Page 1

arXiv:hep-ex/0401009v2 2 Apr 2004

DESY–03–218

December 2003

Search for contact interactions, large extra

dimensions and finite quark radius in ep

collisions at HERA

ZEUS Collaboration

Abstract

A search for physics beyond the Standard Model has been performed with high-

Q2neutral current deep inelastic scattering events recorded with the ZEUS de-

tector at HERA. Two data sets, e+p → e+X and e−p → e−X, with respective

integrated luminosities of 112pb−1and 16pb−1, were analyzed. The data reach

Q2values as high as 40000GeV2. No significant deviations from Standard Model

predictions were observed. Limits were derived on the effective mass scale in

eeqq contact interactions, the ratio of leptoquark mass to the Yukawa coupling

for heavy leptoquark models and the mass scale parameter in models with large

extra dimensions. The limit on the quark charge radius, in the classical form

factor approximation, is 0.85 · 10−16cm.

Page 2

The ZEUS Collaboration

S. Chekanov, M. Derrick, D. Krakauer, J.H. Loizides1, S. Magill, S. Miglioranzi1, B. Mus-

grave, J. Repond, R. Yoshida

Argonne National Laboratory, Argonne, Illinois 60439-4815, USAn

M.C.K. Mattingly

Andrews University, Berrien Springs, Michigan 49104-0380, USA

P. Antonioli, G. Bari, M. Basile, L. Bellagamba, D. Boscherini, A. Bruni, G. Bruni,

G. Cara Romeo, L. Cifarelli, F. Cindolo, A. Contin, M. Corradi, S. De Pasquale, P. Giusti,

G. Iacobucci, A. Margotti, A. Montanari, R. Nania, F. Palmonari, A. Pesci, G. Sartorelli,

A. Zichichi

University and INFN Bologna, Bologna, Italye

G. Aghuzumtsyan, D. Bartsch, I. Brock, S. Goers, H. Hartmann, E. Hilger, P. Irrgang, H.-

P. Jakob, O. Kind, U. Meyer, E. Paul2, J. Rautenberg, R. Renner, A. Stifutkin, J. Tandler,

K.C. Voss, M. Wang, A. Weber3

Physikalisches Institut der Universit¨ at Bonn, Bonn, Germanyb

D.S. Bailey4, N.H. Brook, J.E. Cole, G.P. Heath, T. Namsoo, S. Robins, M. Wing

H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdomm

M. Capua, A. Mastroberardino, M. Schioppa, G. Susinno

Calabria University, Physics Department and INFN, Cosenza, Italye

J.Y. Kim, Y.K. Kim, J.H. Lee, I.T. Lim, M.Y. Pac5

Chonnam National University, Kwangju, Koreag

A. Caldwell6, M. Helbich, X. Liu, B. Mellado, Y. Ning, S. Paganis, Z. Ren, W.B. Schmidke,

F. Sciulli

Nevis Laboratories, Columbia University, Irvington on Hudson, New York 10027o

J. Chwastowski, A. Eskreys, J. Figiel, A. Galas, K. Olkiewicz, P. Stopa, L. Zawiejski

Institute of Nuclear Physics, Cracow, Polandi

L. Adamczyk, T. Bo? ld, I. Grabowska-Bo? ld7, D. Kisielewska, A.M. Kowal, M. Kowal,

T. Kowalski, M. Przybycie´ n, L. Suszycki, D. Szuba, J. Szuba8

Faculty of Physics and Nuclear Techniques, AGH-University of Science and Technology,

Cracow, Polandp

A. Kota´ nski9, W. S? lomi´ nski

Department of Physics, Jagellonian University, Cracow, Poland

I

Page 3

V. Adler, U. Behrens, I. Bloch, K. Borras, V. Chiochia, D. Dannheim, G. Drews, J. Fourletova,

U. Fricke, A. Geiser, P. G¨ ottlicher10, O. Gutsche, T. Haas, W. Hain, S. Hillert11, B. Kahle,

U. K¨ otz, H. Kowalski12, G. Kramberger, H. Labes, D. Lelas, H. Lim, B. L¨ ohr, R. Mankel,

I.-A. Melzer-Pellmann, C.N. Nguyen, D. Notz, A.E. Nuncio-Quiroz, A. Polini, A. Raval,

L. Rurua, U. Schneekloth, U. St¨ osslein, R. Wichmann13, G. Wolf, C. Youngman, W. Zeuner

Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany

S. Schlenstedt

DESY Zeuthen, Zeuthen, Germany

G. Barbagli, E. Gallo, C. Genta, P. G. Pelfer

University and INFN, Florence, Italye

A. Bamberger, A. Benen, F. Karstens, D. Dobur, N.N. Vlasov

Fakult¨ at f¨ ur Physik der Universit¨ at Freiburg i.Br., Freiburg i.Br., Germanyb

M. Bell, P.J. Bussey, A.T. Doyle, J. Ferrando, J. Hamilton, S. Hanlon, D.H. Saxon,

I.O. Skillicorn

Department of Physics and Astronomy, University of Glasgow, Glasgow, United King-

domm

I. Gialas

Department of Engineering in Management and Finance, Univ. of Aegean, Greece

T. Carli, T. Gosau, U. Holm, N. Krumnack, E. Lohrmann, M. Milite, H. Salehi, P. Schleper,

S. Stonjek11, K. Wichmann, K. Wick, A. Ziegler, Ar. Ziegler

Hamburg University, Institute of Exp. Physics, Hamburg, Germanyb

C. Collins-Tooth, C. Foudas, R. Gon¸ calo14, K.R. Long, A.D. Tapper

Imperial College London, High Energy Nuclear Physics Group, London, United King-

domm

P. Cloth, D. Filges

Forschungszentrum J¨ ulich, Institut f¨ ur Kernphysik, J¨ ulich, Germany

M. Kataoka15, K. Nagano, K. Tokushuku16, S. Yamada, Y. Yamazaki

Institute of Particle and Nuclear Studies, KEK, Tsukuba, Japanf

A.N. Barakbaev, E.G. Boos, N.S. Pokrovskiy, B.O. Zhautykov

Institute of Physics and Technology of Ministry of Education and Science of Kazakhstan,

Almaty, Kazakhstan

D. Son

Kyungpook National University, Center for High Energy Physics, Daegu, South Koreag

II

Page 4

K. Piotrzkowski

Institut de Physique Nucl´ eaire, Universit´ e Catholique de Louvain, Louvain-la-Neuve, Bel-

gium

F. Barreiro, C. Glasman17, O. Gonz´ alez, L. Labarga, J. del Peso, E. Tassi, J. Terr´ on,

M. V´ azquez, M. Zambrana

Departamento de F´ ısica Te´ orica, Universidad Aut´ onoma de Madrid, Madrid, Spainl

M. Barbi, F. Corriveau, S. Gliga, J. Lainesse, S. Padhi, D.G. Stairs, R. Walsh

Department of Physics, McGill University, Montr´ eal, Qu´ ebec, Canada H3A 2T8a

T. Tsurugai

Meiji Gakuin University, Faculty of General Education, Yokohama, Japanf

A. Antonov, P. Danilov, B.A. Dolgoshein, D. Gladkov, V. Sosnovtsev, S. Suchkov

Moscow Engineering Physics Institute, Moscow, Russiaj

R.K. Dementiev, P.F. Ermolov, Yu.A. Golubkov18, I.I. Katkov, L.A. Khein, I.A. Korzhav-

ina, V.A. Kuzmin, B.B. Levchenko19, O.Yu. Lukina, A.S. Proskuryakov, L.M. Shcheglova,

S.A. Zotkin

Moscow State University, Institute of Nuclear Physics, Moscow, Russiak

N. Coppola, S. Grijpink, E. Koffeman, P. Kooijman, E. Maddox, A. Pellegrino, S. Schagen,

H. Tiecke, J.J. Velthuis, L. Wiggers, E. de Wolf

NIKHEF and University of Amsterdam, Amsterdam, Netherlandsh

N. Br¨ ummer, B. Bylsma, L.S. Durkin, T.Y. Ling

Physics Department, Ohio State University, Columbus, Ohio 43210n

A.M. Cooper-Sarkar, A. Cottrell, R.C.E. Devenish, B. Foster, G. Grzelak, C. Gwenlan20,

S. Patel, P.B. Straub, R. Walczak

Department of Physics, University of Oxford, Oxford United Kingdomm

A. Bertolin, R. Brugnera, R. Carlin, F. Dal Corso, S. Dusini, A. Garfagnini, S. Limentani,

A. Longhin, A. Parenti, M. Posocco, L. Stanco, M. Turcato

Dipartimento di Fisica dell’ Universit` a and INFN, Padova, Italye

E.A. Heaphy, F. Metlica, B.Y. Oh, J.J. Whitmore21

Department of Physics, Pennsylvania State University, University Park, Pennsylvania

16802o

Y. Iga

Polytechnic University, Sagamihara, Japanf

G. D’Agostini, G. Marini, A. Nigro

Dipartimento di Fisica, Universit` a ’La Sapienza’ and INFN, Rome, Italye

III

Page 5

C. Cormack22, J.C. Hart, N.A. McCubbin

Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, United Kingdomm

C. Heusch

University of California, Santa Cruz, California 95064, USAn

I.H. Park

Department of Physics, Ewha Womans University, Seoul, Korea

N. Pavel

Fachbereich Physik der Universit¨ at-Gesamthochschule Siegen, Germany

H. Abramowicz, A. Gabareen, S. Kananov, A. Kreisel, A. Levy

Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel-Aviv

University, Tel-Aviv, Israeld

M. Kuze

Department of Physics, Tokyo Institute of Technology, Tokyo, Japanf

T. Fusayasu, S. Kagawa, T. Kohno, T. Tawara, T. Yamashita

Department of Physics, University of Tokyo, Tokyo, Japanf

R. Hamatsu, T. Hirose2, M. Inuzuka, H. Kaji, S. Kitamura23, K. Matsuzawa

Tokyo Metropolitan University, Department of Physics, Tokyo, Japanf

M.I. Ferrero, V. Monaco, R. Sacchi, A. Solano

Universit` a di Torino and INFN, Torino, Italye

M. Arneodo, M. Ruspa

Universit` a del Piemonte Orientale, Novara, and INFN, Torino, Italye

T. Koop, J.F. Martin, A. Mirea

Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7a

J.M. Butterworth24, R. Hall-Wilton, T.W. Jones, M.S. Lightwood, M.R. Sutton4, C. Targett-

Adams

Physics and Astronomy Department, University College London, London, United King-

domm

J. Ciborowski25, R. Ciesielski26, P. ? Lu˙ zniak27, R.J. Nowak, J.M. Pawlak, J. Sztuk28,

T. Tymieniecka29, A. Ukleja29, J. Ukleja30, A.F.˙Zarnecki

Warsaw University, Institute of Experimental Physics, Warsaw, Polandq

M. Adamus, P. Plucinski

Institute for Nuclear Studies, Warsaw, Polandq

Y. Eisenberg, L.K. Gladilin31, D. Hochman, U. Karshon M. Riveline

Department of Particle Physics, Weizmann Institute, Rehovot, Israelc

IV

Page 6

D. K¸ cira, S. Lammers, L. Li, D.D. Reeder, M. Rosin, A.A. Savin, W.H. Smith

Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USAn

A. Deshpande, S. Dhawan

Department of Physics, Yale University, New Haven, Connecticut 06520-8121, USAn

S. Bhadra, C.D. Catterall, S. Fourletov, G. Hartner, S. Menary, M. Soares, J. Standage

Department of Physics, York University, Ontario, Canada M3J 1P3a

V

Page 7

1also affiliated with University College London, London, UK

2retired

3self-employed

4PPARC Advanced fellow

5now at Dongshin University, Naju, Korea

6now at Max-Planck-Institut f¨ ur Physik, M¨ unchen,Germany

7partly supported by Polish Ministry of Scientific Research and Information Technology,

grant no. 2P03B 122 25

8partly supp. by the Israel Sci. Found. and Min. of Sci., and Polish Min. of Scient.

Res. and Inform. Techn., grant no.2P03B12625

9supported by the Polish State Committee for Scientific Research, grant no. 2 P03B

09322

10now at DESY group FEB

11now at Univ. of Oxford, Oxford/UK

12on leave of absence at Columbia Univ., Nevis Labs., N.Y., US A

13now at DESY group MPY

14now at Royal Holoway University of London, London, UK

15also at Nara Women’s University, Nara, Japan

16also at University of Tokyo, Tokyo, Japan

17Ram´ on y Cajal Fellow

18now at HERA-B

19partly supported by the Russian Foundation for Basic Research, grant 02-02-81023

20PPARC Postdoctoral Research Fellow

21on leave of absence at The National Science Foundation, Arlington, VA, USA

22now at Univ. of London, Queen Mary College, London, UK

23present address: Tokyo Metropolitan University of Health Sciences, Tokyo 116-8551,

Japan

24also at University of Hamburg, Alexander von Humboldt Fellow

25also at ? L´ od´ z University, Poland

26supported by the Polish State Committee for Scientific Research, grant no. 2 P03B

07222

27? L´ od´ z University, Poland

28? L´ od´ z University, Poland, supported by the KBN grant 2P03B12925

29supported by German Federal Ministry for Education and Research (BMBF), POL

01/043

30supported by the KBN grant 2P03B12725

31on leave from MSU, partly supported by University of Wisconsin via the U.S.-Israel BSF

VI

Page 8

a

supported by the Natural Sciences and Engineering Research Council of

Canada (NSERC)

supported by the German Federal Ministry for Education and Research

(BMBF), under contract numbers HZ1GUA 2, HZ1GUB 0, HZ1PDA 5,

HZ1VFA 5

supported by the MINERVA Gesellschaft f¨ ur Forschung GmbH, the Israel

Science Foundation, the U.S.-Israel Binational Science Foundation and the

Benozyio Center for High Energy Physics

supported by the German-Israeli Foundation and the Israel Science Foundation

supported by the Italian National Institute for Nuclear Physics (INFN)

supported by the Japanese Ministry of Education, Culture, Sports, Science

and Technology (MEXT) and its grants for Scientific Research

supported by the Korean Ministry of Education and Korea Science and Engi-

neering Foundation

supported by the Netherlands Foundation for Research on Matter (FOM)

supported by the Polish State Committee for Scientific Research, grant no.

620/E-77/SPB/DESY/P-03/DZ 117/2003-2005

partially supported by the German Federal Ministry for Education and Re-

search (BMBF)

partly supported by the Russian Ministry of Industry, Science and Technology

through its grant for Scientific Research on High Energy Physics

supported by the Spanish Ministry of Education and Science through funds

provided by CICYT

supported by the Particle Physics and Astronomy Research Council, UK

supported by the US Department of Energy

supported by the US National Science Foundation

supported by the Polish State Committee for Scientific Research, grant no.

112/E-356/SPUB/DESY/P-03/DZ 116/2003-2005,2 P03B 13922

supported by the Polish State Committee for Scientific Research, grant no.

115/E-343/SPUB-M/DESY/P-03/DZ 121/2001-2002, 2 P03B 07022

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

VII

Page 9

1 Introduction

The HERA ep collider has extended the kinematic range of deep inelastic scattering

(DIS) measurements by two orders of magnitude in Q2, the negative square of the four-

momentum transfer, compared to fixed-target experiments. At values of Q2of about

4 × 104GeV2, the eq interaction, where q is a constituent quark of the proton, is probed

at distances of ∼ 10−16cm. Measurements in this domain allow searches for new physics

processes with characteristic mass scales in the TeV range. New interactions between e

and q involving mass scales above the center-of-mass energy can modify the cross sec-

tion at high Q2via virtual effects, resulting in observable deviations from the Standard

Model (SM) predictions. Many such interactions, such as processes mediated by heavy

leptoquarks, can be modelled as four-fermion contact interactions. The SM predictions

for ep scattering in the Q2domain of this study result from the evolution of accurate mea-

surements of the proton structure functions made at lower Q2. In this paper, a common

method is applied to search for four-fermion interactions, for graviton exchange in models

with large extra dimensions, and for a finite charge radius of the quark.

In an analysis of 1994-97 e+p data [1], the ZEUS Collaboration set limits on the effective

mass scale for several parity-conserving compositeness models. Results presented here

are based on approximately 130pb−1of e+p and e−p data collected by ZEUS in the years

1994-2000. Since this publication also includes the early ZEUS data, the results presented

here supersede those of the earlier publication [1].

2 Standard Model cross section

The differential SM cross section for neutral current (NC) ep scattering, e±p → e±X, can

be expressed in terms of the kinematic variables Q2, x and y, which are defined by the

four-momenta of the incoming electron1(k), the incoming proton (P), and the scattered

electron (k′) as Q2= −q2= −(k − k′)2, x = Q2/(2q · P), and y = (q · P)/(k · P). For

unpolarized beams, the leading-order electroweak cross sections can be expressed as

d2σNC(e±p)

dxdQ2

(x,Q2) =

2πα2

xQ4

??1 + (1 − y)2?FNC

2

∓?1 − (1 − y)2?xFNC

3

?

,(1)

where α is the electromagnetic coupling constant. The contribution of the longitudinal

structure function, FL(x,Q2), is negligible at high Q2and is not taken into account in

this analysis. At leading order (LO) in QCD, the structure functions FNC

2

and xFNC

3

are

1Unless otherwise specified, ‘electron’ refers to both positron and electron.

1

Page 10

given by

FNC

2

(x,Q2) =

?

?

q=u,d,s,c,b

Aq(Q2)

?xq(x,Q2) + xq(x,Q2)?

?xq(x,Q2) − xq(x,Q2)?

,

xFNC

3

(x,Q2) =

q=u,d,s,c,b

Bq(Q2)

,

where q(x,Q2) and q(x,Q2) are the parton densities for quarks and antiquarks. The

functions Aqand Bqare defined as

Aq(Q2) =1

2

?(VL

(VL

q)2+ (VR

q)2+ (AL

q)2+ (AR

q)2?

,

Bq(Q2) =

q)(AL

q) − (VR

q)(AR

q) ,

where the coefficient functions VL,R

q

and AL,R

q

are given by:

Vi

Ai

q= Qq− (ve± ae)vqχZ,

q=− (ve± ae)aqχZ,

vf= T3

f− 2sin2θWQf,

af= T3

f,

χZ=

1

4sin2θWcos2θW

Q2

Q2+ M2

Z

.

(2)

In Eq. (2), the superscript i denotes the left (L) or right (R) helicity projection of the

lepton field; the plus (minus) sign in the definitions of Vi

i = L(R). The coefficients vfand afare the SM vector and axial-vector coupling constants

of an electron (f = e) or quark (f = q); Qfand T3

component of the weak isospin; MZand θW are the mass of the Z0and the electroweak

mixing angle, respectively.

qand Ai

qis appropriate for

fdenote the fermion charge and third

3Models for new physics

3.1General contact interactions

Four-fermion contact interactions (CI) represent an effective theory, which describes low-

energy effects due to physics at much higher energy scales. Such models would describe

the effects of heavy leptoquarks, additional heavy weak bosons, and electron or quark

compositeness. The CI approach is not renormalizable and is only valid in the low-

energy limit. As strong limits have already been placed on scalar and tensor contact

2

Page 11

interactions [2], only vector currents are considered here. They can be represented by

additional terms in the Standard Model Lagrangian, viz:

LCI

=

?

i,j=L,R

q=u,d,s,c,b

ηeq

ij(¯ eiγµei)(¯ qjγµqj) ,(3)

where the sum runs over electron and quark helicities and quark flavors. The couplings

ηeq

(Eq. (3)) results in the following modification of the functions Vi

ijdescribe the helicity and flavor structure of contact interactions. The CI Lagrangian

qand Ai

qof Eq. (2):

Vi

q= Qq− (ve± ae)vqχZ+Q2

− (ve± ae)aqχZ+Q2

2α(ηeq

iL+ ηeq

iR) ,

Ai

q=

2α(ηeq

iL− ηeq

iR) .

It was assumed that all up-type quarks have the same contact-interaction couplings, and

a similar assumption was made for down-type quarks2:

ηeu

ij

ηed

ij

= ηec

= ηes

ij

= ηet

= ηeb

ij,

ijij,

leading to eight independent couplings, ηeq

setting limits in an eight-dimensional space, a set of representative scenarios was analyzed.

Each scenario is defined by a set of eight coefficients, ǫeq

±1 or zero, and the compositeness scale Λ. The couplings are then defined by

ij, with q = u,d. Due to the impracticality of

ij, each of which may take the values

ηeq

ij

= ǫeq

ij

4π

Λ2.

Note that models that differ in the overall sign of the coefficients ǫeq

of the interference with the SM.

ijare distinct because

In this paper, different chiral structures of CI are considered, as listed in Table 1. Models

listed in the lower part of the table were previously considered in the published analysis

of 1994-97 e+p data [1]. They fulfill the relation

ηeq

LL+ ηeq

LR− ηeq

RL− ηeq

RR

= 0 ,

which was imposed to conserve parity, and thereby complement strong limits from atomic

parity violation (APV) results [3,4]. Since a later APV analysis [5] indicated possible

2The results depend very weakly on this assumption since heavy quarks make only a very small con-

tribution to high-Q2cross sections. In most cases, the same mass-scale limits were obtained for CI

scenarios where only first-generation quarks are considered. The largest difference between the ob-

tained mass-scale limits is about 2%.

3

Page 12

deviations from SM predictions, models that violate parity, listed in the upper part of

Table 1, have also been incorporated in the analysis. The reported 2.3σ deviation [5]

from the SM was later reduced to around 1σ, after reevaluation of some of the theoretical

corrections [6,7].

3.2Leptoquarks

Leptoquarks (LQ) appear in certain extensions of the SM that connect leptons and quarks;

they carry both lepton and baryon numbers and have spin 0 or 1. According to the general

classification proposed by Buchm¨ uller, R¨ uckl and Wyler [8], there are 14 possible LQ

states: seven scalar and seven vector3. In the limit of heavy LQs (MLQ≫√s), the effect

of s- and t-channel LQ exchange is equivalent to a vector-type eeqq contact interaction4.

The effective contact-interaction couplings, ηeq

of the leptoquark Yukawa coupling, λLQ, to the leptoquark mass, MLQ:

ij, are proportional to the square of the ratio

ηeq

ij

= aeq

ij

?λLQ

MLQ

?2

,

where the coefficients aeq

for scalar leptoquarks. Only first-generation leptoquarks are considered in this analysis,

q = u,d. The coupling structure for different leptoquark species is shown in Table 2.

Leptoquark models SL

supersymmetric theories with broken R-parity.

ijdepend on the LQ species [11] and are twice as large for vector as

0and˜SL

1/2correspond to the squark states˜dRand ˜ uL, in minimal

3.3Large extra dimensions

Arkani-Hamed, Dimopoulos and Dvali [12–14] have proposed a model to solve the hierar-

chy problem, assuming that space-time has 4 + n dimensions. Particles, including strong

and electroweak bosons, are confined to four dimensions, but gravity can propagate into

the extra dimensions. The extra n spatial dimensions are compactified with a radius R.

The Planck scale, MP ∼ 1019GeV, in 4 dimensions is an effective scale arising from the

fundamental Planck scale MDin D = 4 + n dimensions. The two scales are related by:

M2

P

∼ RnM2+n

D

.

For extra dimensions with R ∼ 1mm for n = 2, the scale MD can be of the order of

TeV. At high energies, the strengths of the gravitational and electroweak interactions can

3Leptoquark states are named according to the so-called Aachen notation [9].

4For the invariant mass range accessible at HERA,√s ∼ 300GeV, heavy LQ approximation is applicable

for MLQ> 400GeV. For ZEUS limits covering LQ masses below 400GeV see [10].

4

Page 13

then become comparable. After summing the effects of graviton excitations in the extra

dimensions, the graviton-exchange contribution to eq → eq scattering can be described

as a contact interaction with an effective coupling strength of [15,16]

ηG =

λ

M4

S

,

where MS is an ultraviolet cutoff scale, expected to be of the order of MD, and the

coupling λ is of order unity. Since the sign of λ is not known a priori, both values λ = ±1

are considered in this analysis. However, due to additional energy-scale dependence,

reflecting the number of accessible graviton excitations, these contact interactions are not

equivalent to the vector contact interactions of Eq. (3). To describe the effects of graviton

exchange, terms arising from pure graviton exchange (G), graviton-photon interference

(γG) and graviton-Z (ZG) interference have to be added to the SM eq → eq scattering

cross section [17]:

dσ(e±q → e±q)

dˆt

=

dσSM

dˆt

πλ2

32M8

+dσG

dˆt

+dσγG

dˆt

+dσZG

dˆt

,

dσG

dˆt

dσγG

dˆt

dσZG

dˆt

=

S

1

ˆ s2

αQq

ˆ s2

?32ˆ u4+ 64ˆ u3ˆt + 42ˆ u2ˆt2+ 10ˆ uˆt3+ˆt4?,

(2ˆ u +ˆt)3

ˆt

α

ˆ s2sin22θW

ˆt − M2

= ∓πλ

2M4

πλ

2M4

S

,

=

S

?

±vevq(2ˆ u +ˆt)3

Z

− aeaq

ˆt(6ˆ u2+ 6ˆ uˆt +ˆt2)

ˆt − M2

Z

?

,

where ˆ s,ˆt and ˆ u, withˆt = −Q2, are the Mandelstam variables, while the other coefficients

are given in Eq. (2). The corresponding cross sections for e±¯ q scattering are obtained by

changing the sign of Qqand vqparameters.

Graviton exchange also contributes to electron-gluon scattering, eg → eg, which is not

present at leading order in the SM:

dσ(e±g → e±g)

dˆt

=

πλ2

2M8

S

ˆ u

ˆ s2

?2ˆ u3+ 4ˆ u2ˆt + 3ˆ uˆt2+ˆt3?.

For a given point in the (x,Q2) plane, the e±p cross section is then given by

d2σ(e±p → e±X)

dxdQ2

(x,Q2) = q(x,Q2)dσ(e±q)

dˆt

+ ¯ q(x,Q2)dσ(e±¯ q)

dˆt

+ g(x,Q2)dσ(e±g)

dˆt

,

where q(x,Q2), ¯ q(x,Q2) and g(x,Q2) are the quark, anti-quark and gluon densities in the

proton, respectively.

5

Page 14

3.4Quark form factor

Quark substructure can be detected by measuring the spatial distribution of the quark

charge. If Q2≪ 1/R2

modified, approximately, to:

eand Q2≪ 1/R2

q, the SM predictions for the cross sections are

dσ

dQ2

=

dσSM

dQ2

?

1 −R2

e

6

Q2

?2?

1 −R2

q

6

Q2

?2

,

where Reand Rqare the root-mean-square radii of the electroweak charge of the electron

and the quark, respectively.

4Data samples

The data used in this analysis were collected with the ZEUS detector at HERA and

correspond to an integrated luminosity of 48pb−1and 63pb−1for e+p collisions collected

in 1994-97 and 1999-2000 respectively, and 16pb−1for e−p collisions collected in 1998-99.

The 1994-97 data set was collected at√s = 300GeV and the 1998-2000 data sets were

taken with√s = 318GeV.

The analysis is based upon the final event samples used in previously published cross

section measurements [18–20]. Only events with Q2> 1000GeV2are considered. The

SM predictions were taken from the simulated event samples used in the cross section

measurements, where selection cuts and event reconstruction are identical to those ap-

plied to the data. Neutral current DIS events were simulated using the Heracles [21]

program with Djangoh [22,23] for electroweak radiative corrections and higher-order

matrix elements, and the color-dipole model of Ariadne [24] for the QCD cascade and

hadronization. The ZEUS detector was simulated using a program based on Geant

3.13 [25]. The details of the data selection and reconstruction, and the simulation used

can be found elsewhere [18–20].

The distributions of NC DIS events in Q2, measured separately for each of the three

data sets, are in good agreement with SM predictions calculated using the CTEQ5D

parameterization [26,27] of the parton distribution functions (PDFs) of the proton. The

CTEQ5D parameterization is based on a global QCD analysis of the data on high energy

lepton-hadron and hadron-hadron interactions, including high-Q2H1 and ZEUS results

based on the 1994 e+p data. The ZEUS data used in the CTEQ analysis amount to less

than 3% of the sample considered in this analysis. In general, SM predictions in the Q2

range considered here are dominantly determined by fixed-target data at Q2< 100GeV2

and x > 0.01 [28].

6

Page 15

5Analysis method

5.1Monte Carlo reweighting

The contact interactions analysis was based on a comparison of the measured Q2distri-

butions with the predictions of the MC simulation. The effects of each CI scenario are

taken into account by reweighting each MC event of the type ep → eX with the weight

w =

d2σ

dxdQ2(SM+CI)

d2σ

dxdQ2(SM)

?????

true x,Q2

. (4)

The weight w was calculated as the ratio of the leading-order5cross sections, Eq. (1),

evaluated at the true values of x and Q2as determined from the four-momenta of the

exchanged boson and the incident particles. In simulated events where a photon with

energy Eγis radiated by the incoming electron (initial-state radiation), the electron energy

is reduced by Eγ. This approach guarantees that possible differences between the SM and

the CI model in event-selection efficiency and migration corrections are properly taken into

account. Under the assumption that the difference between the SM predictions and those

of the model including contact interactions is small, higher-order QCD and electroweak

corrections, including radiative corrections, are also accounted for.

5.2Limit-setting procedure

For each of the models of new physics described above, it is possible to characterize

the strength of the interaction by a single parameter: 4π/Λ2for contact interactions;

(λLQ/MLQ)2for leptoquarks; λ/M4

the quark form factor. In the following, this parameter is denoted by η. For contact inter-

actions, models with large extra dimensions and the quark form factor model, scenarios

with positive and negative η values were considered separately.

Sfor models with large extra dimensions; and R2

qfor

For a given model, the likelihood was calculated as

L(η) =

?

i

e−µi(η)·µi(η)ni

ni!

,

where the product runs over all Q2bins, niis the number of events observed in Q2bin

i and µi(η) is the expected number of events in that bin for a coupling strength η. The

5Note that CIs constitute a non-renormalizable effective theory for which higher orders are not well

defined.

7