arXiv:hep-ex/0401009v2 2 Apr 2004
Search for contact interactions, large extra
dimensions and finite quark radius in ep
collisions at HERA
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.
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
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,
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,
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,
A. Kota´ nski9, W. S? lomi´ nski
Department of Physics, Jagellonian University, Cracow, Poland
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
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,
Department of Physics and Astronomy, University of Glasgow, Glasgow, United King-
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-
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,
Kyungpook National University, Center for High Energy Physics, Daegu, South Koreag
Institut de Physique Nucl´ eaire, Universit´ e Catholique de Louvain, Louvain-la-Neuve, Bel-
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
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,
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
Polytechnic University, Sagamihara, Japanf
G. D’Agostini, G. Marini, A. Nigro
Dipartimento di Fisica, Universit` a ’La Sapienza’ and INFN, Rome, Italye
C. Cormack22, J.C. Hart, N.A. McCubbin
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, United Kingdomm
University of California, Santa Cruz, California 95064, USAn
Department of Physics, Ewha Womans University, Seoul, Korea
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
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-
Physics and Astronomy Department, University College London, London, United King-
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
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
1also affiliated with University College London, London, UK
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
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,
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
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
30supported by the KBN grant 2P03B12725
31on leave from MSU, partly supported by University of Wisconsin via the U.S.-Israel BSF
supported by the Natural Sciences and Engineering Research Council of
supported by the German Federal Ministry for Education and Research
(BMBF), under contract numbers HZ1GUA 2, HZ1GUB 0, HZ1PDA 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-
supported by the Netherlands Foundation for Research on Matter (FOM)
supported by the Polish State Committee for Scientific Research, grant no.
partially supported by the German Federal Ministry for Education and Re-
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
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 , 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 .
2Standard 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
??1 + (1 − y)2?FNC
∓?1 − (1 − y)2?xFNC
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
1Unless otherwise specified, ‘electron’ refers to both positron and electron.
?xq(x,Q2) + xq(x,Q2)?
?xq(x,Q2) − xq(x,Q2)?
where q(x,Q2) and q(x,Q2) are the parton densities for quarks and antiquarks. The
functions Aqand Bqare defined as
q) − (VR
where the coefficient functions VL,R
are given by:
q= Qq− (ve± ae)vqχZ,
q=− (ve± ae)aqχZ,
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.
qis appropriate for
fdenote the fermion charge and third
3 Models for new physics
3.1 General 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
interactions , only vector currents are considered here. They can be represented by
additional terms in the Standard Model Lagrangian, viz:
ij(¯ eiγµei)(¯ qjγµqj) , (3)
where the sum runs over electron and quark helicities and quark flavors. The couplings
(Eq. (3)) results in the following modification of the functions Vi
ijdescribe the helicity and flavor structure of contact interactions. The CI Lagrangian
qof Eq. (2):
q= Qq− (ve± ae)vqχZ+Q2
− (ve± ae)aqχZ+Q2
It was assumed that all up-type quarks have the same contact-interaction couplings, and
a similar assumption was made for down-type quarks2:
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
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 . They fulfill the relation
= 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  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%.
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 
from the SM was later reduced to around 1σ, after reevaluation of some of the theoretical
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 , 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
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  and are twice as large for vector as
1/2correspond to the squark states˜dRand ˜ uL, in minimal
3.3 Large 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:
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 .
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 .
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]
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 :
dσ(e±q → e±q)
?32ˆ u4+ 64ˆ u3ˆt + 42ˆ u2ˆt2+ 10ˆ uˆt3+ˆt4?,
(2ˆ u +ˆt)3
ˆt − M2
±vevq(2ˆ u +ˆt)3
ˆt(6ˆ u2+ 6ˆ uˆt +ˆt2)
ˆt − M2
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)
?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)
(x,Q2) = q(x,Q2)dσ(e±q)
+ ¯ q(x,Q2)dσ(e±¯ q)
where q(x,Q2), ¯ q(x,Q2) and g(x,Q2) are the quark, anti-quark and gluon densities in the
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
where Reand Rqare the root-mean-square radii of the electroweak charge of the electron
and the quark, respectively.
4 Data 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 
program with Djangoh [22,23] for electroweak radiative corrections and higher-order
matrix elements, and the color-dipole model of Ariadne  for the QCD cascade and
hadronization. The ZEUS detector was simulated using a program based on Geant
3.13 . 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 .
5 Analysis 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
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.
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
For a given model, the likelihood was calculated as
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
likelihood for the complete e±p data set was obtained by multiplying the likelihoods for
each of the three running periods.
The value of η for which L(η) is maximized is denoted as η◦. First ηdata
best describes the observed Q2spectra was determined. Using ensembles of Monte Carlo
experiments (MCE), the expected distribution of η◦was then determined as a function
of ηMC, the coupling value used as the input to the simulation. The 95% C.L. limit on η
was defined as the value of ηMCfor which the probability that |η◦| > |ηdata
For each value of ηMC, the nominal number of events expected in each Q2bin i, denoted
˜ µi(ηMC) was calculated by reweighting the SM MC prediction according to Eq. (4). The-
oretical and experimental systematic uncertainties were taken into account by treating
each uncertain quantity as a random variable. For each uncertainty, 100% correlation
between systematic variations in different bins was assumed. For each individual MCE,
an independent random variable, δj, with zero mean, was generated for each systematic
uncertainty j. The expected number of events in each Q2bin i was then given by the
product of the nominal expectation, ˜ µi, and Nsysrandom factors which account for the
uncertainties in the estimation of µias follows:
, the value of η that
| was 0.95.
µi =˜ µi(ηMC) ·
(1 + cij)δj.
The coefficent cijis the fractional change in the expected number of events in bin i for a
unit change in δj. This definition of µireduces to a linear dependence of µion each δjwhen
δjis small, while avoiding the possibility of µibecoming negative which would arise if µi
was defined as a linear function of the δj’s. For most of the systematic uncertainties, δj
follows a Gaussian distribution, except for a few where it follows a uniform distribution, as
noted in the next section. For a Gaussian δjdistribution, the definition of µicorresponds
to a Gaussian distribution in logµi. About one million MCEs were generated for each
model, so that the statistical error was negligible.
Uncertainties in the SM cross sections considered in this study were estimated using the
Epdflib program  based on Qcdnum . Fractional variations estimated from
Epdflib were used to rescale the nominal SM expectations calculated with CTEQ5D.
The following uncertainties were included:
• statistical and systematic uncertainties of the data used as an input to the NLO QCD
fit. These errors were the largest uncertainty in the SM expectations. At high Q2, the
uncertainty is up to about 4.5% (3%) for e+p (e−p) data;
• uncertainty in the value of αS(M2
tainties of NC DIS cross sections at high Q2, estimated assuming an error on αS(M2
of ±0.002 , is about 1.6%;
• uncertainties in the nuclear corrections applied to the deuteron data (KD) and to
the data from neutrino scattering on iron (KFe) used in Qcdnum. As suggested in
Epdflib, variations by up to 100% for KDand 50% for KFewere applied, treating
the corrections as uniformly distributed random variables. The corresponding uncer-
tainties of NC DIS cross sections at high Q2, are up to about 1.7% (0.8%) for KDand
up to about 3% (0.7%) for KFe, for e+p (e−p) data.
Z) used in the NLO QCD fit. The resulting uncer-
The PDF uncertainties calculated using Epdflib are similar to those obtained from a
ZEUS NLO QCD fit , when high-Q2HERA data were excluded from the fit.
In addition to the uncertainty in the SM prediction, the following experimental uncer-
tainties were taken into account:
• the scale uncertainty on the energy of the scattered electron of ±(1–3)% depending
on the topology of the event . The resulting uncertainty of NC DIS cross section
at high Q2is about 0.6% (1.3%), for e+p (e−p) data;
• the uncertainty in the hadronic energy scale of ±(1–2)% depending on the topology
of the event . The resulting cross section uncertainty at high Q2is about 1%, for
both e+p and e−p data;
• uncertainties on the luminosity measurement of 1.6% for the 1994-97 e+p data, 1.8%
for the 1998-99 e−p data and 2.5% for the 1999-2000 e+p data. Correlations between
luminosity uncertainties for different data-taking periods are small and were neglected
in the analysis.
As the double-angle method used to reconstruct the kinematics of the events [18–20] is
relatively insensitive to uncertainties in the absolute energy scale of the calorimeter, the
largest experimental uncertainty in the numbers of NC DIS events expected at high Q2
is due to the luminosity measurement.
No significant deviation of the ZEUS data from the SM prediction using the CTEQ5D
parameterization of the proton PDF was observed. For all models considered, the best
description of the data was obtained for very small values of |ηdata
The probability of obtaining larger best-fit coupling from the SM, i.e. the probability that
an experiment would produce a value of |η◦| greater than that obtained from the data,
|, i.e. close to the SM.
|η◦| > |ηdata
cases. Therefore, limits on the strength parameters of the models described in Sec. 3 are
presented in this paper.
|, calculated with MCEs assuming the SM cross section, was above 25% in all
The measured Q2spectra for e+p and e−p data, normalized to the SM predictions are
shown in Fig. 1. Also shown are curves, for VV and AA contact-interaction models
(Section 3.1), which correspond to the 95% C.L. exclusion limits on Λ. The 95% C.L.
limits on the compositeness scale Λ, for different CI models, are compared in Fig. 2 and
Table 1. Limits range from 1.7TeV for the LL model to 6.2TeV for the VV model. Also
indicated in the figure are the best-fit coupling values, ηdata
couplings. For comparison, the positions of the global likelihood maxima with ±1σ and
±2σ error6bars are included in Fig. 2. Systematic uncertainties are taken into account
by averaging the likelihood values over systematic uncertainties. For most models, the
±2σ error bars are in good agreement with 95% C.L. limits calculated with the MCE
Λ2, for positive and negative
The 95% C.L. lower limits on the compositeness scale Λ are compared in Table 1 with lim-
its from the H1 collaboration , the Tevatron [35,36] and the LEP [37–40] experiments
(where only the results from e+e−→ q¯ q channel are quoted). In Table 1 the relations
between CI couplings for the compositeness models considered are also included. The
results on the compositeness scale Λ presented here are comparable to those obtained by
other experiments, where they exist. For many models, this analysis sets the only existing
The leptoquark analysis takes into account LQs that couple to the electron and the first-
generation quarks (u, d) only (Section 3.2). Deviations in the Q2distribution of e+p and
e−p NC DIS events, corresponding to the 95% C.L. exclusion limits for selected scalar and
vector leptoquark models, are compared with ZEUS data in Fig. 3. The 95% C.L. limits
on the ratio of the leptoquark mass to the Yukawa coupling, MLQ/λLQ, are summarized
in Table 2 together with the coefficients aeq
limits range from 0.27TeV for˜SR
the LQ limits obtained by the H1 collaboration  and by the LEP experiments [37,39].
In general, comparable limits are obtained. For the SL
ZEUS analysis provides the most stringent limits.
ijdescribing the CI coupling structure. The
◦model to 1.23TeV for VL
1model. Table 2 also shows
When only the NC DIS event sample is considered, the leptoquark limits obtained in
the contact-interaction approximation are similar to, or better than, the high-mass limits
from the ZEUS resonance-search analysis . However, for SL
previously published limits are more stringent, as the possible leptoquark contribution to
6Errors are calculated from the likelihood variation: ±1σ and ±2σ errors correspond to the decrease of
the likelihood value to logL(η) = logL(η◦) −1
2and logL(η) = logL(η◦) − 2, respectively.
charged current DIS was also taken into account.
For the model with large extra dimensions (Section 3.3), 95% C.L. lower limits on the
mass scale in n dimensions of
> 0.78TeV for λ = +1 ,
> 0.79TeV for λ = −1 ,
were obtained. In Fig. 4, effects of graviton exchange on the Q2distribution, corresponding
to these limits, are compared with ZEUS e+p (Fig. 4a) and e−p (Fig. 4b) data. The limits
on MSobtained in this analysis are similar to those obtained by the H1 collaboration 
and stronger than limits from q¯ q production at LEP . However, if all final states are
considered, the limits derived from e+e−collisions exceed 1TeV . Limits above 1TeV
are also obtained in p¯ p from the measurement of e−e+and γγ production .
Assuming the electron to be point-like (Re= 0), the 95% C.L. upper limit on the effective
quark-charge radius (Section 3.4) of
< 0.85 · 10−16cm
was obtained. The present result improves the limits set in ep scattering by the H1
collaboration  (Rq< 1.0·10−16cm) and is similar to the limit set by the CDF collabo-
ration in p¯ p collisions using the Drell-Yan production of e+e−and µ+µ−pairs  (Rq<
0.79·10−16cm).7The L3 collaboration has presented a stronger limit (Rq< 0.42·10−16cm,
assuming Re= 0), based on quark-pair production measurement at LEP2  and as-
suming the same effective charge radius for all produced quark flavors.
If the charge distribution in the quark changes sign as a function of the radius, negative
values can also be considered for R2
on the effective quark-charge radius squared can be written as:
q. For such a model, the ZEUS 95% C.L. upper limit
< (1.06 · 10−16cm)2.
Cross section deviations corresponding to the 95% C.L. exclusion limits for the effective
radius, Rq, of the electroweak charge of the quark are compared with the ZEUS data in
A search for signatures of physics beyond the Standard Model has been performed with
the e+p and e−p data collected by the ZEUS Collaboration in the years 1994-2000, with
7Limits on the effective quark radius published by the CDF collaboration  were calculated assuming
Rq= Re. For comparison with limits assuming Re= 0, the limit value was scaled by a factor√2.
integrated luminosities of 112 and 16pb−1, reaching Q2values as high as 4 × 104GeV2.
No significant deviation from Standard Model predictions was observed and 95% C.L.
limits were obtained for the relevant parameters of the models studied. For the contact-
interaction models, limits on the effective mass scale, Λ (i.e. compositeness scale), ranging
from 1.7 to 6.2TeV have been obtained. Limits ranging from 0.27 to 1.23TeV have been
set for the ratio of the leptoquark mass to the Yukawa coupling, MLQ/λLQ, in the limit of
large leptoquark masses, MLQ≫√s. Limits were derived on the mass scale parameter in
models with large extra dimensions: for positive (negative) coupling signs, scales below
0.78TeV (0.79TeV) are excluded. A quark-charge radius larger than 0.85 · 10−16cm has
been excluded, using the classical form-factor approximation.
The limits derived in this analysis are comparable to the limits obtained by the H1
collaboration and by the LEP and Tevatron experiments. For many models the analysis
presented here provides the most stringent limits to date.
This measurement was made possible by the inventiveness and the diligent efforts of the
HERA machine group. The strong support and encouragement of the DESY directorate
has been invaluable. The design, construction, and installation of the ZEUS detector has
been made possible by the ingenuity and dedicated effort of many people who are not
listed as authors. Their contributions are acknowledged with great appreciation.
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ZEUS 1994-2000 e±p 95% C.L. (TeV) H1DØCDF ALEPHL3 OPAL
[+1, 0, 0,
[ 0,+1, 0,
[ 0, 0,+1,
[ 0, 0, 0,+1]
[+1, 0, 0,+1]
[ 0,+1, 0,+1]
[ 0, 0,+1,−1]
[+1,−1, 0, 0]eu
[+1, 0,+1, 0]eu
[+1, 0, 0,+1]eu
[ 0,+1,+1, 0]eu
[ 0,+1, 0,+1]eu
[ 0, 0,+1,−1]eu
and the 95% C.L. limits on the compositeness scale, Λ, resulting from the ZEUS
analysis of 1994-2000 e±p data. Each row of the table represents two scenarios
corresponding to η > 0 (Λ+) and η < 0 (Λ−). The same coupling structure applies
to d and u quarks, except for the models U1 to U6, for which the couplings for
the d quarks are zero. Also shown are results obtained by the H1 collaboration, the
p¯ p collider experiments DØ and CDF, and the LEP experiments ALEPH, L3 and
OPAL. For the LEP experiments, limits derived from the channel e+e−→ q¯ q are
Coupling structure [ǫLL,ǫLR,ǫRL,ǫRR] of the compositeness models
ZEUS 1994-2000 e±p 95% C.L.
H1 L3 Model
LL= +1, aeu
0.430.43 0.42 0.48
LL= −1, aeu
1.061.02 0.54 0.59
Table 2: Coefficients aeq
interaction limit MLQ≫√s and the 95% C.L. lower limits on the leptoquark mass
to the Yukawa coupling ratio MLQ/λLQresulting from the CI analysis of the ZEUS
1994-2000 e±p data, for different models of scalar (upper part of the table) and
vector (lower part) leptoquarks. Also shown are results obtained by the H1 collabo-
ration and corresponding contact-interaction limits from the LEP experiments L3
and OPAL. The limits from LEP on the compositeness scale Λ, for models with
coupling structure corresponding to those of scalar (vector) leptoquarks, were scaled
by factor 1/√8π (1/√4π).
ijdefining the effective leptoquark couplings in the contact-
Contact Interactions Limits
ZEUS 94-00 e+p
VV Λ− = 6.2 TeV
VV Λ+ = 5.4 TeV
Contact Interactions Limits
ZEUS 98-99 e-p
AA Λ− = 4.7 TeV
AA Λ+ = 4.4 TeV
mass scale in the VV and AA contact-interaction models, for positive (Λ+) and
negative (Λ−) couplings. Results are normalized to the Standard Model expectations
calculated using the CTEQ5D parton distributions. The insets show the comparison
in the Q2< 104GeV2region, with a linear ordinate scale.
ZEUS data compared with 95% C.L. exclusion limits for the effective
-1/Λ2 best fit value
allowed ±1/Λ2 range
+1/Λ2 best fit value
best fit ±1σ, ±2σ
ZEUS 94-00 e±p 95% C.L.
studied in this paper (dark horizontal bars). The numbers at the right (left) margin
are the corresponding lower limits on the mass scale Λ+(Λ−). The dark filled (open)
circles indicate the positions corresponding to the best-fit coupling values, ηdata
positive (negative) couplings. The light filled circles with error bars indicate the
position of the global likelihood maximum. For calculation of ±1σ and ±2σ errors
on the global maximum position, likelihood values are averaged over systematic
Confidence intervals of ±1/Λ2at 95% C.L. for general CI scenarios
Limits on Heavy Leptoquarks
ZEUS 94-00 e+p
1/2 M/λ=0.83 TeV
L M/λ=0.52 TeV
Limits on Heavy Leptoquarks
ZEUS 98-99 e-p
L M/λ=1.23 TeV
1/2 M/λ=0.47 TeV
the leptoquark mass to the Yukawa coupling, M/λ, for the SL
leptoquarks. Results are normalized to the Standard Model expectations calculated
using the CTEQ5D parton distributions. The insets show the comparison in the
Q2< 104GeV2region, with a linear ordinate scale.
ZEUS data compared with 95% C.L. exclusion limits for the ratio of
1 and VL
Q2 (GeV2) Download full-text
Large Extra Dimensions Limits
ZEUS 94-00 e+p
− = 0.79 TeV
+ = 0.78 TeV
Large Extra Dimensions Limits
ZEUS 98-99 e-p
Quark Radius Limits
ZEUS 94-00 e±p
2 = (0.85 ⋅10-16cm)2
2 = -(1.06 ⋅10-16cm)2
Figure 4: ZEUS e+p data (a) and e−p data (b) compared with 95% C.L. exclusion
limits for the effective Planck mass scale in models with large extra dimensions,
for positive (M+
compared with 95% C.L. exclusion limits for the effective mean-square radius of
the electroweak charge of the quark. Results are normalized to the Standard Model
expectations calculated using the CTEQ5D parton distributions. The insets show
the comparison in the Q2< 104GeV2region, with a linear ordinate scale.
S) and negative (M−
S) couplings. (c) Combined 1994-2000 data