llow ing two

years made many contribu tions to tha t group. The firs t collisions were provided by the

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

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

helped design crite ria to select the deep inelastic charged curren t data. I also studied

the effects o f trigger acceptance, je t reconstruction, and tra ck and vertex reconstruction.

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

work o f '.he Exotics physics group led to the publica tion “ Search fo r Leptoquarks w ith

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

iv


C ontents

Introduction 1

1 T heoretical Framework 3

1.1 The S tandard M o d e l ................................................................................................... 3

1.2 Leptoquarks Beyond the Standard M o d e l............................................................. 6

1.2.1 G rand U n if ic a tio n ............................................................................................ 0

1.2.2 T e ch n ico lo u r................................. 7

1.2.3 Compositeness ................................. 8

1.3 A M odel Independent A p p ro a c h .............................................................................. 0

1.4 E xperim en ta l L im its on L e p to q u a rk s .................................................................... 9

1.4.1 Searches in E lectron-Positron C o llis io n s .................................................. 9

1.4.2 Searches in P ro ton -A n tip ro ton C o llis io n s ....................... 12

1.4.3 Lep ton ic Pion D ecays ..................................................................................... 13

1.4.4 U n ita r ity o f the C K M M a t r i x .................................................................... 15

1.4.5 A tom ic P a rity V io la t io n ............................................................................... 10

1.5 K inem atics o f E lectron-P ro ton S c a tte r in g ............................................................. 18

1.6 Lep toquark P roduction and Decay at H ER A ................................................... 20

2 E xp erim en ta l Setup 27

2.1 The H E R A E lectron-P roton C o l l i d e r .................................................................... 27

v


2.2 The ZEUS D e te c to r ...................................................................................................... 30

2.2.1 O verview .......................................................................................................... 30

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

2.2.3 Centra l Tracking D e te c to r ........................................................................... 37

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

2.2.5 Lum inos ity M on ito r ...................................................................................... 39

2.3 The ZEUS Trigger and Data A cqu is ition S y s te m ................................................. 40

2.3.1 C o n cep ts .............................................................................................................. 40

2.3.2 F irs t Level T r ig g e r ......................................................................................... 42

2.3.3 Second Level T r ig g e r ...................................................................................... 43

2.3.4 T h ird Level T r ig g e r ......................................................................................... 44

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

2.4.1 Event R e co ns tru c tio n ...................................................................................... 4S

2.4.2 O ffline A n a ly s is ................................................................................................ 49

3 D ata A nalysis 52

3.1 Description o f the P ro b le m ......................................................................................... 52

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

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

3.2.2 Track and Vertex R e c o n s tru c t io n ............................................................. 57

3.2.3 C a lo rim ete r T im e ............................................................................................. 59

3.2.4 C a lo rim ete r Energy Islands ........................................................................ 60

3.2.5 M uon F in d e r .................................................................................................... 64

3.2.6 Reconstruction of K inem atic V a r ia b le s ................................................... 66

3.2.7 Lum ino s ity C a lc u la tio n ................................................................................... 67

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

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

3.3.2 The Level Two F i l t e r ..................................................................................... 70

3.3.3 The Level Three F i l t e r .................................................................................... 71

3.3.4 T he Level Four F i l t e r ..................................................................................... 73

v i


3.3.5 The Level F ive F i l t e r .................................................................................... 7-1

3.3.6 F ina l Data S a m p le ....................................................................................... 77

3.4 M onte Carlo S im u la t io n ........................................................................................... 82

3.4.1 Event G e n e ra tio n ............................................................................................ 82

3.4.2 Trigger Acceptance and Selection E f f ic ie n c y ........................................ 33

3.5 K inem atics of the Charged C urrent C a n d id a te ................................................... 88

4 L im its on Leptoquarks 90

4.1 L im it C a lc u la t io n ........................................................................................................ 90

4.2 System atic Checks ..................................................................................................... 91

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

4.3.1 Effect of the Background Subtraction on the L im i t s ........................... 102

4.3.2 Effect of the S truc tu re Functions on the L im its ................................... 102

4.3.3 Effect of the Energy Scale on the L i m i t s ............................................... 103

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

A U pp er L im it C alculation 107

R eferences 110

v ii


List o f Tables

1.1 Scalar and vector leptoquarks and th e ir couplings to quark-lepton pairs . 10

1.2 L im its on leptoquarks from rare processes at low -energy ................................. IS

1.3 P roduction and decay o f leptoquarks in e~p c o ll is io n s ..................................... 22

1.4 Leptoquark cross-sections a t H E R A ........................................................................ 24

2.1 H E R A beam p a ra m e te rs ............................................................................................. 31

2.2 Dimensions o f the ZEUS ca lo rim eter c e lls ............................................................. 35

2.3 C A L F LT trigger tower th resh o ld s ........................................................................... 43

3.1 Parameters used in the ca lo rim eter tim e a lg o r i th m s ........................................ 61

3.2 Integrated lum inosity used in the present a n a ly s is ............................................ 68

3.3 Level two calorim eter tim e re jection c r i t e r i a ...................................................... 71

3.4 Level three calorim eter t im e re jection c rite ria ................................................... 72

3.5 Level four calorim eter t im e re jection c r i t e r ia ...................................................... 73

3.6 Sum m ary of the data selection c r i t e r i a ................................................................. 78

3.7 Properties o f the five events rem ain ing a fter the level five selection require

ments .............................................................................................................................. 79

4.1 Correction to the C A L F L T trigger acceptance due to dead channels . . . 95

4.2 Estim ated system atic e r r o r s ...................................................................................... 99

4.3 Sum m ary of the re s u lts .....................................................................................................106

v ii i


List o f Figures

1.1 D iagram showing the in teraction of a quark, a lcpton, and a lep toquark . (i

1.2 The decay o f a leptoquark v ia the exchange o f an extended Lechnicolour

gauge b o s o n .............................................................................................................. 8

1.3 Lep toquark pair production in e+ e~ c o l l is io n s ..................................................... 11

1.4 Lep toquark pair production in pp c o llis io n s .......................................................... 12

1.5 The decay 7r+ —► e+ uc via the exchange o f an So le p to q u a rk .................. 15

1.6 E lectron-pro ton deep inelastic s c a t te r in g ..................................................... 19

1.7 D irec t and v ir tu a l p roduction o f So leptoquarks in e~p c o ll is io n s ........ 21

1.8 Lep toquark cross-sections at H E R A as a function of leptoquark mass . . 25

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

2.2 The H E R A in jection s y s te m ...................................................................................... 29

2.3 Integrated lum inos ity collected in 1992 as a function o f t i m e ............... 31

2.4 Section o f the ZEUS detector along the beam ................................................ 32

2.5 Schematic view o f an F C A L to w e r .......................................................................... 36

2.6 W ire layout in a 45° sector o f the C en tra l T racking D e te c to r ............... 38

2.7 L um ino s ity M o n ito r ............................................................................................... 40

2.8 The ZEUS trigger and data acqu is ition s y s te m ................................................. 41

2.9 Processors, data lin ks , and contro l lin ks in one branch o f the T L T . . . . 45

2.10 F C A L and R C A L tim e for physics and beam-gas e ve n ts ................................. 47

ix


2.11 Data flow of ZEUS data and Monte Carlo data in the offline environm ent 50

3.1 Event display o f a 150 G e V /c 2 S'o —> v X Monte C arlo e v e n t....... 53

3.2 C5 tim e d is trib u tio n for Run 4272 ......................................................................... 55

3.3 Overall vertex r d is tr ib u tio n from the C5 tim e in fo rm a tion , for the runs

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

3.4 Vertex fitt in g w ith and w ith o u t the beam line c o n s t r a in t .......... 58

3.5 Calorim eter t im e d is tr ib u tio n for Run 4272 ........................................................ 62

3.6 An example o f the ca lo rim eter island a lgorithm ............................................. 63

3.7 p r d is tribu tion for Run 4272 ................................................................................... 69

3.8 Vertex d is trib u tio n o f the data a fter me level fou r f ilte r c rite ria are applied 74

3.9 A z im u tha l angle versus pseudorapid ity o f highest E t is land, for events le ft

before the island p r re q u ire m e n t............................................................ 76

3.10 p r ca'culated using cells from islands w ith p < 3, fo r events entering the

level five f i l t e r ............................................................................................... 76

3.11 T im e difference between the two highest Et islands, fo r events le ft p rio r

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

3.12 Event display o f a cosmic muon e v e n t................................................ 80

3.13 Event, display o f the charged current c a n d id a te ............................... 81

3.14 Generated and reconstructed x d is trib u tio n for 150 G e V /c2 So leptoquarks

decaying in to v X ........................................................................................ 83

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

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

3.17 Generated y d is trib u tio n s for 180 G eV /c2 scalar and vector LQ —► v X events 87

3.18 Reconstructed x d is tr ib u tio n a fter data selection fo r the data and the

charged current DIS M onte C a r lo ........................................................ 87

3.19 Shifts and resolutions in p r , x , y, and Q 2 as a fun c tio n o f reconstructed y,

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

4.1 Mean reconstructed lep toquark mass and mass reso lution as a function of

generated mass for scalar and vector le p to q u a rks ............................ 91

x


4.2 Overall efficiency for L Q —► v X e v e n t s ...............................................................

4.3 Vertex efficiency versus 0mar for neutra l current deep inelastic scattering

Monte C arlo and data ...............................................................................................

4.4 Upper lim its on the cross-sections o f So, S i, V'o, and Vf leptoquarks . . .

4.5 Upper lim its on the couplings o f S0. S i, Vo, and \ \ le p to q u a rks .................

4.6 Effect o f a ±5% shift in the energy scale on the coupling l im i t s .................

X I


Introduction

ZEUS is one o f two large scale detectors at the H E R A electron-proton co llide r in Ham

burg, Germany. H E R A , which collides 26.7 G eV electrons w ith S20GeV protons, is an

ideal too l to s tudy the s tructure o f the p ro ton , as well as to search fo r new particles.

In pa rticu la r, lep toquark bosons, which ca rry b o th electric charge and colour, would

form an s-channel resonance and could be seen as a sharp peak in the x d is tr ib u tio n of

deep ine lastic scatte ring events at H E R A . The num ber o f leptoquark events produced

depends on the lep toquark mass and coup ling to quark-lepton pairs. I f th e ir coupling is

suffic iently large, leptoquarks w ith masses up to the k inem atic l im it (296 G e V /c 2) 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 w ith the ZEUS detector during

1992. T h is sample corresponds to an in tegra ted lum in o s ity of 27.5 nb_1. No leptoquark

candidates are found and lim its on lep toquark masses and couplings are derived.

Th is thesis is organized as follows. In C hapte r 1, various theoretical models p red ic ting

the existence o f leptoquarks are presented, cu rre n t experim enta l lim its on leptoquark

masses and couplings are reviewed, and the p roduc tion and decay o f leptoquarks at

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

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

a description o f the da ta reconstruction and selection processes, and deals w ith issues

1


concerning the M onte Carlo programs used in the analysis. The lim its on lep toquark

masses and couplings are presented in Chapter 4.


Chapter 1

T heoretical Framework

1.1 T he Standard M odel

A ll observed phenomena in e lem entary partic le physics are described by the so-called

Standard Model [1]. According to th is theory, a ll m a tte r consists o f po in tlike sp in-1/2

fcrm ions: quarks and leptons. Exclud ing g rav ita tion , which is o f neglig ib le strength at the

energies achievable by present-day accelerators, there are three fundam enta l interactions

amongst quarks and leptons: the weak force, electrom agnetism , and the strong force.

These forces are described b y local gauge symm etries and are m ediated by vector gauge

bosons. The quarks experience all three forces while the leptons on ly partic ipa te in the

weak and electromagnetic in teractions.

The Standard Model is the com bination o f the Glashow-W einberg-Salam m odel [2]

w ith the theory o f Quantum Chrom odynam ics [3]. I t is based on the gauge group SU(3)<g>

SU(2) ® U ( l) . The G lashow-W einberg-Salam model, based on the gauge group SU(2) ®

U ( l) , provides the description for the weak and e lectrom agnetic interactions. In th is

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 w h ile leaving the

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

Q uantum Chromodynamics is the fie ld theory o f the s trong force, and i t is based on an

exact SU(3) sym m etry acting on the quark colour indices. The strong force is m ediated

3


4

by e ight massless gluons, which are themselves coloured.

The known fermions are usually grouped in to three fam ilies:

leptons

quarks C)U r , d'R

"*« \

/ ' I /

! lr

C)cRi s'n I n • b'n

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

s' = vcd VC3 vcb s

u > \V td Vta V t J \ b j

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

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

v ia the Cabibbo-Kobayashi-Maskawa (C K M ) m a trix [5]:

( l . l )

U n til recently, the i-quark had no t been observed, but its existence was suggested, for

exam ple, by the absence of flavour changing neutra l currents. Recent evidence [()] suggests

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

The S tandard M odel has lead to a num ber o f predictions which have since been con

firm ed experim enta lly : weak neu tra l cu rren t interactions, the existence and the masses

o f the weak gauge bosons. I t is a theory free o f m athem atica l inconsistencies, and it

successfully describes a ll known facts o f e lem entary partic le physics. Nev irtheless, many

physicists do no t believe tha t the Standard Model is the u ltim a te theo ry because i t leaves

several questions unanswered, some o f w h ich are the follow ing:

• The theo ry has a large num ber o f a rb itra ry parameters. There are three gauge

couplings, two CP v io la ting 0 parameters for the SU(2) and SU(3) subgroups, two

param eters for the Higgs p o te n tia l, ten parameters for the qua rk mass m a trix (six

masses, three m ix ing angles, and one CP v io la ting phase), and three charged lepton

masses. I f the neutrinos are massive, one m ust include seven add itio n a l parameters.


5

• Some quantities, such as the ra tio o f the neutrino masses ( i f non-zero) to other

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

mass scale o f strong interactions ( i\ q c d ) compared to the IF * mass, and the 0

parameters, are surpris ing ly small.

• The Higgs mechanism requires unna tu ra l fine-tun ing of parameters. For instance,

rad ia tive corrections to the Higgs mass param eter /z2 are p ropo rtiona l to the square

o f a large cut-ofF param eter A in troduced in the process o f renorm aliz ing the theory:

/z2 —> /z2 + aA 2. (1.2)

The in it ia l value o f /z2 must therefore be chosen to cancel q A2 to great accuracy,

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

• The pa tte rn o f gauge groups is com plica ted and a rb itra ry . Moreover, the three fun

dam ental forces are not really un ified since there are s t il l three coup ling constants.

• The sym m etry between the quarks and leptons w ith respect to the electroweak

in te rac tion is surprising, and so is the existence o f three fam ilies o f ferm ions, w ith

iden tica l properties except for th e ir masses.

• In each fam ily , the quarks and leptons have equal and opposite con tribu tions to

non-renorm alizable divergencies associated w ith ferm ion triang le diagrams. The

con tribu tions cancel each other because the charges o f the ferm ions are related in

the form

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

However, th is re lationship between the quark and lepton charges is n o t a require

m ent o f the Standard Model.

• G ra v ity is absent from the theory.


6

L Q

e -

d, u, ..

F ig u re 1.1 Diagram showing the interaction of a quark, a lepton, and a leptoquark.

1.2 Leptoquarks B eyond the Standard M odel

In order to explain some o f the enigm atic features o f the S tandard Model, many a lte rna

tive theories have been developed. A num ber of these theories predict, or a llow for, the

existence of leptoquarks, spin-0 o r spin-1 particles which ca rry both electric charge and

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

three classes o f models w hich include leptoquarks (grand unified theories, tcchn ico lour

models, and composite models) are brie fly described.

1.2 .1 G rand U nification

G rand un ifica tion is a fram ew ork for the un ifica tion o f the weak, electrom agnetic, and

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

in a single group G, whose sym m etries become m anifest a t some very large energy scale.

A t th is un ifica tion scale, the three coupling constants associated w ith the e lem entary

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

arise from the spontaneous sym m etry breaking o f the underly ing group G.

G rand unified theories m ay res tric t some free param eters o f the Standard M odel, such

as the weak m ix in g angle s in2 6w and the ratios o f quark masses to lepton masses. Q uarks

and leptons usually share m u ltip le ts o f G, im p ly in g the quantiza tion o f the ferm ion

charges. I t is also n a tu ra l fo r these theories to conta in gauge or Higgs bosons w h ich

couple to both quarks and leptons, i.e., leptoquarks. These leptoquarks m ay v io la te


baryon num ber ( B ) and lepton num ber (L ) conservation and induce proton decay.

One a ttrac tive grand un ifica tion model is based on the gauge group SU(5) [8]. I t

is the simplest grand un ifica tion model w ith a single coup ling constant incorpora ting

SU(3) 0 S U (2 )0 U ( I ) . However, the value o f sin2 0\y in th is m odel is inconsistent w ith the

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

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

A recent extension o f this m in im a l SU(5) model [11] includes an add itiona l pa ir of lig h t,

D and L conserving leptoquarks and agrees w ith the measured value o f sin2 0\y. I t is also

m arg ina lly consistent w ith lim its on proton decay. The e x tra leptoquarks do not couple

to pairs of quarks, and hence do not induce proton decay. T h e ir mass is expected to be

o f the order o f 100 G eV /c2.

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

and Eg [14].

1 .2 .2 Technicolour

Technicolour models [15] do away w ith the Higgs sector o f the Standard M odel and

the associated fine-tuning problem s and instead provide a dynam ica l explanation for

the breaking o f the weak gauge sym m etry. A new non-abelian gauge in teraction called

technico lour is introduced, along w ith a new set o f fermions called techniferm ions. A t the

electroweak scale, technicolour becomes strong and, in analogy to Q CD, a technico lour

condensate forms, breaking the electroweak sym m etry. T h is generates masses for the

W ± and Z ° bosons w ithou t a fundam enta l Higgs boson.

In order tha t they be rea lis tic , technicolour models m ust provide a mechanism to

generate masses for the quarks and leptons. T h is is achieved in extended technico lour

models. The idea is to in troduce another in teraction , extended technicolour, which is me

d ia ted by heavy gauge bosons and dynam ica lly broken (somehow) a t very h igh energies.

T he new gauge bosons convert o rd ina ry ferm ions in to techniferm ions, and vice-versa, and

they generate masses for the S tandard M odel quarks and leptons.

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

techn iquark and an an ti-techn ilep ton [16]. The leptoquarks couple to o rd inary quarks


F ig u re 1.2 Diagram for the decay of a leptoquark (L Q ) into a positron and a it-quark, via the exchange o f 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 techn ico lour gauge

boson and tu rn in to a quark and a lepton, as shown in Figure 1.2.

One problem w ith extended technico lour theories is tha t they p red ic t the existence

of some lig h t technistates which should have been observed at LEP, and were not.

1.2.3 C om p ositen ess

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

bosons, are bound states o f more fundam enta l particles called preons, were b u ilt in the

hope o f exp la in ing the vast ferm ion spectrum and reducing the number o f e lem entary par

ticles. Leptoquarks appear na tu ra lly in such models: a composite quark and a composite

lepton can transfo rm themselves in to a lep ton and a quark, respectively, by exchanging

the relevant preons, the bound state consisting o f the exchanged preons being a lep

toquark. In some models [18], the leptoquarks m ay be considerably ligh te r than the

compositeness scale Ac ^ IT e V and may therefore be relevant at IIE R A .

I t is d iffic u lt to explain why the observed ferm ion masses are much sm aller than the

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

quarks and leptons of the Standard M odel [7].


9

1.3 A M odel Independent A pproach

Rather than considering each separate theory p red ic ting the existence o f leptoquarks, i t is

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

most general couplings o f scalar and vector leptoquarks consistent w ith the sym m etries

o f the Standard Model has been presented in [19]. There are seven renorm alizable,

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

pairs for both scalar and vector leptoquarks. T hey are lis ted in Table 1.1. Leptoquarks

may couple independently to fermions o f any fam ily . The leptoquark Yukawa couplings

are denoted A Lq , where H is the lepton he lic ity , LQ is the leptoquark m u lt ip le t, and i

and j are the lepton and quark generations.

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

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

suppressed, couplings to the first-generation ferm ions are im p lied (Ah l q = A l q )- Fu r

thermore, no a ttem pts are made to d iffe ren tia te between the different states o f a given

leptoquark m u ltip le t: isospin states are assumed to be degenerate in mass.

1.4 E xperim ental Lim its on Leptoquarks

L im its on lep toquark masses {ttilq) and couplings (A '/j^g ) have been obta ined from

direct searches at e+ e_ and pp co llider experim ents and have been calculated from rare

processes at low-energy. Those lim its associated w ith B and L conserving couplings to

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

1.4.1 Searches in E lectron -P ositron C ollisions

Leptoquarks carry e lectric charge and could therefore be pair produced in e+ e“ c o lli

sions. The lowest-order Feynman diagram for th is process is shown in F igure 1.3. Scalar

leptoquarks decaying in to leptons plus je ts have been searched for at LEP [20], w ith n u ll

results. The derived lim its depend on the lep toquark e lectric charge and isospin, as w ell

cis on the generation o f the lep toquark decay products, b u t are near the k inem atic l im it


10

Leptoquark J t 3 Q Interaction Lagrangian

So 0 0 - 1 /3 M s . [ (U iY E i - ( D i ) eiV* ] + X ^ U i t 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 y f i X [ s M T N i s l

0 - 1 /3 - 4 s \ { U i r E i ^ { b [ Y N \ \ S \

-1 - 4 /3 - s f l X i s ^ D i Y E i S l

V0 1 0 - 2 /3 M v o [.Djnr E i + + A-{V, / X 7 ' ‘ / • ; ; , } <

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 i r 7 ' ‘ ^ } v.%.

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

- 1 /2 - 1 /3 V t j f t r r E i v U

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

T ab le 1.1 Scalar (S) and vector (F ) leptoquarks, their spin (./) , their electric charge (Q ), the th ird 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.


11

/ LQ

/

\ L Q

F ig u re 1.3 Feynman diagram for the production of leptoquarks in e+e“ collisions,

of ha lf the centre of mass energy:

rnLQ > 41 -4 6 G e V /c 2 (1.4)

at the 95% confidence level (C .L .). S im ila r lim its are expected for vector leptoquarks [16].

In the LEP analyses, the leptoquarks were assumed to decay w ith in a few centim etres

of the p rim a ry vertex. Since the decay w id th o f a leptoquark is related to its Yukawa

coupling (cf. Equations 1.48 and 1.49, Section 1.6), the vertex assum ption im plies th a t

the mass lim its are applicable on ly i f \ l ,r ~ 10“ '.

The D E L P H I collaboration has also searched for the single production o f leptoquarks

[21]. The Feynman diagram fo r th is process is identica l to tha t fo r pa ir production,

except tha t on ly one of the leptoquarks is produced on-shell. No lep toquark candidates

were found and lower mass l im its — from 55 to 80 G eV /c2— as a function o f Yukawa

coup ling— 0.1 to 0.5— were obtained. For a Yukawa coupling equal in strength to th a t o f

the clectrowcak coupling, i.e.,

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

~ 0.31, (1.6)

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

m LQ > 65 G e V /c2 (1.7)


12

<7

/ LQ

\ LQ

9/ , LQ

/

\

g JLQ JL2JLQ JI

LQ

9 JU U L JL Q JL fil_____________ l q

9 --------------- LQ

F ig u re 1.4 Lowest-order Feynman diagrams contritm ling to the processes </(j — LQ LQ and gg — LQ TQ.

at the 95% confidence level.

1.4.2 Searches in P roton -A n tip roton C ollisions

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

ann ih ila tion and in gluon-gluon fusion. The lowest-order Feynman diagrams co n tribu tin g

to these processes [22] are shown in Figure 1.4. The cross-sections fo r 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 Ferm ilab Tevatron [23]. Because o f the large background associated

w ith events in which bo th leptoquarks decay in to a neutrino and a quark, one o f the

leptoquarks was required to decay in to an electron and a je t in the DO analysis while

both leptoquarks were required to decay in to an electron and a je t in the C D F analysis.

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

fraction in to e lectron plus jets. The 95% confidence level lim its on scalar leptoquarks


13

from C D F are

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

m LQ > 80 G eV /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 w ith in a few

m illim e tres of the p rim a ry vertex. Therefore, the mass lim its are applicable as long as

the leptoquark Yukawa coupling is greater than 10“ '.

The C D F lim its on scalar leptoquarks have been trans la ted in to lim its on vector

leptoquarks [24]. The cross-sections for vector leptoquarks are substan tia lly larger than

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

weakest lim its are obta ined in the case k = 0:

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

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

at the 95% confidence level.

1.4 .3 L eptonic P io n D ecays

Charged pions decay w eakly m ostly in to because the decay in to euc is he lic ity sup

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

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

R = (1.2265 ± 0.0034 ± 0.0044) • 10“ 4 (T R IU M F ), (1.14)

R = (1.2346 ± 0.0035 ± 0.0036) • 1 0 "4 (P S I), (1.15)


14

where the second errors are theoretical. Averaging the results o f the two experiments

yields:

R exp = (1.231 ± 0 .0 0 4 ) • 10~‘ . (1.16)

Th is q u a n tity is in very good agreement w ith the latest Standard Model ca lcu la tion [27]:

R» = i + (1.17)

= (1.2352 ± 0.0005) • 1 0 - ', ( I. IS )

where A is a rad ia tive correction.

Leptoquarks coupling to both left-handed and right-handed leptons would contribu te

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

exchange o f an So leptoquark, as shown in F igure 1.5. Note tha t this decay is not helic ity

suppressed. So, £ 1/ 2 , K>, and V \/2 leptoquarks would contribu te an am ount A R to the

ra tio R [16]:

1 M ~ _ 7At ‘ A«' m A x / 1 for 5° a,,d 5 , / '2’ ( 1 1())R lh \ j 2 G Fm lQ m e ^ G Fm lQ m ^ j \ 2 for l/0 and Vl/2 .

I f one assumes th a t there are no cancellations between the leptoquark contribu tions to

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

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

> 135T eV /c2 (S0 and S l/2 ), (1.20)

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

These are very strong lim its . However, they are on ly applicable i f the leptoquarks couple

to bo th le ft-handed and right-handed leptons. I f = 0 or \ r = 0, the lep toquark cou

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

Hereafter, o n ly leptoquarks w ith ch ira l couplings are considered.

Leptoquarks coupling to left-handed electrons and neutrinos would also contribu te to

the decay o f charged pions. For example, a 7r+ could decay in to a righ t-handed positron


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 neu trino v ia the exchange of an S0, an S i, a Vo, or a Vi leptoquark.

Note th a t th is decay is suppressed by he lic ity conservation. So, S i, V0, and Vi leptoquarks

would con tribu te an am ount A R! to R [16, 28]:

\A R '\ _ V 2 X j f 1 ^ So and S i,

R th 4.GFm2LQ \ 2 fo r Vo and Vi,

where is the lep toquark Yukawa coupling to first-generation quarks and leptons. I f

|A /2 '| is required to be less than the sum o f the errors on R exp and R th, the fo llow ing

lim its result:

m LQ/ Ai, > 2 .2 T e V /c 2 (S 0 and SO, (1.23)

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

1.4.4 U n ita r ity o f the C K M M atrix

The weak coupling constant measured in nuclear be ta decay (Gp) is s lig h tly sm a lle r than

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

Kobayashi-Maskawa (C K M ) rotated quarks. The m agnitude o f the C K M m a tr ix element

Vuu is in fact obta ined by comparing Gp and Gf [29]:

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

= 0.9744 ± 0.0010. (1.26)


16

So and Si leptoquarks would con tribu te an amount A Gp to Gp [16]:

|AC„| = ^ 1 . (1.27)om LQ

Vo and V] leptoquarks w ould con tribu te tw ice th a t am ount. The con tribu tion of these

leptoquarks, v ia box diagrams, to G f would be much sm aller and can be neglected.

Assum ing u n ita r ity o f the C K M m a trix , Vud is related to and V„i, as follows:

\vud\2 = l - \ v u3\2- \vub\2. ( 1.28)

E qua tion 1.28, along w ith the experim en ta lly measured quan tities [29]

IK * ! = 0.2205 ±0 .0018 , (1.29)

|Kfc| = 0.0032 ± 0.0009, (1.30)

constra in Vud to be w ith in 0.2% o f its measured value a t the 95% confidence level. I f the

absolute value o f each lep toquark con tribu tion to Gp is required to be less than 0.2%,

the fo llow ing lim its result:

m LQ/X L > 2 .8 T e V /c2 (S0 and S i), (1.31)

m LQ/ \ L > 3 .9 T e V /c2 (VQ and Vt ). (1.32)

In the absence o f u n ita r ity , these lim its would no longer be applicable.

1 .4 .5 A tom ic P arity V io la tion

E xperim ents have dem onstrated cases o f p a r ity v io la tion in atoms during the absorption

o f lig h t [30]. These results are consistent w ith the exchange o f Z ° bosons between the

electrons and the nucleus o f the atoms. The measured p a rity -v io la tin g a m p litude is


17

proportiona l to the weak charge of the atom

Q w = —2 [C iu (2Z + N ) + CU {Z + 2 iV)], (1.33)

where C Ui = - /3 + 2 Q em sin2 Ow at firs t-o rder, and Z and N are the num ber o f protons and

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

yield [29]

Q l? = -71 .04 ± 1.81, (1.34)

consistent w ith the Standard Model ca lcu lation [29]

Q% = -7 2 .9 2 ± 0 .1 0 . (1.35)

In the presence o f leptoquarks, there would be the fo llow ing add itiona l contribu tions

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

v/2A? n

AC,U " 8G Fm lQ X

' +1 for RS0 and L S 1/ 2,

— 1 for LSq, R S l/2 and L S \ ,

+ 2 fo r R V \/2,

—2 for RV0 and L V \/2 ,

. +4 fo r LV i ,

(1.36)

and

A C U =2l r

8 G Fm lQx

+1 for

- 1 for

+2 for

_ 2 for

(1.37)

2 for L S 1 , RVq, and LV i / 2.

In the above two equations, the lep toquark states are preceded by the h e lic ity o f the ir

Yukawa couplings (L or R ). I f the absolute value of each lep toquark con tribu tion to Qw

is required to be less than the sum o f the errors on Q w P and Q w , l im its on the ra tio

ik l q / ^ h l q , ranging from 1.3 to 3 .2 T e V /c 2, are obta ined. T he specific lim its are listed

in Table 1.2. Note th a t in the presence o f two or more lep toquark m u ltip le ts , in d iv id ua l

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


IS

Leptoquark Coupling Helicity

Lower lim it on m Lq lX u Lq (TeV /e2)

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 /X ji cq, in T eV /c2. for leptoquarks w ith chiral couplings to the first-generation fermions, from lcptonic 7r decays, unitarity of the C KM m atrix, and parity violation in Cesium.

be applicable.

The lim its on the ra tio lq calculated from low-encrgy measurements, for

leptoquarks w ith ch ira l couplings to the first-generation ferm ions, are summarized in

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

between d iffe ren t leptoquark con tribu tions to a p a rticu la r process.

1.5 K inem atics o f E lectron-P roton Scattering

Before discussing the p roduction and decay o f leptoquarks at H E R A , the k inem atics o f

e lectron -p ro ton scattering must f irs t be in troduced. The lowest-order Feynman diagram

fo r e~p deep ine lastic scattering (D IS ) is shown in Figure 1.6. The e lectron and the quark

(a u or d valence quark, or a sea quark o r an tiquark o f any flavour) exchange a photon,


19

PPp

Figure 1.6 Feynman diagram for electron-proton deep inelastic scattering. The incoming electron (w ith four-momentum pe) and the quark (w ith 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 o f neu tra l currents

(photon o r Z ° exchange) and a neu trino in the case o f charged currents {W ^ exchange).

The four-m om entum transfer squared at the electron-lepton-boson vertex is

q2 = {pe - p i ) 2, (1-38)

where pe and pi are the four-m om enta1 o f the incom ing electron and outgoing lepton,

respectively. The to ta l ep centre o f mass energy squared is

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

where pp is the pro ton four-m om entum . I f the incom ing electron and p ro to n energies, E e

and Ep, are much larger than the e lectron and proton masses, one can w rite

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 = E 2 — |p|2 is spacelike (e.g., a scattering process) i f p2 < 0 and it is timelike (e.g., the mass squared of a free particle) if p2 > 0.


20

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

I t is convenient to use the positive variable

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

as well as the dimensionlesr variables

Q7x =2 PP • q' Pp-q P p ' P e

(1,12)

The variable y is called the ine las tic ity param eter and is proportiona l to the energy loss

o f the incom ing electron in the proton rest frame. The variable x, in the context o f the

Parton Model [31] where the proton is considered to be made o f partons (i.e., quarks

and gluons), is the frac tion o f the proton m om entum carried by the struck quark. The

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

* » * - « • ( i + = i ± = £ ) . <M.i)\ 2 pp • pe J

~ Q 2. (1.45)

1.6 Leptoquark P roduction and D ecay at H E R A

H E R A provides a unique environm ent for the d irec t production o f leptoquarks. In

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

in F igure 1.7. Th is process, the fusion o f an e lectron and a quark or an tiquark, would

dom inate for lep toquark masses up to m^Q ~ y/s. For h igher masses, one could search

fo r effects arising from the v ir tu a l exchange of leptoquarks.

The leptoquark p roduc tion cross-sections have been calculated in [19] for each le p to

quark m u ltip le t. The s-channel d iffe ren tia l cross-section averaged over the quark sp in ,


21

P

u (d)

P

u (d )

F ig u re 1.7 Feynman diagrams for the direct (s-channel) and v irtua l (u-channel) production o f S0 leptoquarks in e~p collisions.


Leptoquark s-Channel Coupling Leptoquark s-Channel Coupling

s 0 e l uL el uL Ac Vo c[. dR — c; dR A/.

eRuR eRuR A R cr<1l c7;(h. A Re~L uL — vedL —A L (' l (ht — vei iR A/.

So ertdR e~kdR A R Vo c Ttu /. — CjtUl. An

Sl/2 —* eRdR — A R V./2 cRllL ' Ane lu L — e lu L A L ec dR — e jd n A/,

eRUR —*• eRuR A R Cndi. —* ( i{d[. An

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

S, e l t tL — 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 — e ld L — y/2XL r-7hn — c7 11 it \/2 A/.

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

for leptoquarks w ith ch ira l couplings, is

, (* .< ? ’ ) ; 2 '1 ' " „ ,,, (!- '!« )dx dQ 2 32tt ^ (xs - m iQ )2 + m iQ I l Q

for scalar leptoquarks and

do- _ 1 v - , n 2 v _____________ Q2 ~ xs t , 17 \„ ,2 \2 l p2 „2 ,.2 ( ' )d x d Q 2 Sir “ ’ (xs - m \Q)2 + rn2LQY2LQ x 2s2

for vector leptoquarks, where q ( x , Q 2) is the parton d is tribu tion func tion and the sum

is over a ll possible incom ing quark or an tiquark flavours. The relevant p roduction and

decay channels are lis ted in Table 1.3.

T he lep toquark p a rtia l decay w idths 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


23

where A/,,/* denotes the leptoquark coupling to a p a rticu la r final state, as given in Ta

ble 1.3. For exam ple, a scalar leptoquark w ith a mass o f 100 G e V /c2 and a Yukawa

coupling of 0.31 would have a partia l decay w id th o f 200 M eV . The to ta l decay w id th is

obtained by sum m ing over a ll possible fina l states.

A t H E R A , leptoquarks would appear as narrow B re it-W igner resonances in the in

variant mass d is tr ib u tio n of the decay products. Since the incom ing quark m om entum

is equal to xpp (in the Parton M odel), leptoquarks would appear as narrow resonances

in the x d is tr ib u tio n , peaked at

In the l im it o f very narrow leptoquark w id ths (T lq / ttilq —> 0), the cross-section for

a specific fina l state can be approxim ated by [19]

= iPc + *Pp)2 -(1.50)

tha t is at

* - ™2lq / s - (1.51)

fo r scalars,

fo r vectors,(1.52)

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

ra tio in to the final state. The leptoquark cross-sections in this app rox im a tion are lis ted

in Table 1.4. The cross-sections over Yukawa coupling squared as a function o f lep toquark

mass are shown in F igure 1.8. Scalar leptoquarks have a sm aller cross-section than vector

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

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

consider a 100 G eV /c2 So leptoquark w ith — 0.31 and = 0. A fte r co llecting data

corresponding to an in tegrated lum inos ity o f 27.5 nb-1 , one would expect about f if ty

leptoquark events.

The final state o f a leptoquark event consists o f a lep ton (an electron o r a neutrino)

balanced by a je t in transverse m om entum , a long w ith the so-called specta tor je t from

the proton rem nant. The signatures o f lep toquark decays are therefore id en tica l to th a t


s-Channel Cross-Section

Leptoquark Decay to e X Decay to vX

So ^ ( X 2 B Sou + X2r u) 37AL(1 ~ b s0)u

So —

S\/2 ^•[A | u 4- X%(u + d )] —

Sl/2 t M d —

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

Vo ^ { X l B y J + X l d ) f - X l ( l ~ B Vn)d

Vo —

Vl/2 ^■[A i d + 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 ,Q 2), d (x ,Q 2), u (x ,Q 2), and d(x,Q -’) evaluated at x = and Q2 = i t i 2Lq .


25

-oc Scalar. LQ —> e'X

■RS,

10

■IS,I

RS.

I10

10

■310

100 200

t

'k

10

Scalar LQ —> vX

10*

10

1

I10

.210

310

100 200

10

Vector. LQ —» e~X

10

10

LV,I

10

10LV,

■310

100 200Leptoquark mass (GeV/c ) Leptoquark mass (GeV/c )

■Q 10

Vector LQ —> vX

102

10

1

I10

10

■310

100 200Leptoquark 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 M T B1 parton d istribution functions [32]. The branching fractions of the So, S i, V0, and Vi leptoquarks (coupling to left-handed electrons) into e~A' are set to 0.5.


26

o f neu tra l and charged current deep inelastic scattering events. Generally, the leptoquark

am plitudes for e~p —> e ~ X and e~p —> v X in terfere w ith the Standard M odel am plitudes

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

s ta tis tica l methods.


Chapter 2

Experim ental Setup

2.1 The H ER A E lectron-Proton Collider

H E R A 1 [33] is the w orld ’s firs t e lectron-proton co llide r which has been constructed at the

D ESY2 laboratory in Ham burg, Germany. It consists o f tw’o independent accelerators,

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

tive ly . The two accelerators are located in a common tunne l 10 to 25 m below ground

level. The counter-ro tating beams arc brought in to head-on co llis ion at two points along

the ring , Hall South and H all N o rth , thereby provid ing e lectron-pro ton in teractions to tw’o

experim ents, ZEUS and I I I (see Figure 2.1). The e lectron-pro ton centre o f mass energy

at H E R A (296GeV during 1992) is one order o f m agnitude larger than th a t previously

available at fixed target experim ents.

A layout o f the H E R A pre-accelerators is shown in F igure 2.2. Protons are in it ia lly

accelerated as negatively-charged hydrogen ions in the 5 0 M e V H “ L IN A C [34]. The

ions are stripped of th e ir electrons in a th in fo il, and the resu lting protons are in jected

in to the DESY' I I I synchrotron, wfhere they are accelerated to 7.5 GeV. The protons are

then transferred to P E T R A I I , where they are accelerated to 40 GeV. F ina lly , they are

transferred to H E R A and accelerated to 820 GeV.

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

27


2S

HallN orth

H all

East

HE R AH allW est

4 0 GeV { protons

PETRA

14 GeV electrons

H allS o u th

Figure 2.1 The HERA accelerator.


29

UHERAAM n P-820 GeV

30G «V m «'^aGeV

,PETRAHj IINEPETRA

Hall NW

CrYO-. 1 Technic Hal

LlnacJl

PETRA Hall W ,r.a* PlA W 1

PETRA

HERAHill SW

Proton bypass

Figure 2.2 The HERA injection system.

Electrons are libe ra ted from a high voltage cathode and firs t accelerated to 500 MeV

w ith the L IN AC I I linear accelerator. T hey are then accumulated in to a single bunch

in the P IA storage ring and transferred to the D ESY II synchrotron. T here they are

accelerated to T G eV and then transferred to the P E T R A I I storage ring . T h is whole

procedure is repeated u n til P E T R A I I ha.s been filled . Once P E T R A I I is fu ll, the

electrons are accelerated to 14 GeV, transferred to H E R A , and fin a lly accelerated to

26.7 GeV.

The particles in the beams are grouped in bunches. H E R A is designed to store and

collide 210 bunches o f protons and 210 bunches o f electrons. Consecutive bunches are

separated by 28.8 m (96 ns in tim e, since the partic les essentially trave l at the speed of

ligh t). The H E R A pro ton energy is lim ite d by the magnetic fie ld o f the superconducting

dipole magnets needed to keep the protons in o rb it, w h ile the electron energy is lim ite d by

the radio frequency power necessary to replace the energy lost by synchro tron rad iation.

Lum inosity , £ , is an im portan t param eter o f co llid in g beam facilities because i t relates


30

the cross-section o f a p a rticu la r process, a, w ith the rate o f observed events, R:

R = C • a. (2.1)

In term s o f the beam param eters, lum inosity is defined as

c - , W (2 .2)Z x y / v L + v l p y / r f c + t f r

where / is the revo lu tion frequency (47 .3kHz a t H E R A ), k is the num ber o f co llid ing

bunches, N e and N p are the num ber o f electrons and protons per bunch, and <rxc,

axpi and ayp are the horizonta l and vertica l RMS dimensions o f the electron and proton

beams. Design and 1992 values o f H E R A beam parameters are listed in Table 2.1.

Nineteen n ine ty-tw o was the firs t year H E R A delivered lum inos ity to ZEUS and H I.

D u rin g tha t year, the accelerator was operated w ith nine co llid ing bunches, one a dd i

tio n a l unpaired electron bunch and one add itional unpaired proton bunch. The unpaired

bunches, called p ilo t bunches, were used for es tim ating beam-related backgrounds. The

highest lum inos ity recorded by the ZEUS experim ent in 1992 was 1.5 x 1029 cm -2 s-1

(1033cm -2 = ln b -1 ) w h ile the typ ica l lum inos ity was 0.5 x 1029 e r n e s '1. These num

bers are two orders o f m agnitude sm aller than the design lum inos ity o f 1.(5 x 1031 c m ' V .

The integrated lu m in o s ity recorded by ZEUS in 1992 was over 30 nb -1 ; the in te

grated lum inos ity used in the present analysis to ta ls 27.5 nb-1 . A p lo t o f the in tegrated

lu m in o s ity as a function o f tim e :s shown in F igure 2.3.

2.2 The ZEUS D etector

2 .2 .1 O verview

T he ZEUS detector is a m u lti-com ponen t detector designed to measure a large num ber

o f physics processes a t H E R A [36]. L ike many recent high-energy detectors, i t consists

o f

• track ing chambers, fo r m easuring the tra jectories and m om enta o f charged partic les,


31

Parameter

Proton Beam Electron Beam

1992 Design 1992 Design

Energy (GeV) 820 820 26.7 30

Circulating current (m A) 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 ab le 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

8

tu5ec50

25

20

15

10

5

030 35 40 45

Week

F ig u re 2.3 Integrated luminosity collected in 1992 as a function o f time. Only the luminosity from the runs used in the present analysis are included.


O v e r v i e w o f th e ZEUS D e t e c t o r ( lo n g i tu d in a l cut )

uuurggoJ w jB»oumoo»

pr^-0** °7mCRYO-tiU U O

BOX IK

FCALiFDET CTD

W A L l M

-H I-10 m 0 -5 m

F ig u re 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).

• calorim eters, fo r measuring energy deposits, and

• muon chambers, for detecting muons and measuring the ir m om enta.

The asym m etry between the electron and proton beam energies a t I IE R A lead to the

design of an asym m etric detector, as seen in F igure 2.4. The coord ina te system used

th roughou t th is analysis is as follows: the z-axis points in the d irec tion o f the incom ing

p ro ton beam , the t/-axis points upwards, and the x-axis points towards the centre o f the

H E R A ring . The nom ina l crossing o f the beams is at z = 0.

The m a in track ing detectors are the Vertex Detector (V X D ), a sm all cy lind rica l d r if t

chamber im m ed ia te ly surrounding the beam pipe, and the C en tra l T racking Detector

(C T D ), a large je t-type d r if t chamber. A dd itiona l track ing in the rear and forward

regions is p rovided by the Rear and Forward Tracking Detectors (R T D and F T D ), con

sis ting o f one and three planar d r if t chambers, respectively. A superconducting solenoid

magnet ou ts ide the C T D provides a m agnetic field o f up to 1.8 T . A sm aller solenoid


33

magnet is located in the rear region to p rov ide a 5 T magnetic fie ld w h ich compensates

the influence o f the detector solenoid on the beams. The T rans ition R ad ia tion Detector

(T R D ), which consists o f two rad ia to r modules and two d r if t cham ber modules, is in

terleaved between the FT D chambers and helps to d iscrim inate between electrons and

hadrons in the forward region.

The m ain ca lorim eter for ZEUS is a u ran ium -sc in tilla to r ca lo rim e ter (C A L ), which

surrounds the centra l solenoid magnet and tracking detectors. I t is fine ly segmented,

has very good electrom agnetic and hadronic energy resolution, and provides nearly fu ll

angular coverage. The Hadron E lectron Separator (HES) consists o f narrow layers of

silicon diodes inserted in gaps w ith in the ca lo rim eter a t depths o f three rad ia tion lengths

in the rear region. The HES helps to d iscrim ina te between e lectrom agnetic and hadronic

energy deposits. A n iron yoke surrounding the calorim eter re turns the f lu x o f the central

solenoid and also serves as the absorber m a te ria l for the Backing C a lo rim ete r (BAG ).

The BAG uses a lum inum proportiona l tubes inserted in to the yoke as the active m ateria l

and provides a measurement of energy leakage through the C A L .

Muons are detected in the centra l and rear regions w ith the B arre l and Rear Muon

chambers located on both the inner and ou te r sides o f the yoke (B M U I, B M U O , R M U I,

and R M U O ). T h e chambers consist o f tw o double layers o f lim ite d stream er tubes

(LS T ’s). Coils surrounding the yoke provide a toro ida l field o f 1.6 T , a llow ing for momen

tum measurement, in the forward region is a Forward Muon Spectrom eter (F M U O N ),

com prising two magnetized iron toro ids interleaved w ith d r if t chambers and L S T ’s; there

are also d r if t chambers and LS T ’s inside the iron yoke (F M U I).

The C5 detector (C5)— four s c in tilla to r counters surrounding the beam p ipe— and

the Veto W a ll— a large iron wall w ith s c in tilla to r hodoscopes on both sides— are located

in the rear region to provide rejection o f beam -related background events. The Veto W all

also provides sh ie ld ing against partic les fro m the beam halo.

The lu m in o s ity at ZEUS is measured by detecting brem sstrahlung events in two

small e lectrom agnetic calorim eters located a t 2 = —35 m and 2 = —108 m (L U M I).

The ca lo rim e ter at 2 = —35 m is also used to detect electrons from photoproduction

events.


The Leading P ro ton Spectrometer uses the proton beam line magnets and six sm a ll

s ilicon s trip detectors insta lled very close to the beam at c values o f 24, 41, 44. 63, 81,

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

M any ZEUS components were not fu lly installed or instrum ented during the 1992

runn ing period. The present analysis uses the in fo rm a tion from the C A L, C T D , 05 , and

L U M I, which are described in more deta il below.

2 .2 .2 C alorim eter

P h ysical Structure

The ca lorim eter is constructed from stainless steel clad depleted uranium plates in te r

leaved w ith SCSN-38 sc in tilla to r tiles [37, 38]. The thickness o f the uranium plates and

s c in tilla to r tiles, 3.3 m m and 2.6 m m , were chosen such th a t each layer is one rad ia tion

length (Xo) th ick and the response o f the ca lorim eter to the electrom agnetic component

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

The ca lorim eter is d iv ided in to three main mechanical parts: the forward ca lorim eter

(F C A L ) in the polar angle region 2.2° < 0 < 39.9°, the barrel ca lorim eter (B C A L ) in

the region 36.7° < 0 < 129.1°, and the rear ca lorim eter (R C A L ) 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 F C A L and R C A L are each composed o f tw enty-th ree modules which are fu rth e r

d iv ided in to 20 x 20 cm 2 towers. Each tower is segmented long itud ina lly in to an e lec tro

m agnetic cell (E M C ) w ith a depth o f about 2oX 0 (one absorption length A), and two

(one in the R C A L) hadronic cells ( I IA C l, H AC2) o f dep th 3A each. The E M C cells are

fu rth e r segmented transversely to 5 x 20 cm 2 in the F C A L and 10 x 20 cm2 in the R C A L .

A lis t o f the different ca lo rim eter cell dimensions is given in Table 2.2.

The B C A L consists of th ir ty - tw o trapezoidal modules, each spanning 11.25° in az

im u th . The modules are d iv ided lo n g itud ina lly in to an EM C, a H A C l, and a IIA C 2

section. The EM C cells are p ro jective in polar angle (0) and azim utha l angle (<£), w ith

fro n t face dimensions 5 x 23 cm 2 and thickness corresponding to 21X0. The H A C l and


35

Calorimeter Cell Transverse Dimensions

(cm2)

Depth

(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

H A C l 20 x 20 64 3.1

"Dimension of first layer.

T ab le 2.2 Transverse dimension and depth at normal incidence o f the different ZEUS calorimeter cells.

IIA C 2 cells are only pro jective in <j> and are 2A th ick each. The transverse dimensions o f

the first 11 AC 1 layer are 24 x 27 cm 2.

There arc a tota l o f 5918 E M C and MAC cells, and each is read out on both sides by

wavelength sh ifter bars, ligh t guides, and p ho tom u ltip lie r tubes (P M T ’s). The op tica l

readout system of one F C A L tow er is shown in Figure 2.5.

R eadout E lectronics

T he signal from each P M T is sent to e lectronic cards, called Analog Cards, m ounted

on the detector [39], The signal is s p lit in to low gain and high gain. The low gain and

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

p ipe line fifty -e igh t cycles long, the dura tion o f one cycle being 96 ns. A fte r a positive

F irs t Level Trigger decision (see Section 2.3.2), the p ipe line da ta are sent to d ig itiz in g

electronics (D ig ita l Cards) s it t in g in V M E crates in the electronics area o f the experim ent.

T he d ig itiz in g cards have b u ilt- in analog to d ig ita l converters (A D C ’s) and d ig ita l signal

processors (DSP’s). The o u tp u t o f the DSP’s is P M T energy and tim e w ith respect to

the H ER A clock.

A tw o-transputer module (2T P ) sits in the V M E crate: one transputer perform s


36

D eple ted Uranium Scintillator M ate ria l

RotlectorSta in less S tee l

W a v e le n g th Shlltor

Rolloctor

H E SSlotsP h o to m u ltip lie r Tub e

HAC1Section

EM CSection

LightGuide

W ave len g thShiltor

Figure 2.5 Schematic view of an FCAL tower.

ca lorim eter Second Level Trigger tasks, the o ther performs readout tasks. A fte r a positive

Second Level T rigger (see Section 2.3.3), the ou tpu t o f the DSP is read out and sent, to

the Event B u ilde r.

Calibration and R esolution

The na tu ra l ra d io a c tiv ity of the t / 238 provides a very stable ca lib ra tion signal. During

special ca lib ra tion runs, the P M T signals are integrated fo r 20 ms and the results are

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

procedure is repeated at eight hour in tervals. The P M T energy measurement can be

ca lib ra ted to b e tte r than 1% in th is fashion. The electronics are ca lib ra ted w ith a charge

in jec tion system b u ilt in to the Analog Cards.

The ca lo rim e ter energy resolution has been measured in beam tests [38, 40]. The elec

trom agnetic energy resolution is 18% /\/~E fo r FC A L and R C A L modules, and W)%f\/~E

(20% / \ fE w ith the coil) for B C A L modules, where E is expressed in G eV . The hadronic

energy reso lution is 35% / \ f E for R C A L, F C A L , and B C A L modules ( '18 % /y /E for B C A L

modules w ith the co il). The lin e a rity of the response to electrons is w ith in 1% for ener

gies between 15 GeV and 110 GeV in the F C A L and R C A L, and w ith in 1% for energies

between 6 G eV and 90 G eV in the B C A L . The lin e a rity fo r hadrons is w ith in 1% for


^

37

energies between '20 G eV and 110 GeV in the B C A L . The absolute energy scale was also

measured in beam tests, where precise knowledge o f the beam m om entum was available.

A laser and LED ligh t in jection system is used to ca libra te the P M T t im e measure

ment. The P M T tim e resolution is about 1 ns fo r P M T energies above 1 G eV [42].

2.2 .3 C entral Tracking D etector

The Central T racking Detector (C T D ) is a cy lind rica l d r if t chamber surrounding the

Vertex Detector. I t is active in the rad ia l region 18 cm < r < 79 cm and over a length

o f 205 cm. Charged track position and d E / d x energy losses are measured in nine super

layers, each consisting o f e ight layers o f sense wires. The wire layout in a 45° sector is

shown in F igure 2.6. Five o f the superlayers, labelled 1, 3, 5, 7, and 9 in F igure 2.6,

have wires paralle l to the beam line. The other four superlayers have wires a t a stereo

angle o f approx im ate ly ±5 °. The to ta l num ber o f sense wires is 4608. T h e chamber

is read out w ith a system o f flash analog to d ig ita l converters (F A D C ’s). T he wires in

superlayer one and h a lf o f the wires in superlayers three and five are also instrum ented

w ith z -by-tim ing readout. The Lorentz angle is expected to be 45° in a m agnetic fie ld o f

1.8 T . Since the planes o f wires are oriented a t 45° to a rad ia l line from the beam axis,

ion ization electrons should d r if t tangentia lly to the chamber azim uth. T h is allows the

le ft-righ t h it am bigu ities to be easily resolved.

During 1992, on ly z -b y -tim ing in form ation was available, p rov id ing coarse track posi

tion measurement in three superlayers. The ion iz ing gas was a m ix tu re o f argon, carbon

dioxide, ethane, and ethanol in the proportions S8%, 9%, 2%, and 1%; the d r i f t fie ld was

1 .2 kV /cm ; and the m agnetic field was 1.43 T [43]. Under these conditions, the Lorentz

angle was 39° and the d r if t ve locity was 49 /zm /ns. The h it resolution was 4 cm in z and

0.1 cm in r<f>.

2.2 .4 C5 D etec to r

The C5 detector, located near the beam pipe a t z = —314 cm, consists o f tw o pairs of

sc in tilla to r counters, one above and one below the beam pipe, separated by 5 m m o f lead.


38

3. SUPERLAYER

F ig u re 2.6 W ire layout in a 45° sector of the Central Tracking Detector. The sense wires are indicated by solid dots.


39

The counters measure the a rriva l times and rates o f particles in the electron and proton

beam halos, as well as particles created in the in teraction o f the beam or beam halos w ith

gas molecules in the beam pipe, w ith the beam pipe itself, o r w ith the C5 co llim a to r [44].

The C5 tim e in form ation is used at the trigger and offline levels to id e n tify and reject

background events. C5 in fo rm ation is also used online to m o n ito r the background rates

and the q ua lity o f the beams.

2.2 .5 L um inosity M onitor

The purpose o f the Lum inosity M o n ito r (L U M I) is to measure the lu m inos ity delivered

by H E R A during data taking. In order to do so, the L U M I m onitors the rate o f the

brem sstrahlung process ep —► ep7 , which has a d is tinc t experim enta l signature and a

large cross-section given by the B e the-H e itle r fo rm u la [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 in it ia l and fina l e lectron energies, E p is

the pro ton energy, m p and m e are the p ro ton and electron masses, a is the fine s tructure

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

brem sstrahlung process from electrons in te rac ting w ith gas molecules in the beam pipe,

but i t can be determ ined and subtracted using the electron p ilo t bunch.

The layout o f the L U M I is shown in F igure 2.7. A ca lo rim eter located a t z = —35 m

detects the fina l state electron and a ca lo rim eter located a t 2 = —108 m detects the fina l

state photon. Both calorimeters are made of 5.7 cm th ick lead plates interleaved w ith

2.8 m m th ick SCSN-3S sc in tilla to r tiles. The photon ca lo rim eter has a depth o f 22X 0

and a transverse size o f 18 x 18 cm 2; the electron ca lorim eter has a depth o f 24X0 and a

transverse size o f 25 x 25 cm2. B o th detectors have an e lectrom agnetic energy resolution

o f 1 8% /V E , where E is expressed in G eV. For B e the-H e itle r events, the fin a l electron

and photon energies should add up to the in it ia l electron energy.

T he L U M I is also useful in detecting electrons from pho top roduction events and in it ia l

state rad ia tive photons from neu tra l and charged current deep ine lastic scattering events.


•10

0

LUMIG

-0.4

LUMIE

i i i i i i i. i i i i i0 50 100

-z (m)

F ig u re 2.7 Luminosity Monitor. The electron and photon calorimeters are labelled LUM IF and LUM IG .

2.3 The ZEUS Trigger and D ata A cquisition System

2.3 .1 C oncepts

In order to cope w ith the large H E R A bunch crossing rate (10 M H z), the large back

grounds from beam-gas in teractions (10 to 50 kHz at design lum inos ity ), and large event

sizes (up to 200kB ytes per event), ZEUS has adopted a m u lti-leve l trigger system. A

F irs t Level T rigger (F L T ) has the task o f reducing the data rate to 1 kH z, a Second Level

T rigger (SLT) m ust reduce tha t ra te to 100 Hz, and in tu rn , a T h ird Level Trigger (T L T )

must reduce th a t rate to a manageable ra te o f 5 Hz.

A layout o f the ZEUS trigger and data acquis ition system is shown is F igure 2.8.

Each component has its own pipelined readout and local F LT system. T he length o f the

p ipeline is fifty -e ig h t clock cycles o f 96 ns. T he local F L T systems must evaluate the data

and send the ir results to the G lobal F irs t Level T rigger (G F L T ) w ith in tw enty-s ix clock

cycles. The G F L T must make a trigger decision w ith in another twenty clock cycles. A fte r

a positive G F L T decision, the pipelines are read ou t and any rem ain ing analog signal is

d ig itized . The d a ta are then w ritte n to dual p o rt memories, which serve as SLT pipelines.

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


41

Front/End Front/End

CTDCAL

LocalFLT

LocalFLT m u

GFLT

LocalSLT

LocalSLT

EquipmentComputer WLU Digitizer

Buffer

GSLTEquipmentComputer

EquipmentComputer

EVB

CAL dataCTD data

EquipmentComputer

TLT

Branchbus Switch

IBM LinkVAX

Storage on IBM

10 GBytes/s

100 MBytes/s

10 MBytes/s

1 M Byte/s

F ig u re 2.8 The ZEUS trigger and data acquisition system.


elaborate a lgorithm s than the Local F LT processors. The Local SLT results arc sent to

the G loba l Second Level Trigger (G S LT), which then makes a trigger decision. A fte r a

pos itive trigge r decision, the data from the d iffe rent components are assembled by the

Event B u ild e r in one of six m em ory buffers [46]. T he EVB writes the data in A D A M O

s truc tu re [47]. A 64 x 64 crossbar sw itch provides the connection from the components

to the T L T .

The T L T is a fa rm o f th ir ty analysis processors, arranged in to six brandies. Eadi

processor has access to a complete event and has enough tim e to perform sophisticated

a lgorithm s, such as track reconstruction. Triggered events are w ritte n to a disk on the

D ESY IB M 3090 v ia the process called IB M L in k . The events are then archived to

cartridges. A t the moment, the trigger o u tp u t ra te is lim ited by the speed at which

events can be w ritte n to tha t d isk. Some o f the events are also sent to a V A X mainframe

for m o n ito r ing and online event d isp lay purposes.

Because o f the im portance o f the trigger system in understanding efficiencies, the

F irs t, Second, and T h ird Level Triggers are described in further de ta il in Sections ‘2 .3 /'

to 2.3.4. The trigge r algorithm s especially are discussed.

2 .3 .2 F irst L evel Trigger

D uring the 1992 runn ing period, the G F L T trigger was based on ca lo rim e ter ac tiv ity , as

reported by the C A L FLT, along w ith a non-veto by the Co detector. A C5 veto is issued

i f the signals from the P M T ’s reading out the tw o C5 sc in tilla to r counters, e ither above

o r below the beam pipe, are in coincidence.

W ith in the C A L FLT, E M C and H A C ca lo rim eter cells are grouped in to trigger

towers about 20 x 40cm 2 in size [48]. In 1992, the calorim eter was d iv ided in to the

fo llow ing ca lo rim e ter regions [49]: Beam Pipe, com prising the firs t rin g o f cells around

the F C A L beam p ipe; FC AL Inner, com pris ing the next three rings o f cells; F C A L O uter,

com pris ing the rem ain ing F C A L cells; R C A L Beam Pipe, com prising the firs t ring of cells

around the R C A L beam pipe; R C A L Non Beam Pipe, comprising the rem ain ing R C A L

cells; and B C A L , comprising a ll B C A L cells. A positive C A L F L T trig g e r was issued

whenever a tr ig g e r tower in a specific ca lo rim e ter region was above the threshold for th a t


43

Threshold (GeV)

Trigger Type Region DAY1 LO W -R EM C LO W -B E M C

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, LO W -R E M C , and LO W -B E M C configurations.

region. Three C A L F LT trigger configurations were used in 1992: D A Y 1, from June to

mid-September, L O W -R E M C , from m id-Septem ber to early O ctober, and L O W -B E M C ,

from early-O ctober to early-November. A bou t 10%, 60%, and 30% o f the lu m in o s ity was

collected w ith the firs t, second, and th ird configurations, respectively. The tr ig g e r tower

thresholds for each configuration are listed in Table 2.3.

In add ition to these thresholds, a lower R C A L E M C threshold was used to increase the

acceptance o f photoproduction events, bu t on ly in coincidence w ith a pos itive tr igge r from

the L U M I electron calorim eter. A d d itio n a l prescaled triggers were used fo r m on ito ring

purposes. The average G F LT rate du ring the 1992 running period was about 20 Hz.

2.3.3 Second Level Trigger

The SLT processors, many of which consist o f program m able transputers, have about

five milliseconds o f processing tim e to a rrive a t a trigger decision. T he processors can

perform some ite ra tive tasks, such as find ing track segments in the C T D (C T D SLT), or

energy clusters in the ca lorim eter (C A L SLT).

A t the beginning o f the 1992 runn ing period , the GSLT d id not re ject events. A fte r

trigger selection a lgoritu rns had been im plem ented and tested a t the T L T , people gained


confidence in the a lgorithm s and im plemented them at the SLT. For instance, an SLT

version o f the T L T spark and ca lorim eter tim e a lgorithm s, described in Section 2.3.4, was

even tua lly run at the SLT. The GSLT also rejected cosmic rays satisfying the fo llow ing

conditions: a positive B arre l M uon trigger in coincidence w ith calorim eter a c tiv ity and

less than two track segments in the C TD .

2 .3 .4 Third L evel Trigger

S y stem A rchitecture

The T h ird Level T rigger (T L T ) consists o f th ir ty S ilicon Graphics 4D/35S processors

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

R ISC chip set, operating at 36 M H z, and provide a U N IX environm ent to the user. The

to ta l processing power o f the system is over 1000 M IP S 3.

T he reconstruction processors are organized in to six branches. Each branch is m an

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

con tro l links in one branch o f the T L T is shown in F igure 2.9. Events are w ritte n in to

a 5 12kB yte mem ory buffer on the V M E module labelled 2TP, which also comprises two

IN M O S T800 transputers. The 2TP module sits in the Event B u ilde r crate, a V M E crate

separate from the T L T . The Ferm ilab Branchbus [50] is used as the data lin k between

the Event B u ilde r crate and the T L T processors. Branchbus VM Ebus Interface (B V I)

m odules [51] s itt in g in the Event B u ilde r crate provide an interface to the Branchbus. For

increased bandw idth, two B V I ’s serve two sub-branches o f reconstruction processors and

a th ird serves the manager processor. The T L T processors are linked to the Branchbus

v ia V M E bus Branchbus C on tro lle r (V B B C ) modules [52] s itt in g in the V M E adaptor of

the processors.

T he manager processor contro ls data input and o u tp u t and communicates w ith the

T L T equipm ent com puter. C on tro l messages are sent between the manager processor,

the reconstruction processors, and the T L T equ ipm ent com puter via E thernet. The

reconstruction processors read events from the Event B u ild e r buffer, reconstruct them ,

3M illion instructions per second.


45

E v e n t B u ild e r C ra te

2 B B BFrom T V V VE v en t B u ild e r P 1 1 1

M a n a g e r P ro c e s s o r

V

2SS BBC

V

3SSBBC

V

3 5SBBC

V

3 5S BB

C

E th e rn e t

VB 3 5 SBC

VB 3 5 SBC

Five R e c o n s tru c tio n

P ro c e s s o rs

B ra n c h b u s S w itc h

¥T o V A X

¥To IB M

F ig u re 2.9 Schematic diagram of the processors, data links, and control links in one branch o f the Th ird Level Trigger.


•16

and m ake a trigge r decision. Triggered events are transferred to a num ber o f destinations

( IB M , V A X ) v ia a Branchbus Switch.

C ontrol Software

The da ta in p u t, ou tpu t, and analysis tasks are d iv ided in to separate processes, which

were w ritte n 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. Th is program, w ritte n m ostly in F O R T R A N , incor

porates software developed offline. Processes called Manage_.Job, M anage_Input, Man-

age_O utput, and M on ito r_E vent run on the manager processors: Manage_.Job allocates

hardware resources and communicates w ith the T L T supervisor process, C on tro l_T LT .

M anage_Inpu t and M anage_O utput coordinate the event in p u t (fro m the E V B buffer)

and o u tp u t (to the V A X and IB M ). M on ito r_E ven t m onitors the software and hardware

perform ance and sends its results to M on itor_Level_3, a process runn ing on the T L T

equipm ent com puter.

Trigger A lgorithm s

The T L T processors have access to the complete event da ta and can use, on average,

300 ms o f processing tim e per event. T hey can therefore perform sophisticated a lgorithm s,

such as track and vertex reconstruction.

T h e trig g e r selection is done in tw o stages. F irs t, a ll events m ust satisfy general

c r ite r ia aim ed a t re jecting backgrounds. Second, physics events o f p a rticu la r interest

are selected w ith specific filters. Events which do not satisfy any f ilte r requirem ent are

rejected. I t is also possible to prescale in d iv id u a l filters, for exam ple, those associated

w ith large event rates. A great advantage of the T L T system is its f le x ib ility : a new

a lgo rithm can be designed, tested, and im plem ented w ith in a few days.

A n unexpected background in 1992 was due to random e lectrica l discharges from the

ca lo rim eter P M T ’s. A ca lorim eter E M C o r H AC cell was defined as a spark candidate i f


47

e

tF ~o

pl 111Ml i ! |

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 P M T ’s:

E l ~ E rE l + E r > 1.5 G eV A N D

e l + e r> 0.9, (2.4)

where E l and E R are the le ft and r ig h t P M T energies. Events were rejected i f they

contained a single spark candidate and l i t t le o the r calorim eter energy (less than 2 G eV),

and i f the C A L F L T b it corresponding to the appropriate ca lorim eter region was set.

A second a lgo rithm , based on ca lo rim eter t im e in form ation , was used to reject beam-

gas events. Particles o rig inating in beam-gas in teractions reach the R C A L about 12 ns

earlier than particles from e lectron-proton in teractions since they do not go through the

nom inal in te rac tion point, as illus tra ted in F igu re 2.10. P M T ’s w ith energy greater than

I GeV in a 3 x 3 array o f cells around the beam pipe in the R C A L and in a 5 x 5 array

o f cells around the beam pipe in the F C A L were used to calculated a mean R C A L tim e,

t R, and a mean F C A L tim e, t F . Events w ith tw o or more P M T ’s above 1 GeV in the

R C A L and in the F C A L were rejected if:

+ 10.5ns| < 4.5ns A N D \ tR — t R — 10.5ns| < 4.5ns. (2.5)

The spark and calorim eter tim e a lgorithm s provided suffic ient re jection power to

reduce the T L T event inpu t rate to an approp ria te level. However, a d d itio n a l a lgorithm s

were used. Fu ll C T D and V X D track reconstruction was perform ed using the V C T R A K

global tra ck reconstruction program [54], and a num ber o f a lgorithm s were used to classify


•18

events:

• a muon finder based on ca lorim eter tim e and energy, to identify cosmic and beam

muons [55];

• a high track m u lt ip lic ity f ilte r, to iden tify physics events;

e the requirement o f an isolated electrom agnetic energy cluster in the ca lo rim e ter

w ith a matched C T D track, to iden tity neutra l cu rren t deep inelastic scattering

events;

• the requirement o f large m issing transverse energy in the calorim eter, to id e n tify

charged current events.

These a lgorithm s were used to flag events as possible physics candidates. T h is scheme

was expanded and reorganized in 1993 as the filte rin g scheme described earlier.

2.4 The ZEUS Offline Environm ent

2.4 .1 Event R econ stru ction

In 1992, ZEUS data were re trieved from IB M cartridges and reconstructed using a farm o f

three Silicon Graphics m ultiprocessors (SG I 480 U N IX stations), each equipped w ith six

processors. Events were reconstructed w ith the Z E P H Y R 4 program [36], which perform s

track and vertex reconstruction, calorim eter c lustering, and global track and cluster

m atching, and the results were appended to the data. W ith in ZE P H YR , ca lo rim e ter

data are corrected by using o ffline ca libra tion in fo rm a tion and by taking in to account

bad P M T ’s. E M C cells w ith less than 60M eV o f energy and HAC cells w ith less than

110 M eV of energy are removed ( “ zero-suppression” ). In 1992, two independent packages

were used to reconstruct C T D tracks: TC R E C O N [56] and V C T R A K . This analysis uses

the results from V C T R A K .

4ZEUS Physics Reconstruction.


49

A filte r program selects events according to the specifications o f the d ifferent ZEUS

physics groups. Events which satisfy the requirements o f a p a rticu la r group are flagged

by setting a specific b it in a f ilte r word which is added to the data. Reconstructed events

which satisfy the requirements o f a t least one group are kept, copied to the DESY IB M ,

and archived on cartridges. The f ilte r a lgorithm s used for th is analysis are described in

Section 3.3.

2 .4 .2 Offline A nalysis

M onte Carlo events arc produced using a variety o f generator programs. The generators

chosen for th is analysis are discussed in Section 3.4.1. To ensure a standard data fo rm at,

the generators are interfaced to a common shell called ZD IS . T he ZEUS detector is

sim ulated w ith M O Z A R T 5, w h ich uses the G E A N T fram ew ork [57] for describing the

detector geometry and tracking partic les through the detector media. Shower term ina to rs

have been added to speed up the s im u la tion of energy deposits in the central ca lorim eter,

and the ca lorim eter response in the M onte Carlo has been tuned to reproduce results

from beam tests [58].

T he fo rm at of the M onte C arlo data is identica l to th a t o f the ZEUS data and one

uses a common reconstruction and analysis chain for both the M onte Carlo and the ZEUS

data, as shown in F igure 2.11. T he Z G A N A program provides a deta iled s im ulation o f the

F irs t, Second, and T h ird Level Triggers. The trigger results are appended to the M onte

C arlo data and are available fo r trigger acceptance studies. M onte Carlo data are then

reconstructed using Z E P H Y R . D uring the reconstruction, e lectron ic noise and uran ium

noise arc added to the sim ulated ca lorim eter P M T energies, before the zero-suppression

process.

The detector s im ulation, tr ig g e r s im u la tion, and reconstruction o f large numbers o f

M onte Carlo events necessitates considerable com puting power. The Funnel environ

m ent [59] has been developed fo r th is purpose. I t makes use o f over f if ty personal com

puters (DECstations from D ig ita l Equipm ent C orporation) used by ZEUS collaborators

5Monte Carlo for ZEUS Analysis, Reconstruction, and Trigger.


50

ZDISPhysics Generator

MOZARTDetector Simulation

ZEUSDAQ

ZGANA

Trigger Simulation

Reconstruction ZEPHYR

FILTERD ST Filter

EAZEEvent Analysis

Event Display

LAZE

Figure 2.11 Data flow of ZEUS data and Monte Carlo data in the offline environment.


51

at DESY. ZDIS events are d is tribu ted to in d iv id u a l nodes v ia E thernet. The nodes run

the same versions of M O Z A R T , Z G A N A , and Z E P H Y R , and re turn fu lly reconstructed

events to the Funnel com puter.

Physics analysis is performed using the E A Z E 6 shell. Users w rite the ir 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 d isp lay (L A Z E ) and a three-dim ensional

event display (G A ZE ) are available to d isplay M onte Carlo and ZEUS data.

6Easy Analysis of ZEUS Events.


Chapter 3

D ata A nalysis

3.1 D escription of th e Problem

The a im o f this thesis is the extraction o f a possible lep toquark signal from the ZEUS

data collected in 1992. In the present analysis, leptoquarks arc searched for in the channel

L Q —> v X . The signature o f these events is identica l to th a t of charged current deep

ine lastic scattering events and is qu ite s trik ing . The neu trino , which carries a large

frac tion o f the centre o f mass energy, goes undetected and, in consequence, there is

missing energy in the event. The disp lay o f a Monte Carlo lep toquark event is shown in

F igure 3.1.

Because the ZEUS ca lo rim e ter does not detect partic les escaping through the beam

pipe, i t does not provide a good measure o f to ta l m issing energy. However, i t does

provide a good measure o f m issing transverse energy, also called transverse m om entum

o r p r • Transverse m om entum is defined as the m agnitude o f the vectorial sum of the

transverse m om entum vectors, px{X + p yiy , associated w ith each ca lorim eter cell i:

Pri = E i s>n 0{ cos (3.1)

p y i = E{ sin O i sin (/>,-, (3.2)

52


53

UCAL tran sverse energy

F ig u re 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.


where 0 ,-, and 4>i are the energy, polar angle, and azim utha l angle o f cell i.

A fte r a p x requirem ent o f 10 GeV, the dom inant e lectron-proton background to lepto

quark events decaying in to neutrino plus je ts is charged current deep ine lastic scattering,

which has a cross-section o f 0.07 nb. However, there are a number of o the r backgrounds:

• Incom ing protons in te rac ting w ith gas molecules inside the beam pipe can deposit

a lo t o f energy in the ca lorim eter and lead to p r > 10 GeV.

• P roton beam halo partic les in te rac ting w ith m ateria l upstream o f the detector can

lead to large pr-

• Cosmic muons, cosmic showers, and muons from the proton beam halo can e m it a

high-energy photon and also lead to large pr-

In order to id e n tify and reject these backgrounds, a num ber o f tools are used: ca lorim e

te r tim e a lgorithm s, a track and vertex reconstruction program, a ca lorim eter clustering

a lgorithm , and a muon finder a lgorithm . These and other relevant analysis too ls are

described in Section 3.2. The data selection procedure used in this analysis is presented

in Section 3.3. T h e M onte Carlo generation o f charged current DIS, and scalar and vec

to r leptoquark events, necessary fo r es tim ating the trigge r acceptance and data selection

efficiency, is described in Section 3.4.

3.2 A nalysis Tools

3.2.1 C5 T im e

The C5 tim e in fo rm a tion is used a t the trig g e r and offline levels to re ject background

events. In a dd ition , C5 tim e d is tribu tions are very useful in m on ito ring the q u a lity o f

the beams and es tim a ting the z position o f ep collisions. D uring each run , the C5 tim e

d is tr ib u tio n is h istogram m ed, com bining in fo rm a tion from a ll bunches. A typ ica l tim e


55

protons

satellite electrons

electrons

20 6040 5030C5 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 tr ib u tio n is shown in F igure 3.2. The larger peak corresponds to the passage o f proton

bunches, while the sm aller peaks correspond to the passage o f p rim ary electron bunches

and sa te llite electron bunches Sns la ter. The unwanted sa te llite electron bunches are

created early in the accelerator chain in the P IA storage ring , which has an RF frequency

o f 125 M Hz (1 /12 5 M H z = Sns).

The C5 electron and pro ton tim es, t e and tp, are re la ted to the 2 position o f the

in teraction vertex:

c = { tp — tc)~ + zcs, (3.4)

where c is the speed o f ligh t and zc 5 is the r position o f the C5 counters (zcs = —314 cm ).

The RMS w id th o f the e lectron bunches, typ ica lly a few centim etres, is sm all compared

to the C5 tim e resolution o f about 0.5 ns. The e lectron t im e d is tribu tion is therefore a

measure o f the C5 tim e reso lution. The proton tim e d is tr ib u tio n is broader than the C5


56

reso lu tion and can therefore be used to ob ta in the length o f the pro ton bunches. For each

run, fits to the p rim a ry electron and sate lhte electron tim e d is tribu tions are performed

using a Gaussian function coupled to an exponentia l ta i l1, as described in [-hi]. The

unsmeared pro ton tim e d is tribu tion , f ( t p), is assumed to be a quadra tic function of

f ( ‘ p) = h ( l - T ( t , - [ „ )■ ) .

where h, t p, and ZP± A are the height, mean, and zeros of the function. A f it to the proton

tim e d is tr ib u tio n is performed using f { t p) coupled to a Gaussian and an exponential ta il.

The unsmeared tim e d istributions for the p rim a ry and sa te llite e lectron bunches (spikes),

and fo r the pro ton bunches (inverted parabola) for Run 4272 are shown in Figure 2.2.

The mean p rim a ry electron tim e and mean proton tim e are used to refine the calorim eter

tim e re jection c rite ria , as described in Section 3.2.3.

S ub s titu ting Equation 3.4 in to Equation 3.5, one obtains the vertex d is tribu tion for

the run . The average vertex z d is tr ib u tio n for the entire running period, / '’( - ) , b obtained

by sum m ing the ind iv id ua l vertex d is trib u tio n s over a ll runs, w eighting w ith the run

in tegra ted lu m in o s ity X,-:

F ( z ) = { [ ( . - + =cs) \ + ( „ ] - i p i } ^ .

D u rin g the fa ll 1992 running period, the r-vc rte x mean and RMS w id th varied up to

20 cm from run to run. The average vertex z d is tr ib u tio n for the runs used in the present

analysis is shown in F igure 3.3 [60]. I t has a mean o f —6 cm and an RMS w id th of 22 cm,

in agreement w ith the vertex d is tr ib u tio n determ ined from photoproduction events, for

w h ich the detector acceptance does not depend much on 2 [61]. A lso shown in Figure 3.3

is the vertex d is tr ib u tio n used ir *he M onte C arlo s im ula tion: a Gaussian function, G(z),

centred around z = 0 w ith RMS w id th o f 25 cm . In order to sim ula te the z d is tribu tion

o f the data in the M onte Carlo, one can weight the M onte Carlo da ta w ith the function

F ( z ) /G ( z ) .

1 According to [44], the exponential tail is an effect of the C5 detector itself.


57

10050-50 0-100Vertex z (cm)

F igu re 3.3 Overall vertex z distribution from the C5 time information, for the runs used in the present analysis (solid curve); vertex z d istribution used in the Monte Carlo simulation (dashed curve).

F ina lly , the C5 tim e d is tribu tions are used to correct the effect o f the sa te llite electron

bunches on the measured lum inosity. E lectrons from sate llite bunches in te rac t w ith

protons at z ~ 1.2 m, close to the F C A L . Such events are rejected a t the trigge r or

offline level w ith ca lorim eter tim e a lgorithm s, as described in Section 3.2.3. T hey do,

however, con tribu te to the measurement o f the lum inosity. The in tegra ted lum inos ity

must therefore be appropria te ly corrected on a run by run basis, according to the size

o f the sa te llite e lectron bunches. D u ring the fa ll 1992 running period, the size o f the

sate llite electron bunches relative to the p rim a ry electron bunches varied from 0 to 23%;

the correction to the integrated lum inos ity for the entire running period is 6% [44].

3.2.2 Track and V ertex R econ stru ction

CTD track and vertex reconstruction is perform ed w ith version 5.0 o f the V C T R A K

program [54]. V C T R A K first perform s two-dim ensional pa tte rn recogn ition in r<fi space,

s ta rting w ith h its in the outermost superlayer and searching for tracks p o in tin g towards

x = y — 0. The tracks are then reconstructed in three-dimensions using the z -by-tim ing


5S

Track 1

Track 2

F ig u re 3.4 Vertex fitting w ith 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 w ith x = y = 0 but lead to a vertex away from a: = y = 0 if the beam line constraint is not used.

in fo rm a tion . Tracks are required to have a m in im um num ber o f h its in each superlayer:

• fo r tracks extending to superlayer live, three hits ou t o f a possible eight in superlayer

one, and two h its out o f fo u r in both superlayers three and five, are required;

• fo r tracks extending to superlayer three only, three h its in superlayer one and two

h its in superlayer three are required;

• fo r tracks w ith h its in superlayer one only, four h its are required.

The track candidates are fitte d to a five-parameter he lix . For each track the num ber of

degrees o f freedom is N y = n — 5, where n is the num ber o f hits.

T he tracks are then fit te d to one or more vertices using the fu ll f it techniques described

in [62]. A diffuse beam line (x = 0, y = 0, and crx = cry = 0 .7 cm) is added to the lis t o f

tracks before the vertex fit . T h is helps the vertex reconstruction efficiency in the case o f

im precise track tra jectories. Consider, for example, the tw o tracks shown in F igure 3.4.

W ith o u t the beam line cons tra in t, one would reconstruct a vertex away from x = y = 0,

even though both tracks are consistent w ith x = y = 0. The beam line constra in t

in troduces no bias in z.


59

W ith the poorer resolution o f the 2 -b y -tim ing system, some vertices are not well

reconstructed when all tracks are assumed to belong to the same vertex. A n op tion to

reconstruct m u ltip le vertices helps to reduce this problem and was used for th is analysis.

3.2 .3 Calorim eter T im e

C alorim eter tim e is a powerful too l to reject beam-gas and cosmic muon backgrounds. In

1992, s im ple rejection a lgorithm s based on out-o f-tim e ca lo rim eter energy deposits were

used at the SLT and T L T . In add ition , a number o f re jection c rite ria were used offline

either as part o f the filte r a lgo rithm running on the ZEUS reconstruction processors or

at h igher levels o f data selection.

The general concepts are as follows. A n average tim e is calculated for a p a rticu la r

ca lorim eter region (R C A L, R C A L Beam Pipe, FC A L, e tc.) using P M T ’s above a certain

threshold. The average can be a sim ple average or a weighted average. In the case o f a

weighted average, the error on the tim e o f each P M T , cr,-, is param eterized as a function

o f the P M T 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. T h is function was

obtained by f it t in g the tim e resolution o f single P M T ’s as a function o f P M T energy for

beam-gas events. The weighted average tim e is given by

‘ = T E R ) ' (3's)i

where the sum is over P M T ’s above threshold in the appropria te ca lorim eter region. The

error on t is given by

St =- 1 /2

(3.9)

Eighteen different ca lorim eter t im e re jection c rite ria , based on different P M T thresh

old, o r d ifferent requirem ents on the num ber o f P M T ’s o r to ta l energy sum in a p a rticu la r

ca lorim eter region, were used in the selection o f the present data. They are described


60

in Section 3.3 and relevant parameters are listed in Table 3.1. Here is an example o f a

re jection a lgorithm :

A weighted average R C A L tim e, t p , is calculated using R C A L P M T ’s above

200 M eV (E min = 200 M eV). A m in im um of two P M T ’s above threshold

is required ( N p m t > 2), the energy sum o f P M T ’s above threshold must

be greater than 1 GeV ( £ jum > lG e V ) , and the \ 2 per degree of freedom

associated w ith tp must be less than three ( x 2/N<if < 3). I f

tp < m in ( —4 .5 ns, — 3 6tn) OR In > m ax(6ns,3 6//*), (3.10)

then the event is rejected. S im ila rly , a weighted average F C A L tim e , </••, is

calculated using P M T ’s in the F C A L region, w ith s im ila r requirem ents on

Emin, N p m t , E ,um, and x 2/A rdf. Events are rejected if

\tp\ > max(6 ns, 3 8tp). (3.11)

Events which satisfy the E m{„, N p m t , E^um, and X2f^ d / requirem ents for

both tp and tp are also rejected i f

\ If ~ £r| > m a x (6 n s ,3 \JS t2F + 5 l2R). (3.12)

A p lo t o f I f — tp versus tn for Run 4272, calculated as described above, is shown in

F igure 3.5. A clear d is tinc tion between proton-gas events, sa te llite clcctron-gas events,

and e lectron-pro ton events can be observed.

3 .2 .4 C alorim eter E nergy Islands

A n a lgo rithm is used to group ca lo rim eter cells in to energy clusters. The a lgorithm ,

w h ich is depicted in F igure 3.6, operates on ca lorim eter towers: an F C A L tower consists

o f fou r E M C , one HAC1, and one H A C 2 cell; an R C A L tow er consists o f two EM C

and one H AC 1 cell; a B C A L tower consists o f one HAC1, one HAC 2, and four EM C


61

Parameter Description

Region Designated calorimeter region, for example, RCAL, RCAL Beam Pipe, FCAL, etc.

Emin Per PM T energy requirement

N P M T Number of PM T’s in the designated region w ith energy greater than Emin

p Energy sum of all P M T ’s in the designated region

E',um Energy sum of all P M T ’s in the designated region w ith energy greater than Emin

t Average time computed as a simple average and using P M T ’s w ith 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 PM T is 1 /o f

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 P M T ~ 1

T a b le 3.1 Parameters used in the calorimeter time algorithms.


62

p-gas300

200

ep physics100 -

sate ll ite e-gas

-10-20-10

F ig u re 3.5 Weighted FCAL and RCAL time (tp — tR versus l R) for Run 4272. A PM T threshold o f 200 MeV is used. Only events satisfying the following requirements for both the RCAL and FCAL are included in the plot: N PMT > 2, E ’um > 1 GeV, and x 2/N<ir < 3- Protongas events, satellite electron-gas events, and clectron-proton events are easily separated. The events rejected w ith the criteria o f Equations 3.10, 3.11, and 3.12 are shown in black.


63

F ig u re 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 o f pointers lead to three different peaks, corresponding to three islands.

cells. The forward (rear) B C A L MAC tower is smaller and on ly encompasses two (three)

EM C cells. Each ca lorim eter tower is assigned neighbouring towers. Those are adjacent

or d iagonally adjacent towers in the same ca lorim eter vo lum e, o r adjacent towers in a

d ifferent ca lorim eter volume. The a lgo rithm is as follows:

• One loops over all towers and, fo r each tower, sets a po in te r to the tow er’s highest

energy neighbour. A tower w ith a po in ter to itse lf is called a peak.

• One loops again over a ll towers and follows the tra ils o f pointers. Each tra il leads

to one and on ly one peak. The towers w ith pointers leading to the same peak form

an island.

One can calculate the to ta l energy, E isiand, and the energy-weighted position, Xisiand,

o f each island by sum m ing over co n tribu tin g ca lorim eter cells:

Eittand = (3‘13)t


61

' island

where £,■ is the centre o f cell z. One can also calculate a weighted island tim e:

I

w ith error-1 - 1 / 2

aland — ^ ]( 1/ ) (3.16)

The sums in Equations 3.15 and 3.16 are over all con tribu ting P M T ’s. The e rro r on the

tim e o f each P M T , cr,-, is given by Equation 3.7.

3.2 .5 M u on F inder

A muon finde r called IS IT A M U [63] is used to iden tify cosmic and beam halo muon

events. The a lg o rith m is based on the fo llow ing facts:

1. Cosmic muons can leave a tra il o f ca lorim eter cells above threshold in the FC A L

or R C A L aligned in a s tra igh t line.

2. Beam halo muons can leave a tra il o f ca lorim eter cells above threshold in the B C A L

aligned in a s tra igh t line.

The a lgo rithm operates on the (x , y , z ) position o f ca lorim eter cells above 100 MeV and

searches for cells aligned in the xy plane (F C A L and R C A L) or xz plane (B C A L ). The

Pearson coefficient, r , and the c ircu la rity , c, are calculated in d iffe rent planes and, de

pending on the results, a flag is re turned w ith value 2 (muon candidate), 1 (probable

muon candidate), 0 (unclear ob jec t), o r —1 (not a muon).

Consider an event w ith n cells above threshold in the R C A L. The Pearson corre lation

coefficient between the X{ and i/,- positions o f the cells is

r = £(*» - g)(y» - y) (3 . 17)


65

where

x = a;,-, (3 .IS)n

y = (3-19)

Before ca lcu lating the c ircu la rity , the coordinate system is firs t m odified, as follows. The

centre o f the cell c luster is defined as (x 0,2/o), where

xq = (smallest o f all X i ’s + largest o f a ll x , ’s )/2 , (3.20)

j/o = (smallest o f all y i ’s + largest o f a ll y i ’s ) / 2 . (3.21)

The coefficients x,- and y, are fitted to a s tra igh t line x = a + by. The coordinate system

is then moved to the centre o f the cell cluster and ro tated through an angle 0 , where

co s , = (3.22)

s in , = j J & p (3.23)

In the new coordinate system, the centre o f the cell c luster is

(*o» Vo) = (a + by0, y0). (3.24)

and the new cell positions are

x'i = [X i - Xq) cos 0 - ( y i - y'0) sin 6 , (3.25)

y'i = {yi - y'o) cos 6 + (x,- - Xo) sin 6. (3.26)

The c ircu la rity in the new coordinate system is

, ,/E *f-E s -i2)J+4(i>;!/;)2C = 1 ----------------- e x ? + e j ? -------------- • ( 3 ' 2 7 )

A n event w ith |r| > 0.7 and c < 0.1, fo r exam ple, is classified as a muon candidate.


66

3 .2 .6 R econstru ction o f K inem atic V ariables

K inem atic x is an im p o rta n t variable since i t is related to the leptoquark mass. (Recall

th a t x ~ m ^ q /s . ) The k inem a tic variables :r, y, and Q2 o f leptoquark events decaying

in to neu trino plus jets, and o f charged current DIS events, can only be reconstructed from

the je t particles since the outgo ing lepton is a neutrino. In th is case, the Jacquet-Blondel

m ethod [64] m ust be used. The outgoing hadrons can be described by the four-m om entum

w:

v, = £h.

/ lk \Pxh

Pyh

\ P z h /

where the sum is over a ll hadrons. Consequently, the four-m om entum transfer q can be

expressed as

( [ .h

q = w - p p = (3.29)

f( 'ZEk)-Ep\h '

r . Pxh.hy,Pyh.h

(y,pSh)-Ep)x h j

where E p is the incom ing p ro ton energy. Using Equations 1.41 and 1.43, one obtains:

V =

Q2 =

EiEk-p*)_h___________

2 E e

f e p r Ov h ' v h '

i - y

(3.30)

(3.31)

where E e is the incom ing e lectron energy.

For L Q —> v X events and charged current events, Equations 3.30 and 3.31 become:

y -

Q2 =

E - P z 2 E e

Pt

i - y ’

(3.32)

(3.33)


67

where E is the to ta l energy, p . is the to ta l energy in the z d irection , and px is the

transverse mom entum . The k inem atic x variable is then s im p ly

O 2x = 2 - . (3.34)

sy

Note tha t the kinem atic variables reconstructed w ith the Jacquet-B londel m ethod

are not largely affected by undetected particles escaping through the beam pipe because

those particles give a small co n tribu tio n to E — pz and px-

3 .2 .7 L um inosity C alcu lation

Integrated lum inos ity is given by the ra te of ep brem sstrahlung photons detected in the

L U M I photon calorim eter, Rep, d iv ided by the ep brem sstrahlung cross-section corrected

for detector acceptance, cr°£\ The rate o f ep brem sstrahlung can be estim ated using the

fo llow ing form ula:

R ep = ( R to t - Rcgas ~ (3.35)

where Rloi is the to ta l rate o f events in the photon ca lorim eter, R egas is the rate o f

elcctron-gas background events, and R se*tell,ic is the rate o f ep brem sstrahlung events

from sa te llite electron bunches. The ra te o f electron-gas events is estim ated using the

e lectron p ilo t bunch:J t o t

Regas — .pilot R p i lo t i (3.36)1e

where I * ot and I ^ ,loi are the to ta l e lectron and p ilo t electron currents, and R pu0t is the ra te

o f events for the electron p ilo t bunch. The con tribu tion from sa te llite e lectron bunches

is estim ated using the C5 tim e d is tribu tions (cf. Section 3.2.1).

D uring 1992, the integrated lum in o s ity measured by ZEUS was over 30 nb -1 . The

in tegrated lum inos ity used in th is analysis is lis ted in Table 3.2 fo r the three C A L F L T

trigger configurations o f 1992.


Trigger Configuration Integrated Luminosity

(n b - ‘ )

D A Y l 2.20 ± 14%

LOW _REM C 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 D ata Selection

The selection o f the data is broken down in to five levels o f filte rs. The level one and level

two filte rs are run on the offline reconstruction processors as part of the selection process

for the ZEUS Exotics physics w orking group. The level three filte r is used by the Exotics

group as a firs t step in the data analysis. The level four and level five filte rs are used in

the last stage o f data selection. These last two filte rs u tilize selection c rite ria developed

by the Exotics group and a lgorithm s designed specifically for the present analysis. Events

rem aining a fte r the f ilte r selection are v isua lly scanned w ith the LAZE event d isplay and

form the final event sample.

3.3 .1 T h e L evel O ne F ilter

The firs t selection c rite rion used at the level one f ilte r is aimed at ide n tify in g LQ — > v X

events and charged curren t DIS events. I t is based on the to ta l ca lo rim eter transverse

m om entum :

p r > 10 GeV. (3.37)

The p t sum is over a ll good calorim eter cells. A cell is considered bad i f the fo llow ing

three conditions are satisfied:

1. The energy o f the cell is greater than 200 M eV.


69

410

10

1

60 80 1000 20 40pT(GeV)

F ig u re 3.7 pT distribution for Run 4272.

2. The energy imbalance between the ce ll’s le ft and r ig h t P M T ’s, |(£ x — E r ) / ( E l +

E r ) |, is greater than 0.7.

3. Both P M T ’s are good channels, according to the lis t o f bad channels for the run.

Bad cells arc usually cells w ith undetected sparks, cells w ith bad P M T ’s which have not

yet been included in the bad channel lis t, or cells adjacent to the beam pipe and w ith

energy deposits from particles entering only in to the wavelength sh ifter. The p r d is tr ib u

tion for Run 4272 is shown in F igure 3.7. O ut o f a to ta l o f 2391S events (corresponding

to an integrated lum inos ity o f 0.9 nb -1 ), only 321 events (1.3%) are le ft a fter the px

requirem ent.

The subsequent selection c rite ria are aimed at re jecting standard backgrounds:

• Beam pipe P M T ’s w ith energy greater than 1 G eV are used to calculate sim ple

average FC A L and R C A L times. Events w ith tw o o r more beam pipe P M T ’s

above 1 GeV in both the F C A L and R C A L are re jected i f

|f/? + 14 ns| < 6 ns A N D \tp — tn — 14ns| < 6ns. (3.38)


70

The above was an early im p lem enta tion of the T L T ca lorim eter tim e a lgorithm . A l

though it is less restrictive than the updated T L T a lgorithm , i t rejects background

events w h ich were kept at the T L T for m on itoring purposes.

• Events are rejected i f they were flagged as a spark candidate at the T L T . (For

m on ito ring purposes, some spark events were not rejected at the T L T .)

o Events w ith the Co trigger b it set, ind ica ting a veto by the C’5 detector, are rejected.

A ll events rem ain ing after the level one filte r c rite ria are passed to the level two filte r.

3 .3 .2 T h e Level Tw o F ilter

The level two f ilte r c rite ria are aimed at re jecting cosmic and beam muons, spark events

w ith a bad channel, and general o u t-o f-tim e backgrounds:

• Events are rejected i f flagged as a muon candidate by the IS IT A M IJ muon finder.

• Events are rejected i f the highest energy cell in the ca lorim eter has a bad P M T and

i f the energy sum of a ll o ther ca lo rim e ter cells is less then 2 GeV.

• Events are rejected based on ca lo rim eter tim e, as described below.

There are five calorim eter tim e re jection c rite ria used at the level tw o filte r, each one

dealing w ith a different ca lorim eter region. The regions are F C A L Extended Beam Pipe

(com pris ing the 5 x 5 array o f cells surround ing the beam pipe in the F C A L ), R C AL Beam

P ipe (com pris ing the 3 x 3 array o f cells surrounding the beam pipe in the R C A L), R C AL,

F C A L , and E n tire C A L (the entire ca lo rim eter). A weighted average tim e is calculated

fo r each region using P M T ’s above a specific threshold F min, as described in Section 3.2.3.

O n ly P M T ’s fro m good ca lorim eter cells are considered. There are requirem ents on the

num ber o f P M T ’s above threshold, N pmt, the energy sum o f P M T ’s in the region, E „ im ,

and the x 2 Per degree of freedom associated w ith the average tim e . T he tim e c rite ria

and associated parameters are lis ted in Table 3.3. For an event to be rejected based on

a pa rticu la r t im e crite rion , a ll associated requirements m ust be satisfied.


71

Region Aprnt F ■

(GeV)

p sum

(GeV)X ' / N d f Rejection Criterion

FCAL Extended Beam Pipe 4 0.20 1 3 |£f| > max(6 ns, 3 Stp)

FCAL 6 0.08 1 3 I f f l > 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 |ff i| > max(6 ns, 3 <5</j)

Entire CAL 16 0.08 — — |f] > max(8 ns,4 6t)

Table 3.3 Level two calorimeter time rejection criteria. For a description o f the parameters, see Table 3.1. Events are rejected only i f the requirements on Npmt, Em{n, E aum, and x 2/ATdj are satisfied. An entry w ith “ —” indicates no requirements.

O ut o f the 4 x 106 events triggered in 1992, 1S989 events are le ft a fte r the selection

crite ria o f the level one and level two filte rs and are passed to the level three filte r .

3.3.3 T h e L evel Three F ilter

The level three f ilte r c rite ria are as follows:

• Events are re jected i f flagged as a probable muon candidate by the IS IT A M U finder.

• Events are rejected if the C A L data stayed in the analog pipelines longer than one

thousand beam crossings. T h is c rite rio n targets a very sm ail num ber o f events for

w hich the C A L data stayed in the p ipe line for an extended period o f t im e and, as

a resu lt, were degraded.

• Events are rejected w ith the ca lo rim e ter tim e c rite ria described below.

The level three ca lorim eter tim e re jection c rite ria and relevant param eters are listed

in Table 3.4. W eighted average tim es are calculated using good cells in three ca lorim eter

regions: F C A L , R C A L , and E ntire C A L . In d iv id u a l P M T energy thresholds o f 80 M eV,

200 M eV, and 1 G eV are used, along w ith requirem ents on the num ber o f P M T ’s above

threshold, N pmt, the energy sum o f P M T ’s above threshold in the region, ££um, and the

X2 per degree o f freedom associated w ith the average tim e.


Reproduced

with perm

ission of the

copyright ow

ner. Further

reproduction prohibited

without

permission.

Region(s) N p m t F ■

(GeV)

pmsum

(GeV)

X ' / N jj Rejection Criterion

FCAL, RCAL 2 ,2 1.00 1, 1 3, 3 — i H| > max(6ns,3 \J6t% + 6t%)

FCAL, RCAL 2 ,2 0.20 1, 1 3, 3 - *«| > max(6 ns, 3 \/6t% + 6t%)

FCAL, RCAL 4 ,4 0.08 1,1 3, 3 - in i > max(Gns,3 \ /6 t2F + 6t%)

FCAL 2 1.00 1 3 | / f | > max(6ns,3 6 if )

FCAL 2 0.20 1 3 j t f l > max(6ns, 3 S t F )

FCAL 4 0.08 1 3 |ij,| > max(6 ns, 3 6tF)

RCAL 2 1.00 1 3 i n < m in(—4.5ns, —3 6ff l) OR Ir > m ax(6ns,3 StR)

RCAL 2 0.20 1 3 i r < m in(—■4.5 ns, - 3 6 1 r ) OR I r > max(6ns,3<5f/i)

RCAL 4 0.08 1 3 tR < m in (-4 .5 ns, — 3 6tR) OR I r > max(6ns,3 61r )

Entire CAL 8 0.08 — — |f| > max(6 ns,4 6t)

Table 3.4 Level three calorimeter time rejection criteria. For a description o f the parameters, see Table 3.1. Events are rejected only if the requirements on Npmt, E m £ ‘um, and \ 2/A rd/ are satisfied. An entry w ith u—” indicates no requirements.

—i t o

73

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, Emin, and E ’um are satisfied.

The level three muon a lgo rithm reduces the event sample from 18989 to 10909 events.

The requirem ent tha t the C A L data should not sit in the analog pipelines longer than one

thousand beam crossings rejects an add itiona l 206 events. T he level three ca lorim eter

tim e rejection c rite ria reduce the sample to 5595 events, w h ich are passed to the level

four filte r.

3.3 .4 T he Level Four F ilter

In the firs t three filte r levels, there are no requirements o f an event vertex. The level four

filte r consists o f general background rejection a lgorithm s plus the requirem ent o f a C TD

vertex w ith |r | < 75 cm:

• Events are rejected i f the C T D was not on for th a t event.

• Events are rejected i f there is more than 5 GeV o f energy in the electron ca lorim eter

o f the lum inosity m on ito r. T h is c rite rion targets pho top roduction background.

• Events are required to occur in one o f the nine co llid ing e lectron and proton bunches

(i.e ., not in a p ilo t electron o r proton bunch).

• Events are rejected w ith the ca lorim eter tim e c rite ria lis ted in Table 3.5.

• F ina lly , events are required to have a reconstructed ve rtex , as described below.

Tracks and vertices are reconstructed using the V C T R A K program , w ith the beam

line constra in t and m u ltip le vertices options. The highest m u lt ip lic ity vertex is taken as

the event vertex and m ust satisfy the fo llow ing requirem ents:


74

a 60

REJECT REJECT

100Vertex z - Z nm (cm)

200-200 -100

F ig u re 3.8 Vertex z — z run distribution o f the data after the level four filter criteria (excluding the vertex requirement) are applied.

1. X'2 Per degree o f freedom less than ten.

2. |z — zTun| < 75 cm, where z run is the mean vertex c for the run , as calculated from

the C5 electron and proton tim es (cf. Section 3.2.1).

Since V C T R A K is run w ith the beam line constra int option , there are no requirements

on the x and y positions o f the reconstructed vertex. The vertex d is trib u tio n o f the

data, a fte r the level four f ilte r c rite ria (excluding the vertex requ irem ent), is shown in

F igure 3.8. O n ly vertices w ith x 2/^ d f < 10 are included in the p lo t.

T he num ber o f events rem ain ing a fte r each level four re jection crite rion is listed in

Table 3.6. O u t o f the 5595 events en te ring the level four filte r, 836 events remain a fte r the

level fou r f i l te r c rite ria , w ith most o f the re jection being due to the vertex requirem ent.

3 .3 .5 T h e L evel F ive F ilter

T he level five f ilte r c rite ria are:

• Require p r > 10 GeV, where p r is now corrected for the event vertex.


75

• Require p r > 10 GeV, excluding cells from islands w ith pseudorap id ity2 p > 3. The

m otiva tion o f this requirem ent is given below.

• Require y, reconstructed w ith the Jacquet-B londel m ethod and corrected for the

event vertex, to be less than one.

• Require the calorim eter island tim es to be consistent w ith cp events, as described

below.

It was discovered tha t there was a class o f beam halo background events w ith asym

m etric energy deposits in the F C A L , leading to large p r- These events m ight be due

to co llim ators w hich were positioned asym m etrica lly. The frac tion o f those background

events changed from run to run, suggesting th a t this effect is related to the q u a lity o f the

beams. The events have between 150 GeV and 300 GeV o f energy in the F C A L and very

lit t le R C A L or B C A L energy. Furtherm ore, 95% o f the ca lorim eter energy is located in

one island centred around 7/ ~ 3.5 (0 ~ 3.5°) and <f> ~ 7r, i.e., centred on the F C A L cell

on the r ig h t o f the beam pipe (negative x value). Th is is shown in F igure 3.9. The island

consists, on average, of a hundred ca lo rim e ter cells. To reject th is class o f events, but

keep a large efficiency for LQ —► u X and charged current events, p r is recalculated using

only cells from islands w ith p < 3 (0 > 5.73°) and is required to be greater than 10 GeV.

The p r d is tr ib u tio n calculated in th is m anner, for events entering the level five filte r, is

shown in F igure 3.10.

The Jacquet-B londel y crite rion targets background events which have somehow sur

vived the previous selection crite ria . O ut o f the th irteen events re jected w ith th is last

c rite rion , eleven have over 80 GeV o f energy in the R C A L, which c lea rly indicates a

non-cp in te rac tion [66].

The purpose o f the island tim e requirem ent is to reject cosmic muons and events w ith

hardware problems. For each event:

Consider the two highest E r islands in the event. I f they both have more

than 500 M e V o f energy, then require the tim e difference between the tw o

2Pseudorapidity is related to polar angle as follows: p = — In[tan(0/2)].


76

2_-Si■».Q“5

•g

6

5

4

3

2

1

0■2 0 2 4■4

Island pseudorapidity

F ig u re 3.9 Azimuthal angle versus pseudorapidity o f 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

COfN

a.a363

10 ■

10

, I , M0 20 40 60 80 100

pT excluding forward islands (GeV)

F ig u re 3.10 pT, calculated using cells from islands w ith tj < 3, for events entering the level five filter.


77

a

1.5

0.5

Figure 3.11 Time difference between the two highest Et 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 o r 5 \fStJ3landl + Stfsland2, whichever is larger.

T he island tim e difference, fo r events le ft p rio r to the island tim e requirem ent, is shown

in Figure 3.11. There is a c luster o f events at \ t isiandi ~ tisiand2\ — 10 ns, characteristic of

cosmic muons.

The level three, level four, and level five filte r selection c r ite r ia are listed in Table 3.6,

along w ith the number o f events le ft a fte r each crite rion . The island pj- requirem ent

rejects 95% o f the events entering the level five filte r, reducing the sample to th irty -e ig h t

events. The Jacquet-Blondel y requirem ent and the island tim e requirem ent reduce tha t

num ber to five events.

3 .3 .6 F inal D a ta Sam ple

Five events remain a fte r the f ilte r procedure. T h e ir properties are sum m arized in

Table 3.7. Upon scanning the events w ith the LA Z E event d isplay, four are found to be

cosmic muon or cosmic shower events, and one is a charged cu rren t candidate. D u ring

the scan, an event is classified as a cosmic m uon or cosm ic shower event based on the


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 C T D on •18-17

Require L U M I 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 p r > 10 GeV (vertex corrected) 011

Require p r > 10 GeV (excluding forward islands) 35

Require y jB < 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.


79

Run Event

(cm)% Zrun

(cm)

r / N df N tr P t

(GeV)

X y Q2(GeV2)

\A t\

(ns)

5 a

(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.

Table 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 o f 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 o f tracks associated w ith 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.

follow ing crite ria : the event has energy clusters in the top and bo ttom halves o f the

calorim eter; the energy clusters are o u t o f tim e ; and C T D tracks align w ith the clusters

in a s tra ight line. I t was found that the cosmic muon events go through the interface of

two ca lorim eter regions (see Figure 3.12) and fa il the is land tim e re jection c rite ria . The

cosmic shower events have energy clusters in the top and bottom sections o f the B C A L

but the tim e difference between the tw o highest E t islands is w ith in 5a.

The charged current candidate has a d is t in c tly d ifferent topologv than the cosmic

muon and cosmic shower events. It consists o f tw o h ig h -p r jets in to the F C A L ; the je ts

are clearly identified by two ca lorim eter clusters w ith associated C T D tracks. The event

vertex is at z = —36 cm and the reconstructed p r , a fte r vertex correction, is 81.5 GeV.

The k inem atic variables reconstructed using the Jacquet-B londel m ethod and corrected

for the event vertex, are x = 0.31, y = 0.41, and Q 2 = 11000 G eV2. The event is shown

in Figure 3.13.

The efficiency o f the scan for leptoquark events is d iffic u lt to estim ate. As a check,

one can replace the scan w ith the fo llow ing a lgorithm :

I f the event vertex consists of tw o tracks and i f the highest E t is land in the


so

ZEUS

ZR

F ig u re 3.12 Event display o f a cosmic muon event remaining after the filte r procedure. A z r projection of the detector is shown on the left and an xy projection is shown on the right.


81

[TA PH

F ig u re 3.13 Event display of the charged current candidate. A lego plot o f 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).


75444585

S»\

event has —0.5 < r/ < 0.1 then reject the event.

T h is a lgorithm rejects all fou r cosmic events and would lower the elliciency o f scalar and

vector leptoquark events by less than 0.2%.

3.4 M onte Carlo Sim ulation

3.4.1 Event G eneration

Scalar leptoquark events ( e~p —► 5'o —> v X ) are generated w ith a m odified version o f the

general-purpose M on te C arlo event generator P Y T II IA 3 [07]. Vector leptoquark events

(e~p —*■ Vo —> v X ) are generated w ith the L Q U A R K generator [68]. Both generators

include leptonic in it ia l state rad ia tion and use the Lund parton shower model for Q ( 'l)

fragm entation (v ia JE T S E T [69]).

Samples o f scalar leptoquarks, a thousand events each, were generated at the fo llow ing

lep toquark mass points: 50, SO, 100, 120, 150, 180, 220, and 280 G e V /c2. Samples of

vector leptoquarks, also a thousand events each, were generated at the follow ing mass

points: 50, 80, 120, 150, 180, 220, and 2 50 G cV /c2. The leptoquark Yukawa coupling was

set to 0.31 (electroweak coupling strength) and the s truc tu re function param eteri/.ation

used was M T B l.

The interference between the leptoquark and the charged current DIS contribu tions

to e~p —► v X is expected to be small. According to LQ U A R K the ra tio o f the in

terference cross-section to the leptoquark cross-section is less than 4% for leptoquark

masses between 30 G eV /c2 and 150 G eV /c2. For higher masses the effect is larger: +37%)

for 225 G eV /c2 So —► v X and —32% for 225 G eV /c2 Vo —> v X . In th is analysis, the

interference te rm is neglected.

The d iffe ren tia l cross-sections fo r the processes c~p —► So —> u X and c~p —> .S'| —> u X

are identica l. S im ila rly , the d iffe ren tia l cross-sections fo r 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.


u— l- iC L ~ U c i : ,L j i I l _ j i I i i i I i i i___

0 0.2 0.4 0.6 0.8 I

x

F ig u re 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 (V q ) leptoquarks

also applies to S i (V i) leptoquarks.

Charged cu rren t deep inelastic scattering events are generated w ith the HERACLES

generator [70] coupled to A R IA D N E [71]. A R IA D N E sim ulates QCD cascades based

on the co lour d ipo le model. QCD rad ia tion is described as rad ia tion from the colour

dipole form ed between the struck quark and the proton rem nant, an approach which

has been shown to agree well w ith the neu tra l current DIS da ta [72]. A to ta l o f 5000

charged curren t events were generated, w ith M T B i s tructure functions and including

lep ton ic in it ia l state rad iation. The to ta l charged current cross-section, as calculated

w ith H E R A C LE S , is 0.07 nb.

3.4 .2 T rigger A ccep tan ce and S election Efficiency

The M onte C arlo s im u la tion o f the detector is done w ith M O Z A R T , the trigge r acceptance

is calculated w ith Z G A N A , and the same f ilte r program used fo r the data is used for the

M onte C arlo samples. The effect c f the detector s im ulation on the x d is tr ib u tio n of

150 G e V /c2 scalar leptoquark events is shown in Figure 3.14.


84

The trigger acceptance as a function o f lep toquark mass, fo r scalar and vector lepto

quarks, is shown in Figure 3.15. The acceptance is 70% to 90% for lep toqua rk masses

between 50 G oV /c2 and 100 G eV /c2. For higher masses the acceptance is close to 100%.

The selection efficiency is shown in F igure 3.16. The efficiency ranges from 70% to 90%

for scalar leptoquarks w ith masses between 5 0 G e V /c2 and 250G eV /c2. The efficiency

for vector leptoquarks is lower, ranging from 65% to S5%, w ith most o f the inefficiency

being due to the vertex requirement.

The difference in efficiency between scalar and vector leptoquarks is explained by the

different k inem atic y d is tribu tions o f scalar and vector events. Scalar lep toquarks have a

fia t y dependence, while vector leptoquarks have a y d is trib u tio n p roportiona l to (1 — y )2,

as shown in F igure 3.17. The hadrons in low-y events tend to go in the forw ard d irection

and, as a result, i t is d ifficu lt to reconstruct tracks and vertices in those events. Consider

the case o f 180 G e V /c 2 vector leptoquarks. O u t o f 991 events le ft a fte r the level three

filte r requirem ents:

• 94 events (9% ) have no tracks;

• 26 events (3% ) have one or more tracks b u t no vertices;

• 79 events (8% ) have a vertex b u t 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 fo r charged current D IS events is esti

mated to be 68%. The estimated background con tribu tio n from charged cu rren t events

to the data sample is therefore:

0.07 nb • 27.5 nb-1 • 68% = 1.3 events. (3.39)

The reconstructed x d is tribu tion o f charged curren t DIS M onte Carlo data , a fte r trigger

acceptance and selection efficiency, is consistent w ith the reconstructed x o f the charged

current candidate, as shown in F igure 3.18.


S5

&

'jS?

0.75

0.5

0.25

6 P > S q > V X

o DAYl □ LOW_REMC a LOW_BEMC• Luminosity-Weighted Average

i i t i i i t . I50 100 150 200 250

•>Leptoquark mass (GeV/c )

&

uS£j

0.75

0.5

0.25

1 e p —> V0 -> V X

o D A Yl □ LOW _REMC a LOW _BEMC• Luminosity-Weighted Average

i i i i I i ' ' ' I i i i i I ' i i i I50 100 150 200 250

2Leptoquark mass (GeV/c )

F ig u re 3.15 Trigger acceptance for S0 and V0 leptoquarks decaying into u X . (The statistical errors are smaller than the data points.)


S6

0.75

0.5

0.25

050 100 150 200 250

Leptoquark mass (GeV/c~)

T

_ 6 p —> S q —* v X

" o Trigger□ pT > 10 G eV

~ a Vertexa pT > 10 G eV (excl. islands)

1 1 1 1 1 ! ! 1 i 1 . 1 1 1 1 1 1 1 1 1

I -■2iis,

0.75

0.5

0.25

T

1 e p - > V0 - ¥ vX

o Trigger □ pT > 10 G eV

~ 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 250Leptoquark 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.)


F ig u re 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

I10 l■3 ■2

1010 10

F ig u re 3.18 Reconstructed x d istribution 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.


ss

3.5 K inem atics of the Charged Current C andidate

The reconstructed kinem atic variables o f the charged current candidate are

pT = 31..5 GeV, (3.40)

x = 0.31, (3.41)

y = 0.41, (3.42)

Q 2 = 11000 GeV2. (3.43)

One can estim ate the true k inem atic variables using the scalar lep toquark M onte Carlo

samples, which have an approxim ate ly fla t generated y d is tr ib u tio n , and a narrow gen

erated x d is tr ib u tio n centred around x = tti2Lq / s. The event sample generated w ith

iulq = 180 G e V /c 2 is best suited here since i t corresponds to a generated x o f 0.37 and

a reconstructed x of about 0.21 to 0.31. T he shifts and resolutions in px, x , y , and

Q 2 as a function o f reconstructed y, a fte r da ta selection, are shown in F igure 3.19. For

1UB — 0.41, one obtains:

[ T T tru e ~ P T ) ) / P T t r u e = 15% ± 10% (3-44)

(x iruc — x JB ) / x truc. = 30% ± 19% (3.45)

(y tru e -y jB ) ly tru e = -3 % ± 34% (3.46)

( Q L e - Q j B ) / Q l u e = 29% ± 18% (3.47)

Hence, the estim ated true values for the charged current candidate are

pT = 96 ± 1 0 GeV, (3.48)

x = 0.44 ± 0 .0 8 , (3.49)

y = 0.40 ± 0 .1 4 , (3.50)

Q2 = 16000 ± 3 0 00 G eV2. (3.51)


Q2 s

hift

(%)

y sh

ift (

%)

x sh

ift (

%)

pT

shift

(%

)

Figure 3.19180 GeV/c2 6

89

r ■ ' ' 111 i ! i n l ; i0 0.2 0.4 0.6 0.8 1

y t.t

• ? 50 ^ 40,Q

| 30 c§ 20 K

^ 10

0 I I 1 ! 1 1 ! I I I ' I ' ' I

0 0.2 0.4 0.6 0.8 I

50

25

0

-25

-50

0 0.2 0.4 0.6 0.8 1

Si.5

50

40

30

20

10

00 0.2 0.4 0.6 0.8 I

50

25

0

-25

-50

0 0.2 0.4 0.6 0.8 1

S.,5

"5

50

40

30

20

10

00 0.2 0.4 0.6 0.8 I

>'j b y'jn

50

25

0

-25

-50

0 0.2 0.4 0.6 0.8 1

si5

"5£Cl

50

40

30

20

10

00 0.2 0.4 0.6 0.8 I

>'j b yJB

Shifts and resolutions in pT, x, y, and Q 2 as a function o f reconstructed y , for ’n —► v X events.


Chapter 4

Limits on Leptoquarks

4.1 Lim it C alculation

One event remains a fte i the data selection process described in Chapter 3, w hich is

consistent w ith the estim eted 1.3 events expected from charged current deep ine lastic

scattering. Since there are no lep toquark signals, lim its on scalar and vector lep toquark

cross-sections and couplings have been calculated. They are presented in th is chapter.

F irs tly , the reconstructed lep toquark mass d is tr ib u tio n , m rcc, is p lo tted and f it te d to

a Gaussian d is trib u tio n for each separate leptoquark M on te C arlo sample. Note th a t

m rcc = \ A JB ' where x j b is k inem atic x reconstructed w ith the Jacquet-B londel

m ethod and corrected for the event vertex. The means ( f t ) and standard deviations

(a ) o f the Gaussian d is tribu tions , as a function o f generated lep toquark mass, are shown

in F igure 4.1.

Secondly, the means are f itte d to firs t-o rder po lynom ia ls in m,LQ and the standard

deviations are fitted to second-order polynom ials in t t i l q . The results o f 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)

90


91

§o

■aSiu

250

200

150

100

50

02001000

%

Leptoquark mass (G eV/c)

535"s3

UhJsc

250

200

150

100

50

0

§o,3

"3

100 200Leptoquark mass (GeV/c )

30

10

00 100 200

Leptoquark mass (CeV/c~)

30

20

,0

00 100 200

Leptoquark mass (GeV/c")

F ig u re 4.1 Mean reconstructed leptoquark mass and mass resolution as a function of generated 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)

<r(mLQ) = 1.9 + 0.03S ■ m.LQ + 0.000006 ■ m 2L Q , (4.4)

for vectors. In the above four equations, /z, cr, and are expressed in G eV /c2. The fits

are shown as curves in F igure 4.1. The reconstructed masses o f scalar (vector) leptoquarks

are 12% (7%) sm aller than the generated masses.

T h ird ly , a search region as a func tion o f leptoquark mass is defined as ±


92

%cr(mLQ). T h is search region is chosen such th a t i f there was a lep toquark signal to

observe at i t would be visib le w ith in th is w indow. The overall efficiency, a fter trigger

acceptance, f ilte r selection, and the requirem ent tha t the reconstructed lep toquark mass

is w ith in 3 <7 o f /r, is calculated for each lep toquark M onte Carlo sample. The overall

efficiencies as a function o f leptoquark mass are shown in Figure 4.2. For leptoquark

masses between 50 G eV /c2 and 225 G e V /c2, the overall efficiency is 70% to 80% for

% —»■ v X , and 60% to 85% for Vo —> u X . The efficiencies are fitte d to a fourth -order

polynom ial in ttilq. Those are shown as curves in Figure 4.2.

Upper lim its on the leptoquark cross-sections, as a function of lep toquark mass, are

calculated using the lim it expression for Poisson statistics in the presence o f background

given in A ppend ix A . For ttilq ranging from 5 0 G eV /c2 to 225G e V /c2, the num ber of

observed data events and the number o f expected charged current D IS background events

inside the search region, i.e., w ith

u { m L Q ) - Z a - { m i Q ) < m TCC < n { m L Q ) + 3c r ( m L Q ) , (4.5)

are counted. The 95% confidence level (C .L .) upper lim its on the lep toquark con tribu tion

are then calculated using Equation A .15. The parameterized efficiencies, along w ith

the integrated lum inos ity o f the data, are then used to calculate an upper l im it on the

leptoquark cross-sections:$ l im i t

G lim i t — 7 “e • L

The theoretica l So (Vo) leptoquark cross-section, as a function o f lep toquark mass, is

calculated using the P Y T H IA (CO M PO S [73]) M onte Carlo program . The cross-section

calculation includes lepton ic in it ia l state rad ia tive corrections, ignores the lep toquark-D lS

interference te rm , assumes an LQ - * v X branching fraction o f 1 /2, assumes a coupling

Af, = 0.31 (the electroweak coupling s treng th ), and uses the M T B l parton d is trib u tio n

functions. T he cross-section is calculated fo r d ifferent ttilq values (in steps o f about

25 G eV /c2). For masses between these values, the cross-section is in te rpo la ted assuming

an exponentia l behaviour for the cross-section.

F ina lly, upper lim its on the lep toquark couplings, as a function o f ttilq, are calculated


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 - _

0.25 -

e p — > Vq — > vX

o Trigger• Trigger and filte rm Trigger, filter, and mass requirement

100 150 200 250. f 2 ,Leptoquark mass (GeV/c )

F ig u re 4.2 Overall efficiency for So and V0 leptoquarks decaying into u X . (The statist errors are smaller than the data points.)


94

using

A , , w , = 0 . 3 1 . p ^ . (4.7)Y crAi =0.31

Before showing the lim its , the question o f systematic errors is addressed in the fo llow ing

section.

4.2 System atic Checks

In the present analysis, system atic uncerta inties are due to the integrated lum inosity,

the theoretical leptoquark and charged current cross-sections, and the leptoquark e ffi

ciency. The error on the in tegrated lum inos ity is 6% (see Section 3.2.7). Comparisons of

the leptoquark cross-sections calculated w ith COM POS, L Q U A R K , and P Y T H IA , show

variations o f 6% [74]. The in te rpo la tion of the cross-sections to d ifferent m iQ values

introduces an add itiona l e rro r o f 4%. The overall uncerta in ty on the leptoquark cross-

sections is therefore estim ated to be 7%. The uncerta in ty on the charged current DIS

cross-section is due to the choice o f the structure function param eterization. Com paring

d ifferent param eterizations (e.g., MRS DO, MRS SO [75], M T B l, M T S i [32], and GRV

HO [76]) gives an estimated unce rta in ty o f 6%.

The uncerta in ty on the lep toquark efficiency can be d iv ided in to uncerta inties on

the trigger acceptance, the efficiency o f the background re jection c rite ria (ca lorim eter

tim e , etc.), the vertex efficiency, and the fit o f the overa ll efficiency. The uncerta in ty

on the ca lorim eter energy scale can affect the overall efficiency, v ia the p r > 10 GeV

and ij j b < 1 requirements, b u t i t can also affect the reconstructed leptoquark masses

and consequently, the lim its on leptoquark couplings and masses. Th is uncerta in ty is

considered in Section 4.3.

Trigger Acceptance

T he SLT and T L T are expected to be close to 100% e ffic ien t for physics events collected

in 1992. T he main trigger ineffic iency (and uncerta in ty) comes from the C A L FLT. The

C A L F LT sim u la tion w ith in Z G A N A does not take in to account trigge r towers which were


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 po in t du ring the running period. These dead channel effects arc*, however,

sim ulated w ith a standalone program. Samples o f scalar leptoquark events have been

processed w ith th is program [77] and the results are listed in Table 4.1. The correction

to the trigger acceptance ranges from —4.8% for 5 0 G eV /c2 leptoquarks to —0.4% for

2S0 G eV /c2 leptoquarks.

Background R ejection C rite ria

The ca lo rim eter tim e rejection a lgorithm s are not perform ed in the selection o f the M onte

Carlo data, b u t are expected to be over 99.5% efficient [Go]. The other background

re jection c rite ria , such as spark re jection and cosmic rejection, are applied to the M onte

Carlo data.

V e rte x Efficiency

A study o f the efficiency o f the vertex requirem ent was performed w ith a neutra l current

DIS data sample in which the scattered electron is em itted very close to the R C A L beam

pipe (and hence is no t expected to produce a track in the C TD ). T he data sample was

obtained by f ilte r in g a fou rth o f the 1992 data (7 nb -1 ) using the fo llow ing requirem ents:

• Same requirem ents as in the level one, level two, and level three charged current

filte rs (cf. Sections 3.3.1 to 3.3.3), w ith the exception o f the p r > 10 G eV require-


96

ment.

• Require C TD on.

• Require less than 5 GeV o f energy in the electron ca lorim eter o f the lum inos ity

m on ito r (to reject pho toproduction events).

• Require the events to occur in one o f the nine buckets w ith co llid ing bunches.

• Events must not be rejected w ith the ca lorim eter tim e c rite ria o f the level four

charged current f ilte r (cf. Section 3.3.4).

• The quan tity 8 = C — pz, where E and pz are the to ta l ca lorim eter energy and to ta l

calorim eter energy in the ^ d irection , respectively, m ust be between 35 GeV and

60 GeV. Th is crite rion selects neutra l current events, fo r which 8 should be about

tw ice the in it ia l electron energy (2 x 26.7 G eV), and i t rejects photoproduction and

other backgrounds.

• Events are required to have an electron found w ith the E E X O T IC electron finder

[61]. w ith energy greater than 5 GeV and w ith measured position at least 6 cm away

from the beam pipe, i.e.,

|ar| > 16 cm O R | t / |> 1 6 c m . (4.S)

The last requirem ent is to ensure tha t the e lectron energy and position are well-

measured and are not affected by energy leakage in to the beam pipe.

• In order for the vertex efficiency to be due solely to the je t particles, the electron

is required 1 0 be in the R C A L , w ith position

|a : |< 2 5 c m A N D |y l< 2 5 c m . (4.9)

The above c rite ria lead to a data sample o f 566 events. The backgrounds in the sample

are expected to be small: about 2% e-gas, very l i t t le pho toproduction , and neglig ib le

p-gas [61].


97

N e u tra l cu rren t M onte Carlo events were generated w ith the H E R A C LE S Monte Carlo

program coupled to A R IA D N E . The sample includes rad ia tive corrections and uses the

M T B1 s tru c tu re functions. The M onte Carlo events were weighted according to the

vertex d is tr ib u tio n of the data sample (as calculated from the C5 electron and proton

tim es fo r the appropriate runs). A to ta l o f 11531 M onte Carlo events were processed

th rough the Z G A N A sim ulation and through the data selection requirem ents described

earlier, a fte r w hich 2970 events remained.

The efficiency o f the vertex requirem ent

X 2/ N df < 10 A N D |s| < 75cm (4.10)

for the neu tra l current data was compared w ith the efficiency o f the same requirement,

for neu tra l cu rren t Monte Carlo events. The vertex efficiency is p lo tted as a function as

Qman where 6max is the polar angle o f the calorim eter island w ith largest polar angle1.

The variable 0max indicates where there is a c tiv ity in the ca lo rim eter and therefore where

there should be C TD tracks. One expects the vertex efficiency to be large for large 0mnx

values and sm all for small 6max. The results are shown in F igure 4.3. For 0max > 80°,

the vertex efficiency is lower for the data than for the M onte Carlo by about 5%. This

is consistent w ith the vertex efficiency s tudy performed in [78]. For 0max < 60°, the

effic iency is h igher for the data by 5% to 20%. This last result is not well understood

b u t can conservatively be ignored.

F it P rocedure

The overa ll efficiencies for each lep toquark Monte Carlo sample (solid squares in F ig

ure 4.2) are a ll w ith in 2% of the fit te d efficiencies (curves in F igure 4.2). The uncerta inty

due to the efficiency f it is estim ated 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.


98

/-

0.8

0.6

0.4

0.2

015050 100

0mnt (degrees)

F ig u re 4.3 Vertex efficiency versus 6max for neutral current DIS Monte Carlo (dashed histogram) and data (solid circles).

O verall U n c e rta in ty on Efficiency

The uncerta in ties on the trigger acceptance, on the efficiency o f the background rejection

c rite ria , and on the efficiency o f the vertex requirem ent are added linearly . T h ey are then

added in quadra tu re w ith the uncerta in ty on the efficiency f it . Th is leads to an overall

uncerta in ty o f + 2 % /—10% on the efficiency. For a breakdown o f the uncerta in ties, see

Table 4.2.

The u nce rta in ty on the efficiency, the u nce rta in ty on the lum inos ity , and the uncer

ta in ty on the lep toquark cross-sections are added in quadrature and lead to an overall

uncerta in ty o f + 9 % /—14%. The overall unce rta in ty on the efficiency o f the charged

current DIS background is estimated to be + 6 % /—13%.


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%

Tab le 4.2 Estimated systematic errors.

4.3 R esults

T he 95% confidence level upper lim its on the cross-sections and on the couplings o f the

So and Vo leptoquarks, and o f course S i and V j, are calculated as described in Section 4.1.

The lim its are then recalculated tak ing in to account system atic errors:

• The estim ated num ber o f charged current DIS background events is reduced by

13%.

• Since the lim its on the lep toquark cross-sections depend on the product L • c, the

overall lep toquark efficiencies entering the ca lcu la tion o f those lim its are reduced

by 12%.

• Since the lim its on the lep toquark couplings depend on the product a • L • c, the

overall lep toquark efficiencies entering the ca lcu la tion o f those lim its are reduced

by 14%.

The lim its on the cross-sections, w ith and w ith o u t system atic errors, are shown in F ig

ure 4.4. The kinks in the l im 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 l im it on the lep toquark mass is 154 G c V /c 2 fo r scalars

(So and S i) and 108G e V /c 2 fo r vectors (Vo and V i).


100

0.5

•*»o•5 0.4

i -

0.2

0.1

200150*»

Leptoquark mass ( G eV /c ')

100

0.5

6

0.2

0.1

150 2002

Leptoquark mass (G eV/c )

100

F ig u re 4 .4 95% confidence level upper lim its on the cross-sections times branching fraction o f 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.


101

I e~p -» S0 -» vX0.8

0.6

0.4

0.2

100 150 200Leptoquark mass (G eV/c2)mass

1

0.8

0.6

0.4

0.2

020050 100 150

2Leptoquark mass (GeV/c )

F ig u re 4.5 95% confidence level upper lim its on the couplings XL o f S0 and Si (top p lot), 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.


102

4.3.1 Effect o f the B ackground Subtraction on th e Lim its

The dom inant e lectron-proton background to LQ —► u X events is charged current deep

inelastic scattering and on ly this process was taken in to account in the ca lcu lation of

the icp toquark lim its . The num ber o f neu tra l current DIS events expected a fte r the

requirem ents p r > 10GeV, vertex w ith \z\ < 75cm , and p j > 10G eV after vertex

correction, as estimated using M onte Carlo events generated w ith H E R A C LE S , is 0.3

where the error is sta tistica l. M in im u m bias resolved pho toproduction events have been

sim ulated w ith P Y T H IA . No events are le ft a fte r the requirem ent p? > 10 GeV, which

leads to an upper lim it o f 2.9 events a t the 90% C.L.

Not inc lud ing neutral current D IS and photoproduction backgrounds leads to a more

conservative lim it . The effect of no t doing any background sub trac tion is to raise the

coupling lim its by less than 5% fo r scalar leptoquarks, and less than 2% for vector

leptoquarks.

4.3 .2 E ffect o f the S tructure Functions on th e L im its

The s truc tu re functions used throughout th is analysis are M T B l . Using the P D F L IB

package [79], one can reweight the lim its fo r a different set o f s tru c tu re functions using

the approx im ationI n P D F

\ P D F \ M T B 1 9 _______ n \/ ' / i m x ' £ — ” l i m i t y q M T B l '

where q is the u-quark (fo r scalars) o r d-quark (for vectors) pa rton d is tr ib u tio n function

evaluated a t x = m ^g /s and Q2 = m 2Lq. For example, w ith the G R V HO structure

functions, com patib le w ith the la test s truc tu re function measurements at H E R A [80],

the coup ling lim its would change by —3% to +8% over the range of masses 50 G eV /c2

to 215 G e V /c 2 fo r scalars, and by —S% to —4% over the range o f masses 50 G eV /c2 to

150 G e V /c 2 for vectors.


103

4 .3 .3 Effect o f th e Energy Scale o n th e Lim its

Comparison o f the ca lib ra tion o f the ca lorim eter energy using halo muons and using

cosmic muons shows differences o f at most 4% [S i]. These differences are a ttr ib u ta b le

to the higher m om entum of the halo muons. Com parison of the electron energy in

neutra l current DIS da ta and M onte Carlo shows a discrepancy o f about 5% [61]. Th is

discrepancy is believed to be due to inactive m a te ria l not being properly modeled in the

M onte Carlo.

The effect o f a ± 5 % m isca libra tion o f the M on te Carlo calorim eter energy scale on

the coupling lim its was studied. A sh ift in the energy scale would affect variables such

as reconstructed p r and y j B i which are used in the selection o f the M onte C a rlo data. I t

would also m odify , v ia shifts in x j b , the param eterized means and standard deviations

fo r the reconstructed lep toquark masses. The effects o f a sh ift E —» E ( l + 8) in the

energy scale on the variables p r , t / jg , x j b , and Q 2B are

P T -> p r ( l + <$), (4.12)

V j b y j B { l + °), (4.13)

x j b x j b 1 +

Q 2jb Q2J B 1 +<5 +

1 - V j b ( 1 + < $ )

< 5(1+*)

(4.14)

(4.15)

The analysis o f the lep toquark and charged cu rren t DIS M onte Carlo da ta was redone

w ith a —5% sh ift ir. the M onte Carlo energy scale:

• The ca lorim eter energies were sh ifted by —5% in the M onte Carlo data.

• The new reconstructed lep toquark masses, a fte r trigger acceptance and data selec

tion, v/ere f it te d to Gaussian d is tribu tions.

• The means and standard deviations were in tu rn fitte d to firs t- and second-order

polynom ials.

• The overall efficiencies, a fte r trigger acceptance, data selection, and 3<r mass re

quirem ent, were calculated and param eterized.


104

• The num ber o f background events in each search reg ion was recalculated.

• L im its on the couplings were recalculated (tak ing in to account system atic errors).

The above procedure was repeated for a shift in the energy scale o f +5%.

The lim its on the leptoquark couplings calculated in th is manner are shown in F ig

ure 4.6. The effect o f a ±5% sh ift in the Monte Carlo energy scale is a :p5% sh ift in the

position o f the kink in the l im it curve for scalars. The coup ling l im it for scalars, away

from the k ink , is sh ifted by less than ±3% . For vectors, the effect on the lim it is less

than ±2% .

4.4 Conclusions

In th is thesis, So, S i, Vo, and V) leptoquarks decaying in to v X have been searched for

in a sample o f events collected w ith the ZEUS detector in 1992 and corresponding to an

integrated lum inos ity o f 27.5 nb -1 . One event is le ft a fte r the f ilte r selection and scan

procedure, consistent w ith the 1.3 events expected from charged current DIS background.

The overall efficiency for scalar leptoquarks, a fte r trigger acceptance, data selection, and

3 i t leptoquark mass requirem ent, is 70% to 80% for lep toquark masses in the range

50 G eV /c2 to 225 G eV /c2. The overall efficiency for vector leptoquarks is 60% to S5% for

the same mass range.

The upper lim its on leptoquark Yukawa couplings versus leptoquark mass shown in

F igure 4.5 extend the region already excluded by co llide r experim ents. Assum ing an

electroweak coupling (A^, = 0.31) and a leptoquark branching frac tion in to electron plus

je ts , £?, o f 0.5, the 95% C.L. lower l im it on the lep toquark mass is 154 G eV /c2 fo r 5’o

and Si leptoquarks and 108 G e V /c2 fo r Vo and Vi leptoquarks. T he lim its calculated in

th is thesis are compared w ith o the r lim its from co llider experim ents 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 fo r in a sample o f e~p —> e ~ X

events collected in 1992 w ith the ZEUS detector v ia the L Q —» e ~ X channel [82, 74].

T h is channel enables one to probe all possible lep toquark species. No leptoquark signals


105

0.8

Energy scale *0.95 Energy scale * 1.00 Energy scale *1.05

0.6

0.4

0.2

100 150 20050Leptoquark mass (GeV/c )

0.8

0.6

0.4— Energy scale * 0.95 Energy scale * 1.00 Energy scale * 1.050.2

20015050 100Leptoquark mass (GeV/c )

F ig u re 4 .6 Effect of a ±5% shift in the energy scale on the coupling lim its \ L o f Sa and ,S'| (top p lo t), and VQ and Vi (bottom p lo t) leptoquarks.


106

Leptoquark B

95% C.L. Lower L im it on the Leptoquark Mass

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 GeV/c2, for XL = 0.31

Table 4.3 Summary o f the results.

were found and lim its on leptoquark masses and couplings were presented. The H I

collaboration has also searched for leptoquarks decaying in to e~X and v X in a sample of

‘24 nb-1 collected in 1992 [S3], and the ir results are comparable to the results from ZEUS.

Since 1992, which was the firs t year o f data tak ing at H E R A , there has been a large

increase in lum inos ity and the qua lity o f the beams and performance o f the detectors have

improved. T h is w ill lead to more stringent lim its on leptoquark masses and couplings,

which w ill be published in the very near fu tu re [84], Furtherm ore, the H E R A experim ents

w ill eventua lly be able to probe lep toquark masses well above the k inem a tic l im it o f

y/s = 296 GeV by looking for effects from the v ir tu a l exchange of lep toquarks [85].


Appendix A

U pper Limit Calculation

W hen a search for a p a rticu la r signal is inconclusive, fo r instance when the data collected

are consistent w ith estim ated backgrounds, an upper l im it on the signal cross-section can

be calculated using Poisson sta tis tics [29]. I f the signal and background cross-sections, <7,

and (7ft, were known, then the num ber o f observed events would be expected to fo llow a

Poisson d is tr ib u tio n w ith mean s + b, where s and b are the mean signal and background

contribu tions:

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 lum inosity.

The p ro ba b ility o f observing N events would therefore be given by

P( s + b , N ) = ^ e - ^ +bH s + b f . (A .3)

In practice, one counts the num ber of events in a sample, estimates the background

co n tribu tio n to th a t sample, and calculates an upper l im it on the signal con tribu tion .

Assum ing a un ifo rm p ro b a b ility density function for s before the experim ent, the proba

b il i ty density function for s a fte r the experim ent, g{s), is p roportiona l to P{s + b, iV ) [86].

107


108

Hence,

(A .4 )

where A is a norm alization factor such th a t

/•oo/ <7(s) ds

Jo1. (A .5)

The p ro ba b ility that s is less than an upper lim it s0 is called the confidence level and is

given by

C =r QI g{s)ds,

r h c~t'*t>{s+bfdsThe integral

can be solved as follows [87]:

I

3 0 + 6 1

me~l t N d t ,

— [ e ~ l l NN l I r-r--"w-4

1 Y ' g -« ^ - n

N

3 0 + 6

)6

= E " 7 (e "66n - e - ^ + 6 ) (5o + 6)n)n = 0 71 •

In the lim it s —> oo:N

7 ^ E r? e" ‘ i,n-±Tn n\

(A .6 )

(A .7 )

(A .S)

(A .9 )

(A .10)

(A .11)

(A .12)

(A .13)

(A .14)n = 0


109

The confidence level C can therefore be w ritte n as

£ i e-^+6>(*0 + &rc = . (A . 15)

;V iV - i e - 6 bn t u «!

The 95% confidence level upper l im it on the signal con tribu tion is obtained by sub

s titu t in g C = 0.95 in Equation A. 15 and so lving num erically for .su. T h is lim it on s can

be converted in to a lim it on the signal cross-section using Equation A . I .


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