Comparison of ZEUS Data with Standard Model Predictions For

DESY 97-025 ISSN 0418-9833

Comparison of ZEUS Data

with Standard Mo del Predictions

+ + 2

for e p ! e X Scattering at High x and Q

ZEUS Collab oration

Abstract

+ +

Using the ZEUS detector at HERA, wehave studied the reaction e p ! e X for

2 2

Q > 5000 GeV with a 20:1pb data sample collected during the years 1994 to

2 2

1996. For Q b elow 15000 GeV , the data are in go o d agreement with Standard

2 2

Mo del exp ectations. For Q > 35000 GeV ,twoevents are observed while 0:145

0:013 events are exp ected. A statistical analysis of a large ensemble of simulated

Standard Mo del exp eriments indicates that with probability 6.0, an excess at

least as unlikely as that observed would o ccur ab ove some Q cut. For x>0:55

and y>0:25, four events are observed where 0:91 0:08 events are exp ected.

A statistical analysis of the two-dimensional distribution of the events in x and y

yields a probability of 0.72 for the region x> 0:55 and y>0:25 and a probability

2 2

of 7.8 for the entire Q > 5000 GeV data sample. The observed excess ab ove

Standard Mo del exp ectations is particularly interesting b ecause it o ccurs in a

previously unexplored kinematic region.

To b e submitted for publication in Z. f. Physik

The ZEUS Collab oration

J. Breitweg, M. Derrick, D. Krakauer, S. Magill, D. Mikunas, B. Musgrave, J. Rep ond,

R. Stanek, R.L. Talaga, R. Yoshida, H. Zhang

Argonne National Laboratory, Argonne, IL, USA

M.C.K. Mattingly

Andrews University, Berrien Springs, MI, USA

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

1 2

G. Bruni, G. Cara Romeo, G. Castellini , L. Cifarelli , F. Cindolo, A. Contin, M. Corradi,

I. Gialas ,P. Giusti, G. Iacobucci, G. Laurenti, G. Levi, A. Margotti, T. Massam, R. Na-

nia, F. Palmonari, S. De Pasquale, A. Pesci, A. Polini, G. Sartorelli, Y. Zamora Garcia ,

A. Zichichi

University and INFN Bologna, Bologna, Italy

C. Amelung, A. Bornheim, I. Bro ck, K. Coboken, J. Crittenden, R. De ner, M. Eck-

ert, L. Feld , M. Grothe, H. Hartmann, K. Heinloth, L. Heinz, E. Hilger, H.-P. Jakob,

U.F. Katz, E. Paul, M. Pfei er, Ch. Rembser, J. Stamm, R. Wedemeyer

Physikalisches Institut der Universitat Bonn, Bonn, Germany

D.S. Bailey, S. Campb ell-Robson, W.N. Cottingham, B. Foster, R. Hall-Wilton, M.E. Hayes,

G.P. Heath, H.F. Heath, D. Piccioni, D.G. Ro , R.J. Tapp er

H.H. Wil ls Physics Laboratory, University of Bristol, Bristol, U.K.

M. Arneo do ,R.Ayad, M. Capua, A. Garfagnini, L. Iannotti, M. Schioppa, G. Susinno

Calabria University, Physics Dept.and INFN, Cosenza, Italy

J.Y. Kim, J.H. Lee, I.T. Lim, M.Y. Pac

Chonnam National University, Kwangju, Korea

9 10

A. Caldwell , N. Cartiglia, Z. Jing, W. Liu, J.A. Parsons, S. Ritz , S. Sampson, F. Sciulli,

P.B. Straub, Q. Zhu

Columbia University, Nevis Labs., Irvington on Hudson, N.Y., USA

P. Borzemski, J. Chwastowski, A. Eskreys, Z. Jakub owski, M.B. Przybycien, M. Zachara,

L. Zawiejski

Inst. of Nuclear Physics, Cracow, Poland

L. Adamczyk, B. Bednarek, K. Jelen, D. Kisielewska, T. Kowalski, M. Przybycien,

E. Rulikowska-Zarebska, L. Suszycki, J. Za jac

Faculty of Physics and Nuclear Techniques, Academy of Mining and Metal lurgy, Cracow,

Poland

Z. Dulinski, A. Kotanski

Jagel lonian Univ., Dept. of Physics, Cracow, Poland 1

G. Abbiendi , L.A.T. Bauerdick, U. Behrens, H. Beier, J.K. Bienlein, G. Cases, O. Depp e,

K. Desler, G. Drews, D.J. Gilkinson, C. Glasman, P.Gottlicher, J. Groe-Knetter, T. Haas,

W. Hain, D. Hasell, H. Heling, Y. Iga, K.F. Johnson , M. Kasemann, W. Ko ch, U. Kotz,

13 14

H. Kowalski, J. Labs, L. Lindemann, B. Lohr, M. Lowe , J. Mainusch ,O.Ma nczak,

15 16 14

J. Milewski, T. Monteiro , J.S.T. Ng , D. Notz, K. Ohrenb erg ,A.Pellegrino, F. Peluc-

chi, K. Piotrzkowski, M. Ro co , M. Rohde, J. Rold an, A.A. Savin, U. Schneekloth,

18 19

W. Schulz , F. Selonke, B. Surrow, E. Tassi, T. Vo ,D.Westphal, G. Wolf, U. Wollmer,

C. Youngman, A.F. Zarnecki, W. Zeuner

Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany

B.D. Burow, H.J. Grab osch, A. Meyer, S. Schlenstedt

DESY-IfH Zeuthen, Zeuthen, Germany

G. Barbagli, E. Gallo, P.Pelfer

University and INFN, Florence, Italy

G. Maccarrone, L. Votano

INFN, Laboratori Nazionali di Frascati, Frascati, Italy

A. Bamb erger, S. Eisenhardt, P. Markun, T. Trefzger ,S.Wol e

Fakultat fur Physik der Universitat Freiburg i.Br., Freiburg i.Br., Germany

J.T. Bromley, N.H. Bro ok, P.J. Bussey, A.T. Doyle, D.H. Saxon, L.E. Sinclair, E. Strick-

land, M.L. Utley ,R.Waugh, A.S. Wilson

Dept. of Physics and Astronomy, University of Glasgow, Glasgow, U.K.

I. Bohnet, N. Gendner, U. Holm, A. Meyer-Larsen, H. Salehi, K. Wick

Hamburg University, I. Institute of Exp. Physics, Hamburg, Germany

22 23

L.K. Gladilin , R. Klanner, E. Lohrmann, G. Po elz, W. Schott , F. Zetsche

Hamburg University, II. Institute of Exp. Physics, Hamburg, Germany

T.C. Bacon, I. Butterworth, J.E. Cole, V.L. Harris, G. Howell, B.H.Y. Hung, L. Lamb erti ,

25 26

K.R. Long, D.B. Miller, N. Pavel, A. Prinias , J.K. Sedgb eer, D. Sideris, A.F. Whit eld

Imperial Col lege London, High Energy Nuclear Physics Group, London, U.K.

U. Mallik, S.M. Wang, J.T. Wu

University of Iowa, Physics and Astronomy Dept., Iowa City, USA

P. Cloth, D. Filges

Forschungszentrum Julich, Institut fur Kernphysik, Julich, Germany

S.H. An, S.B. Lee, S.W. Nam, H.S. Park, S.K. Park

Korea University, Seoul, Korea

F. Barreiro, J.P.Fernandez, R. Graciani, J.M. Hern andez, L. Herv as, L. Labarga, M. Martinez,

J. del Peso, J. Puga, J. Terron, J.F. de Tro c oniz

Univer. Aut onoma Madrid, Depto de F sicaTe or ca, Madrid, Spain

F. Corriveau, D.S. Hanna, J. Hartmann, L.W. Hung, J.N. Lim, W.N. Murray,A.Ochs,

M. Riveline, D.G. Stairs, M. St-Laurent, R. Ullmann

a b

McGil l University, Dept. of Physics, Montr eal, Qu ebec, Canada ;

T. Tsurugai

Meiji Gakuin University, Faculty of General Education, Yokohama, Japan 2

V. Bashkirov, B.A. Dolgoshein, A. Stifutkin

Moscow Engineering Physics Institute, Mosocw, Russia

G.L. Bashindzhagyan, P.F. Ermolov, Yu.A. Golubkov, V.D. Kobrin, I.A. Korzhavina,

V.A. Kuzmin, O.Yu. Lukina, A.S. Proskuryakov, L.M. Shcheglova, A.N. Solomin, N.P. Zo-

tov

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

C. Bokel, M. Botje, N. Brummer, F. Chlebana , J. Engelen, M. de Kamps, P. Ko oijman,

A. Kruse, A. van Sighem, H. Tiecke, W. Verkerke, J. Vosseb eld, M. Vreeswijk, L. Wiggers,

E. de Wolf

NIKHEF and University of Amsterdam, Netherlands

D. Acosta, B. Bylsma, L.S. Durkin, J. Gilmore, C.M. Ginsburg, C.L. Kim, T.Y. Ling,

P. Nylander, T.A. Romanowski

Ohio State University, Physics Department, Columbus, Ohio, USA

H.E. Blaikley, R.J. Cashmore, A.M. Co op er-Sarkar, R.C.E. Devenish, J.K. Edmonds,

28 25

N. Harnew, M. Lancaster , J.D. McFall, C. Nath, V.A. Noyes , A. Quadt, J.R. Tickner,

H. Uijterwaal, R. Walczak, D.S. Waters, T. Yip

Department of Physics, University of Oxford, Oxford, U.K.

A. Bertolin, R. Brugnera, R. Carlin, F. Dal Corso, U. Dosselli, S. Limentani, M. Morandin,

M. Poso cco, L. Stanco, R. Stroili, C. Voci

Dipartimento di Fisica del l' Universita and INFN, Padova, Italy

J. Bulmahn, R.G. Feild , B.Y. Oh, J.R. Okrasinski, J.J. Whitmore

Pennsylvania State University, Dept. of Physics, University Park, PA, USA

G. Marini, A. Nigro

Dipartimento di Fisica, Univ. 'La Sapienza' and INFN, Rome, Italy

J.C. Hart, N.A. McCubbin, T.P. Shah

Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, U.K.

E. Barb eris , T. Dubbs, C. Heusch, M. Van Ho ok, W. Lo ckman, J.T. Rahn, H.F.-

W. Sadrozinski,

A. Seiden, D.C. Williams

University of California, Santa Cruz, CA, USA

O. Schwarzer, A.H. Walenta

Fachbereich Physik der Universitat-Gesamthochschule Siegen, Germany

30 31

H. Abramowicz, G. Briskin, S. Dagan ,T.Doeker, S. Kananov, A. Levy

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

University, Tel-Aviv, Israel

T. Ab e, J.I. Fleck ,M.Inuzuka, T. Ishii, M. Kuze, K. Nagano, M. Nakao, I. Suzuki,

K. Tokushuku, K. Umemori, S. Yamada, Y. Yamazaki

Institute for Nuclear Study, University of Tokyo, Tokyo, Japan

R. Hamatsu, T. Hirose, K. Homma, S. Kitamura , T. Matsushita, K. Yamauchi

Tokyo Metropolitan University, Dept. of Physics, Tokyo, Japan 3

R. Cirio, M. Costa, M.I. Ferrero, S. Maselli, V. Monaco, C. Peroni, M.C. Petrucci, R. Sac-

chi, A. Solano, A. Staiano

Universita di Torino, Dipartimento di FisicaSperimentale and INFN, Torino, Italy

M. Dardo

II Faculty of Sciences, Torino University and INFN - Alessandria, Italy

D.C. Bailey, M. Brkic, C.-P.Fagerstro em, G.F. Hartner, K.K. Jo o, G.M. Levman, J.F. Mar-

tin, R.S. Orr, S. Polenz, C.R. Sampson, D. Simmons, R.J. Teuscher

University of Toronto, Dept. of Physics, Toronto, Ont., Canada

J.M. Butterworth, C.D. Catterall, T.W. Jones, P.B. Kaziewicz, J.B. Lane, R.L. Saunders,

J. Shulman, M.R. Sutton

University Col lege London, Physics and Astronomy Dept., London, U.K.

B. Lu, L.W. Mo

Virginia Polytechnic Inst. and State University, Physics Dept., Blacksburg, VA, USA

34 35

J. Cib orowski, G. Grzelak , M. Kasprzak, K. Muchorowski , R.J. Nowak, J.M. Pawlak,

R. Pawlak, T. Tymieniecka, A.K. Wr oblewski, J.A. Zakrzewski

Warsaw University, Institute of Experimental Physics, Warsaw, Poland

M. Adamus

Institute for Nuclear Studies, Warsaw, Poland

30 30 30

C. Coldewey, Y. Eisenb erg ,D.Hochman, U. Karshon ,D.Revel

Weizmann Institute, Nuclear Physics Dept., Rehovot, Israel

W.F. Badgett, D. Chapin, R. Cross, S. Dasu, C. Foudas, R.J. Loveless, S. Mattingly,

D.D. Reeder, W.H. Smith, A. Vaiciulis, M. Wo darczyk

University of Wisconsin, Dept. of Physics, Madison, WI, USA

S. Bhadra, W.R. Frisken, M. Khakzad, W.B. Schmidke

York University, Dept. of Physics, North York, Ont., Canada 4

also at IROE Florence, Italy

now at Univ. of Salerno and INFN Nap oli, Italy

now at Univ. of Crete, Greece

supp orted byWorldlab, Lausanne, Switzerland

nowOPAL

retired

also at UniversityofTorino and Alexander von Humb oldt Fellow

now at Dongshin University, Na ju, Korea

also at DESY and Alexander von Humb oldt Fellow

Alfred P. Sloan Foundation Fellow

supp orted by an EC fellowship numb er ERBFMBICT 950172

visitor from Florida State University

now at ALCATEL Mobile Communication GmbH, Stuttgart

now at DESY Computer Center

supp orted by Europ ean Community Program PRAXIS XXI

now at DESY-Group FDET

nowatFermi National Accelerator Lab oratory FNAL, Batavia, IL, USA

now at Siemens A.G., Munich

now at NORCOM Infosystems, Hamburg

nowatATLAS Collab oration, Univ. of Munich

now at Clinical Op erational Research Unit, University College, London

on leave from MSU, supp orted by the GIF, contract I-0444-176.07/ 95

now a self-employed consultant

supp orted by an EC fellowship

PPARCPost-do ctoral Fellow

now at Conduit Communications Ltd., London, U.K.

now at Department of Energy,Washington

nowatLawrence Berkeley Lab oratory, Berkeley

nowatYale University, New Haven, CT

supp orted by a MINERVAFellowship

partially supp orted by DESY

now at CERN

present address: Tokyo Metrop olitan College of Allied Medical Sciences, Tokyo 116,

Japan

supp orted by the Polish State Committee for Scienti c Research, grant No. 2P03B09308

supp orted by the Polish State Committee for Scienti c Research, grant No. 2P03B09208 5

supp orted by the Natural Sciences and Engineering Research Council of

Canada NSERC

supp orted by the FCAR of Qu eb ec, Canada

supp orted by the German Federal Ministry for Education and Science,

Research and Technology BMBF, under contract numb ers 057BN19P,

057FR19P, 057HH19P, 057HH29P, 057SI75I

supp orted by the MINERVA Gesellschaft fur Forschung GmbH, the German

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

supp orted by the German Israeli Foundation, and by the Israel Science

Foundation

supp orted by the Italian National Institute for Nuclear Physics INFN

supp orted by the Japanese Ministry of Education, Science and Culture the

Monbusho and its grants for Scienti c Research

supp orted by the Korean Ministry of Education and Korea Science and Engi-

neering Foundation

supp orted by the Netherlands Foundation for Research on Matter FOM

supp orted by the Polish State Committee for Scienti c Research, grant

No. 115/E-343/ SPUB/P03/ 120 /9 6

supp orted by the Polish State Committee for Scienti c Research grant No. 2

P03B 083 08 and Foundation for Polish-German Collab oration

partially supp orted by the German Federal Ministry for Education and Science,

Research and Technology BMBF

supp orted by the German Federal Ministry for Education and Science, Re-

search and Technology BMBF, and the Fund of Fundamental Researchof

Russian Ministry of Science and Education and by INTAS-Grant No. 93-63

supp orted by the Spanish Ministry of Education and Science through funds

provided by CICYT

supp orted by the Particle Physics and Astronomy Research Council

supp orted by the US Department of Energy

supp orted by the US National Science Foundation 6

1 Intro duction

Deep{inelastic scattering DIS of leptons on nucleons has b een an imp ortant to ol for

understanding nucleon structure and many elements of the Standard Mo del, including

b oth the electroweak interaction and quantum chromo dynamics QCD. At the HERA

collider, DIS pro cesses are b eing studied at a center of mass energy s = 300 GeV and

at Q the negative of the square of the four-momentum transfer exceeding the squares

of the weak vector b oson masses. In this regime, lepton{nucleon scattering allows unique

and sensitive tests of the Standard Mo del as well as of certain extensions to it [1].

This pap er presents results from e p running with the ZEUS detector during the years

1994 to 1996, at proton and p ositron b eam energies of E = 820 GeV and E =27:5GeV.

p e

With the integrated luminosityof20:1pb collected in this p erio d, it has b ecome p ossible

+ +

to study the reaction e p ! e X in the region where the exp ected DIS cross section is

in the subpicobarn range. This region of high Q and x the Bjorken scaling variable

has never b efore b een explored. The ab ove reaction is understo o d to b e a p ositron{

quark collision with center{of{mass energy xs. Initial cross section measurements by

the ZEUS [2] and H1 [3] collab orations are in go o d agreement with Standard Mo del

2 4 2

exp ectations for Q up to ab out 10 GeV . In this pap er, we rep ort on a more sensitive

2 2

search for deviations from Standard Mo del predictions in the region Q > 5000 GeV .

2 Neutral Current Deep{Inelastic Scattering

The reaction studied is:

+ +

e + p ! e + X 1

where X represents the nal state hadronic system. In the high Q regime, the Standard

Mo del neutral current NC cross section for 1 dep ends on well{measured electroweak

parameters and on the parton densities in the proton. Though the latter have not yet b een

measured at high Q , p erturbative Quantum Chromo dynamics pQCD predicts their

values through evolution from high{precision measurements made at lower Q values.

The Born cross section [4] for the NC DIS reaction 1 with unp olarized b eams is

2 2

n o

d 2

2 2

= Y y F x; Q Y y xF x; Q ; 2

+ 2 3

2 4

dx dQ xQ

where is the electromagnetic coupling. The cross section is given in terms of Q and the

2 2

DIS scaling variables x and y = Q =sx. In the region of large x and Q studied here, the

parity{violating xF term substantially reduces the e p cross section, while increasing the

cross section for e p scattering where the second term has p ositive sign. The explicit

y {dep endence, which is due to the helicity dep endence of electroweak interactions, is

contained in the functions

Y y = 11 y ; 3

We neglect the contribution to the cross section 2 of the longitudinal structure function, F , which

we estimate from pQCD and the parton densities[5 ] to b e less than 1 in the kinematic range under

study. 7

while the dep endence on the quark structure of the proton, and on the Z propagator is

absorb ed in the p ositive structure functions:

! !

2 2 2 2

F x; Q qx; Q ] C Q [q x; Q +

= x 4

2 2 2 2

xF x; Q C Q [q x; Q q x; Q ]

q =quarks

written in terms of the quark densities in the proton q = u; d; c; s; t; b and the

+ 2

q . For e p scattering, the Q {dep endent co ecient corresp onding antiquark densities

q q

functions, C and C , are given by:

2 3

2 2 2 2 2 2 2

C Q = e 2e v v +v +a v + a

q q e Z

q q q e e Z

2 2

C Q = 2e a a +2v a 2v a

q q e Z q q e e

with

Q 1

= : 6

2 2

Q + M

4 sin cos

w w

In eqs. 5 and 6, M is the Z mass, e is the quark charge in units of the p ositron charge,

Z q

v =T 2e sin and a = T are the vector and axial vector couplings of the quark

q 3q q w q 3q

to the Z , v and a are the corresp onding electron couplings, is the weak mixing angle,

e e w

and T is the third comp onent of the weak isospin. All relevant electroweak parameters

have b een measured to high precision [6].

The QCD{evolved structure functions [7] of equation 4, evaluated at a given x at high

2 2

Q , dep end on quark and gluon densities in the proton measured at lower values of Q

and higher values of x.At high x, u quarks give the dominant contribution to the cross

section b ecause they have the largest density [8] and b ecause e =2=3. In addition, the

antiquark q density is small [9].

Uncertainties in the Born-level e p DIS cross section predictions in this region of high x

and Q are estimated to b e ab out 6:5 see Section 8, mainly due to uncertainties in

the evolved quark densities.

It should b e noted that an anomalously high cross section for the pro duction of jets with

high transverse energy in pp collisions, as recently rep orted by the CDF collab oration

[10 ], can b e explained by adjusting the gluon density in the proton [11 ] which raises

the rate of gluon{quark collisions at high x, rather than by adjusting quark densities.

This variation of the gluon density,however, has only a small e ect on the cross section

predictions relevant to this pap er see Section 8.

3 ZEUS Detector and Monte{Carlo Simulation

3.1 Exp erimental Setup

A description of the ZEUS detector can b e found in references [12, 13 ]. The primary

comp onents used in this analysis were the comp ensating uranium{scintillator calorimeter,

the central tracking detector, and the luminosity detector. 8

The calorimeter [14 ] is divided into three parts, forward FCAL covering the p olar angle

interval 2:6 < <37 , barrel BCAL: 37 < <129 and rear RCAL: 129 < <176:1 . The

calorimeters are sub divided into towers which each subtend solid angles from 0:006 to

0:04 steradians. Eachtower is longitudinally segmented into an electromagnetic EMC

section and two hadronic HAC sections one in RCAL. EachHAC section consists of

a single cell, while the EMC section of eachtower is further sub divided transversely into

four cells twoinRCAL. In test b eam conditions, for particle energies up to 120 GeV,

q q

energy resolutions of =E =18= E GeV for electrons and =E =35= E GeV for

E E

hadrons have b een measured. The cell-to-cell variations in the energy calibration are

approximately 2 for the EMC cells and 3 for HAC cells. The FCAL and BCAL

energy scales are presently understo o d to an accuracy of 3. The time resolution is

b elow 1 ns for energy dep osits greater than 4:5GeV . The impact p oint of the scattered

p ositron at the calorimeter, determined using pulse height sharing, has a resolution of

ab out 1 cm.

In the physics analysis, only those calorimeter cells with energy dep osits ab ove thresholds

of 60 MeV and 110 MeV for EMC and HAC cells resp ectively were used.

The central tracking chamb er CTD [15 ] op erates in a 1:43 T solenoidal magnetic eld.

It is a drift chamb er consisting of 72 cylindrical layers, organized into 9 sup erlayers. A

momentum measurement requires a track to pass through at least two sup erlayers, cor-

resp onding to a p olar angle region of 15 < <164 . The transverse momentum resolution

is p =p =[0:005p GeV] 0:016 for full length tracks. For full length tracks with

t t t

momenta p>5GeV the vertex resolution is 0:1 cm in the transverse plane and 0:4cm

along Z .

Events were ltered online by a three{level trigger system [13]. The trigger criteria used in

this analysis relied primarily on the energies measured in the calorimeter. The rst level

trigger decision was based on electromagnetic energy and total transverse energy E .

The second level trigger rejected backgrounds mostly p{gas interactions for which the

calorimeter timing was inconsistent with an ep interaction. In addition, the second level

trigger applied increased E thresholds and also required a minimum value of E p see

t Z

Section 5, where E and p are the summed energy and Z -comp onent of the momentum

measured in the calorimeter. The third level trigger applied more stringent timing cuts

as well as increased energy and E p thresholds. In all cases, the requirements were

less stringent than those imp osed by the oine event selection.

The luminositywas measured by the rate of high energy photons from the pro cess

ep ! ep detected in a lead{scintillator calorimeter [16] lo cated at Z = 107 m. The

uncertainty asso ciated with luminosity measurements is addressed in section 8.

3.2 Monte Carlo Simulation

NC DIS events were simulated using the meps option of lepto [17] interfaced to her-

acles [18 ] via django [19] and the MRSA parton distribution set [20 ]. The event sim-

ulation included electroweak radiative corrections, leading order QCD e ects and parton

showers. Hadronization was simulated with jetset[21 ].

The right-handed ZEUS co ordinate system is centered on the nominal interaction p ointZ =0

and de ned with the Z axis p ointing in the proton b eam direction, and the horizontal X axis p ointing

towards the center of HERA. 9

Large samples of simulated photopro duction events[22]were used for background studies.

Samples of b oth direct and resolved photopro duction events including the pro duction of

cc and bb pairs were generated using b oth pythia [21] and herwig [23]. Direct and

resolved photopro duction of events with prompt photons were simulated with herwig.

Pro duction of W and Z b osons was studied using the epvec [24 ] generator. Finally, the

+ +

pro cesses ! e e and ! were simulated using zlpair [25 ].

All MC events were passed through a geant [26] based simulation of the ZEUS detector

and trigger, and analyzed with the same reconstruction and oine selection pro cedures

as the data.

4 Positron Identi cation and Event Kinematics

2 + +

Akey signature of high Q e p ! e X events is an isolated high transverse momentum

p ositron. In order to identify and reconstruct this p ositron, while rejecting events in

which other nal state particles mimic a p ositron, an algorithm was used which combines

calorimeter and CTD information.

In a rst step, the calorimeter cells are clustered by joining each cell to the highest energy

cell among its adjacent neighb ours. All clusters are evaluated as p ositron candidates. The

cluster energy, E , is the sum of the cell energies b elonging to the cluster. The cluster

clu

angle, , is set equal to the p olar angle obtained by joining the energy-weighted mean

clu

p osition of the cluster with the eventvertex obtained from the tracks measured with

the CTD. For candidates with p olar angle within the CTD acceptance > 17:2 ,

clu

a matching track is required. A track is considered to match if the distance of closest

approach DCA b etween the extrap olation of the trackinto the calorimeter and the

p osition of the cluster center is less than 10 cm, where the r. m. s. resolution on the DCA

is 1.8 cm.

In the second step, several quantities, , are calculated for each p ositron candidate: the

fraction of the cluster energy in the HAC sections of the calorimeter, the parameters

related to lateral energy pro les, and the total energy E in all calorimeter cells

cone

not asso ciated with the cluster but lying within an ; pseudorapidity,azimuth cone of

radius 0.8 centered on the cluster. If a matching track is present, we also evaluate the

p olar and azimuthal angle di erences b etween the track and the cluster p osition, and the

quantity1=E 1=P , where P is the track momentum.

clu trk trk

Finally,we transform each into a quality factor Q . Candidates are accepted as

i i

p ositrons if the pro duct of the Q exceeds a threshold determined from Monte Carlo

studies. The eciency for nding p ositrons in a neutral current DIS sample with Q >

2 0

5000 GeV is 91. In accepted events, the p ositron energy, E , is set equal to the cluster

energy, E , and the p ositron angle, , is set equal to . The resolution in is typically

clu e clu e

b etter than 0:3 .

For eachevent with an accepted p ositron, the following global event quantities were

We do not consider candidates with > 164 which are also b eyond the CTD acceptance limit,

clu

since they corresp ond to Q values b elow the range of this analysis. 10

calculated from the energy dep osits in the calorimeter:

! !

2 2

X X

i i

p = p + p ;

X Y

i i

E p = E p ;

i i

2 2

p +p ; 7 E =

X Y

! !

2 2

X X

0 0

i i

p = p + p ;

t had

X Y

i i

E p = E p ;

Z had

where the sums run over all calorimeter cells with energy dep osits ab ove threshold and

the ~p are the momenta assigned to each calorimeter cell calculated assuming zero mass

with the direction obtained from the cell center and the measured vertex p osition. The

primed sums exclude the cells asso ciated with the p ositron.

To describ e the hadronic system, we use the angle, , and energy, E , de ned as

raw q

2 2

p p E p

t had t Z

had had

and E = : 8 cos =

q raw

2 2

p +E p sin

t Z raw

had had

Resolution e ects and systematic shifts of have b een studied with MC simulations.

raw

The reconstructed is systematically higher than the generated value by ab out 2:7 .

raw

To remove this bias, we compute a corrected value, , which dep ends on and . The

raw e

2 2

r. m. s. resolution of is ab out 2:5 for x> 0:55 and Q > 5000 GeV .

In the quark{parton mo del, for a p erfect detector, and E are interpreted as the scat-

tering angle and energy of the massless quark q in the reaction eq ! eq .

At a given value of s, the kinematic variables x, y , and Q can b e reconstructed from

anytwo of the four measured quantities: E , , E , and . Di erent combinations have

e q

b een used by the HERA exp eriments. At high x and Q where the calorimeter energy

resolution functions are narrow, the dominant uncertainties in energy measurements are

due to systematic e ects such as energy loss in inactive material in front of the calorime-

ter, nonuniformities and nonlinearities in the calorimeter resp onse, longitudinal energy

leakages, and energy carried awayby neutrinos and muons. For the hadronic system, the

raw measured energies are typically 15 less than the true energies. For p ositrons, the

raw measured energies are typically 4 less than the true values.

Wecho ose the double{angle metho d [27] b ecause it is least sensitive to uncertainties in

the energy measurement. In this scheme, the kinematic variables are obtained from

and as follows:

E sin sin

e e

x = ;

E 1 cos 1 cos

p e

sin 1 cos

y = ; 9

sin + sin sin +

e e

Q = sx y :

DA DA

DA 11

For y>0:25 and x>0:45, the resolution in x is 9; it improves to 6 for y>0:5.

The resolution in Q is typically 5 at large x and y .

For selected events with high x and high Q we also present the kinematic variables

calculated from the scattered p ositron energy E and angle using the equations:

E 1 + cos E

e e

; x =

E 2E E 1 cos

p e e

1 cos ; 10 y = 1

e e

Q = sx y :

e e

We apply a test{b eam based correction to E to account for energy loss in inactive material

and nonuniformities of the calorimeter resp onse.

5 Event Selection

Imp ortantcharacteristics of reaction 1 that distinguish it from background pro cesses

include i the presence of an energetic isolated p ositron, ii p balance, and iii E p

t Z

2E =55GeV. In addition, at large Q , the transverse energy E typically exceeds

e t

100 GeV.

Ab out 10 events were accepted by the trigger requirements describ ed in section 3.1. The

oine event selection criteria are describ ed b elow.

E p

The net E p as measured in the calorimeter is required to b e in the range

40 GeV 17:2 <

Z Z e e

+ +

17:2 . The lower cut rejects backgrounds such as photopro duction or e p ! e X

events with a hard initial state photon, for which energy escap es through the rear

b eam hole see b elow. The 70 GeV cut removes a small number of events with a

misreconstructed vertex p osition.

Longitudinal vertex p osition

The eventvertex reconstructed from CTD tracks must havea Z p osition Z

vtx

within 50 cm of the nominal interaction p oint. The Z distribution of the data is

vtx

roughly Gaussian with hZ i = 2cm. The r. m. s. spread in Z , 12 cm, is largely

vtx vtx

due to the length of the proton b eam bunches.

Positron requirements

An isolated p ositron candidate with energy E > 20 GeV and E < 5GeVmust

cone

b e found by the algorithm describ ed in section 4. Additional requirements dep end

on the p olar angle of the p ositron:

For > 17:2 , where the p ositron candidates are within the CTD acceptance,

a matching track with momentum ab ove 2 GeV is required. 12

For < 17:2 , where the p ositron either misses the CTD altogether or is on

the edge of the CTD acceptance, the numb er of fake p ositron candidates is

large. These have a sharply falling transverse momentum sp ectrum. To reduce

this background, we require p ositron candidates in this angular range to have

transverse momenta ab ove30GeV.

To remove Compton scattering events ep ! e X , we reject anyevent which has

two isolated electromagnetic clusters in the calorimeter, each with E > 8GeV and

clu

E < 2GeV.

cone

Momentum transfer

2 2

We require Q to exceed 5000 GeV .

The overall selection eciency, estimated using Monte Carlo NC events generated with

2 2

Q > 5000 GeV , is 81. For the 191 events which pass all cuts, the mean measured

E p is 51:9GeV with an r. m. s. width of 4:2GeV , in go o d agreement with the Monte

Carlo e p NC simulation which predicts a mean of 51:8GeV and an r. m. s. of 4:0GeV.

While no cut was applied to the net transverse momentum p , the surviving events have

a mean p of 7:5GeV , again in go o d agreement with the e p NC Monte Carlo prediction

of 7:1GeV.

6 Data and Exp ectations at Large x and Q

Figure 1 shows the distribution in the x ;y plane of the 191 events satisfying the

DA DA

selection criteria. In Table 1, the numb ers of observed events are compared with the

Standard Mo del exp ectations in bins of x and y . In general, the agreementbetween

DA DA

the data and the Standard Mo del exp ectations is go o d. However, veevents, in four

x ;y bins o ccur at high x and Q where the exp ected numb ers of events are

DA DA DA

small. Four lie in the region x > 0:55 and y > 0:25, while the fth has x =0:48

DA DA DA

andavery high Q . These veevents are selected for more detailed discussion b elow.

Figures 2 and 3 show the x for y > 0:25 and Q distributions of the nal event

DA DA

sample. In b oth gures, the e p NC prediction for the same integrated luminosityis

sup erimp osed as a solid histogram. Again, the agreement with the Standard Mo del is

go o d at lower values of x and Q , but an excess is observed at high x and at high

DA DA

Q .

Table 2 shows the kinematic variables, b efore applying the corrections discussed in section

4, asso ciated with the ve selected events. Included are the uncorrected values of x ,

y , and Q calculated using aswell as the corrected value of .Table 3 gives

DA raw

the kinematic variables and their estimated uncertainties obtained using the double{angle

and electron metho ds. The uncertainties have b een estimated from the resolutions in

and ,aswell as estimates of the systematic uncertainty in the {correction pro cedure

discussed in Section 4. The quoted r. m. s. errors on the electron variables include the

uncertaintyin , the calorimeter energy resolution, the uncertainty asso ciated with the

calorimeter nonlinearity, and the uncertainty on corrections applied for inactive material

and nonuniformities. Though is used in b oth the DA and electron metho ds, it makes

e 13

only a small contribution to each error. Hence the errors on the two measurements are

essentially indep endent.

All events listed in Tables 2 and 3, except the rst, have a track matching the electromag-

netic shower of the scattered p ositron in the calorimeter. In these events, the p ositron

track momentum is consistent with the calorimeter energy within measurement errors .

The rst event 11-Oct-94 has a p ositron candidate at to o small an angle to pro duce an

observable track in the CTD. We showevent displays of the rst twoevents in Figs. 4

and 5.

The veevents have clean, well-identi ed and isolated p ositrons and jets in the nal state.

None lie close to any of the selection cuts describ ed in the previous section. For these

events, the scattering angles and energies of the nal state p ositrons and jets are measured

with go o d precision, making it unlikely that resolution smearing has moved any of these

2 2

events from low Q to the measured Q .

Initial state radiation ISR from the incoming p ositron, where the radiated photon es-

cap es through the rear b eam hole is a p ossible source of uncertainty in the determination

of the event kinematics. Since ISR a ects the DA and electron variables di erently,itis

p ossible to estimate the energy E of the radiated photon. For each of the veevents,

E is consistent with zero within resolution and the measured values of E p limit

E 3 GeV.

7 Background Estimation

Potential backgrounds to e p DIS events at large x and y are those pro cesses which yield

an isolated p ositron or electron of high transverse energy, or a photon or which could

b e misidenti ed as a scattered p ositron. The latter event class contributes predominantly

to the background of events in which the p ositron is very forward 17:2 and no

track information is available for the p ositron candidate e.g. the rst eventinTables 2

and 3. At larger angles, photon conversions in inactive material b etween the interaction

p oint and the CTD can also mimic p ositron candidates with matching tracks, but this

e ect, which is included in the detector simulation, is much smaller.

In the following, we describ e the physical pro cesses studied as p ossible sources of back-

ground. Limits are quoted at 90 con dence level.

Prompt photon photopro duction p ! X has b een studied using herwig.We

generated an event sample with the nal state photon transverse momentum ex-

ceeding 20 GeV . The cross section is 1:6 pb , of which 86 14 is due to direct

resolved photopro duction. The observed cross section due to this pro cess in the

region x > 0:45 and y > 0:25 is 0.28 fb 0.006 events.

DA DA

Photopro duction of high E jets can contribute to the background if a jet is misiden-

ti ed as a p ositron. Using herwig,wehave generated event samples for b oth direct

It should b e noted that the p ositron energies in table 2 are so large that the tracking error do es not

allow an unambiguous determination of the particle charge.

There are hits in the innermost layer of the CTD, aligned in azimuth with this p ositron candidate.

However, the hits are to o few to qualify as a track according to our standard criteria. 14

and resolved pro cesses which include heavy quark pro duction and decay. In these

samples, no event satis es the selection criteria for x > 0:45 and y > 0:25,

DA DA

providing an upp er limit of 1:8 fb 0.04 events.

QED Compton scattering ep ! e X could pro duce background if one of the

electromagnetic showers is not recognized as such. Monte Carlo studies show that

this probability is negligible, with an upp er limit on the contribution to the observed

cross section of 0:2 fb 0.004 events.

Two photon pro duction of lepton pairs ! ``was studied using zlpair.No

+ +

events from the pro cess ! e e were found after the selections. For ! ,

where one decays via ! e , the quantity E p as well as the electron transverse

energy are typically muchlower than for high Q NC events. We obtain the upp er

limit on the contribution to the observed cross section of 0:1fb 0:002 events.

Leptonic decays of W b osons have b een studied using a Monte Carlo sample gen-

erated with epvec. The total cross section for pro duction of W b osons and their

subsequent decay via W ! e is approximately 0:1 pb . The nal state contains a

antineutrino with high transverse momentum of order 40 GeV , whichtypically

results in large missing E p as well as p . We estimate the accepted cross

Z t

section for this pro cess to b e less than 0.5 fb 0.01 events. Decays of the neutral

0 +

b oson, Z ! e e , are rejected by the cut on two electromagnetic clusters and are

exp ected to contribute a negligible background.

The estimated cross sections from these background sources are listed in Table 4 along

with the e p NC cross section. The backgrounds are much smaller than the DIS signal

in the region of interest, and are neglected.

8 Uncertainties of the Standard Mo del Predictions

The predicted numb ers of e p NC DIS events dep end on i the measured luminosity, ii

the electroweak parameters, iii electroweak radiative corrections, mainly due to initial

state radiation ISR, iv the quark densities in the relevant region of x and Q and v

the Monte Carlo simulation of the detector. Wenow discuss the precision to which these

quantities are known and describ e the studies p erformed to determine the uncertainties

of the predictions.

Luminosity measurement

The luminosity is measured to a precision of ab out 1.5 using the ZEUS luminosity

monitor. The recent 1996 running p erio d has a larger uncertainty due to e ects from

b eam satellite bunches. Also, the oine calibration of the luminosity detector is

not yet nalized. Including these uncertainties from recent data, the uncertainty for

the full data sample is 2.3.

Electroweak parameters

The relevant electroweak parameters have b een measured to high accuracy [6] and

contribute a small uncertainty in the predicted cross section over the HERA kine-

matic range [28 ]. The heracles program calculates NC DIS cross sections to rst 15

order using input values for the Fermi constant G , M , the top mass m , and the

Z t

Higgs mass. Varying M =91:187 0:007 GeV and m = 180 12 GeV within their

Z t

exp erimental errors [6] changes the predicted cross section in the kinematic range

rep orted in this pap er by only 0:25.

Radiative corrections

The program hector [29], which includes the e ects of second order QED radiative

corrections was used to check the cross sections computed using heracles. The

di erences were found to b e ab out 1:5 for the integrated cross sections in the

region x > 0:5 and y > 0:25.

DA DA

The luminosity monitor records data for all triggered events, and so measures di-

rectly, with an acceptance of ab out 30, the ISR sp ectrum for accepted events. The

exp erimental data are in quantitative agreement with the ISR sp ectrum calculated

for the accepted sample.

Corrections due to initial state radiation convoluted with the exp erimental resolu-

tion, based on studies [30] made for lower values of x, pro duce uncertainties of less

than 2 in the accepted cross sections. This numb er is used as the estimate of the

uncertainty due to radiative corrections.

Structure functions

The least well known inputs to the predicted cross section in equation 2 are the

structure functions. To estimate the uncertainty asso ciated with parton densities, we

p erformed a NLO QCD t to xed-target F lepton-proton data with x> 0:1 from

the NMC [31 ], SLAC [32], and BCDMS [33] collab orations and xF andq =xF results

3 3

from the CCFR collab oration [9]. A complete treatment of statistical and correlated

exp erimental systematic errors was included in the t. The results of the t are

consistent with the MRSA [20 ] and CTEQ3 [34] parton density parameterizations

2 4 2

up to Q of 5 10 GeV .

The t was used to estimate the two largest uncertainties due to the structure

functions: the exp erimental uncertainties and the uncertainty of the quark-gluon

coupling, , used in the evolution to higher Q . The e ects of exp erimental un-

certainties in the xed-target data result in a 6:2 uncertainty in the integrated

cross section at HERA for x>0:5 and y>0:25. The uncertainty due to was

estimated byvarying the value of M used in the QCD evolution from 0.113 to

s Z

0.123, which pro duces an uncertaintyof 1:9. From the ab ove studies, we take

the overall uncertainty in the cross section due to structure function uncertainties

to b e 6:5 over the kinematic range of interest.

Other sources of uncertainty in the structure functions were found to b e small.

Changing the strange quark fraction in the QCD t from 10 to 30 pro duced less

than 0:1 change in the predicted cross section. Removing BCDMS data from the

t pro duced a change of only 1.7. Removing data with W = sy 1 xbetween

10 and 25 GeV had no signi cant e ect. Since the contribution of charm to the

cross section for x>0:5 and y>0:25 is 0:5, uncertainties in the charm quark

mass and the charm evolution renormalization scale can b e safely neglected.

As a cross check, the uncertaintyof6:5 was compared to the di erences in cross

section predicted byvarious parton density parameterizations. For example, a com-

parison of integrated cross sections predicted by the MRSA, CTEQ3, and GRV94 16

[35 ] parameterizations pro duces an r. m. s. of 2. A comparison of the CTEQ4 HJ

parameterization [11 ] whichwas tuned to the CDF high E jet cross section [10 ]

with the nominal CTEQ4 parameterization pro duced an increase in cross section

of only 1:9, demonstrating the small e ect at HERA of a larger gluon density

at high x. Finally, a crude estimate of the contributions from QCD corrections at

higher than NLO can b e estimated by comparing the cross sections predicted by the

GRV94 LO and NLO parameterizations, which pro duced a cross section di erence

of only 1.

Table 5 summarizes the structure function uncertainties as well as the cross checks

whichwere p erformed.

Detector simulation

To estimate the uncertainties in the exp ected event yields due to p ossible inaccu-

racies in the detector simulation, we made several mo di cations to the simulation

to re ect uncertainties in the overall calorimeter energy scale and in the simulation

of the calorimeter and CTD resp onse to p ositrons. The FCAL and BCAL energy

scales were separately varied by 3, our present estimate of this uncertainty. Each

of the seven measured quantities used in the p ositron identi cation algorithm was

varied by an amount consistent with the di erences b etween the data and the nom-

inal simulation. For the region x > 0:55 and y > 0:25, the resulting uncertainty

DA DA

in the exp ected number of events is 4.4.

We conclude that at the large x and Q values discussed in this pap er the overall uncer-

tainty of the number of events predicted within the Standard Mo del is 8:4.

9 Comparison of Data with Standard Mo del and Sig-

ni cance of Excess

+ +

Table 1 compares the data with the e p ! e X exp ectations in bins of x and y

DA DA

2 2

for Q DA > 5000 GeV . There is very go o d agreementover the entire plane, except in

the region of high x and y . The numb ers of observed and exp ected events ab ove

DA DA

various Q thresholds are given in table 6. The data agree well with the Standard Mo del

2 4 2

predictions up to Q of 1:5 10 GeV .

2 2 2

Fig. 6a shows the number of events with Q >Q as a function of Q . Figure 7a

DA DA DA

shows the number of events with y > 0:25 and with x >x , as a function of x .

DA DA

On each of the two plots, the e p NC DIS Monte Carlo exp ectation is shown as a dotted

line.

We de ne the Poisson probability corresp onding to the eventnumb ers in Fig. 6a as

P Q = e 11

n=N

obs

2 2

where N is the numb er of observed events with Q >Q , and is the number

obs

DA DA

of events exp ected from NC DIS in the same region. In Fig. 6b P Q is shown as a

2 2

function of Q . The minimum probabilityofPQ =0:39 corresp onding to 2.7

DA DA 17

2 4 2

Gaussian standard deviations o ccurs at Q =3:75 10 GeV where twoevents are

observed while 0:091 0:010 are exp ected. If the exp ected number of events is increased

by its error, P Q increases to 0.47.

Wehave p erformed a similar analysis of the x sp ectrum in the region y > 0:25. The

DA DA

probability P x is shown as a function of x in Fig. 7b. Here the minimum value

DA DA

P x =0:60 corresp onding to 2.5 Gaussian standard deviations o ccurs at x =0:57

DA DA

where four events are observed and 0:71 0:06 are exp ected. If the exp ected number of

events is increased by its error, P x increases to 0.79. The corresp onding results for

di erent y cuts app ear in Table 7.

To gauge the signi cance of these probabilities, one must consider that it is p ossible

to observe a statistical uctuation ab ove any Q or x within the region studied.

DA DA

We generated a large ensemble of simulated exp eriments according to Standard Mo del

assumptions, each with a luminosity of 20.1 pb and asked how often an exp eriment

2 2

would have a probability P Q < 0:39 for any Q . The resulting probabilityto

DA DA

nd such a uctuation was 6:0. Similarly,we determined that the probability for an

exp erimenttohave Px < 0:60 in the region y > 0:25 for any x was 7.2. The

DA DA

same analysis was applied for other y cuts and the results app ear in Table 7.

Finally,wehave p erformed a statistical analysis which computes a probability for the two{

2 2

dimensional distribution of the events in the x ;y plane with Q > 5000 GeV .

DA DA

Here the data from each simulated exp erimentwere binned as in Table 1. Over a given

region R of the x ;y plane, which is de ned as a subset of the bins shown in Table 1,

DA DA

we compute the likeliho o d for a given exp erimentas

L = e ;

N !

i2R

where N is the number of events observed and is the number of events exp ected in bin

i i

obs

i.For region R,we denote by L the value of L obtained from the data.

Using the ensemble of simulated exp eriments, we determined the probability that L <

obs

L for several choices of the region R.IfRis the entire x ;y plane, the probability

DA DA

obs

that L < L is 7:8. If R consists of the entire x ;y plane, except for x > 0:55

R DA DA DA

obs

and y > 0:25, the probability that L < L is 50.2, indicating that the data are in

DA R

go o d agreement with the Standard Mo del in this region. In contrast, the probability that

obs

L < L in the region R de ned by x > 0:55 and y > 0:25 is 0:72.

R DA DA

10 Conclusions

+ + 2

Using the ZEUS detector at HERA, wehave studied the reaction e p ! e X for Q >

5000 GeV with a 20:1pb data sample collected during the years 1994 to 1996.

2 2

For Q b elow 15000 GeV , the data are in go o d agreement with Standard Mo del exp ec-

2 2

tations. For Q > 35000 GeV ,twoevents are observed while 0:145 0:013 events are

exp ected. A statistical analysis of a large ensemble of simulated Standard Mo del exp eri-

ments indicates that with probability 6.0, an excess at least as unlikely as that observed

cut. would o ccur ab ove some Q 18

For x> 0:55 and y>0:25, four events are observed where 0:91 0:08 events are exp ected.

A statistical analysis which assigns a probability to the two-dimensional distribution of

the events in x and y yields a probability of 0.72 for the region x> 0:55 and y>0:25

2 2

and a probability of 7.8 for the entire Q > 5000 GeV data sample.

The observed excess ab ove Standard Mo del exp ectations is particularly interesting b e-

cause it o ccurs in a previously unexplored kinematic region.

Acknowledgements

We appreciate the contributions to the construction and maintenance of the ZEUS de-

tector by many p eople who are not listed as authors. We thank the DESY computing

sta for providing the data analysis environment. The HERA machine group is esp ecially

acknowledged for the outstanding op eration of the collider. Finally,we thank the DESY

directorate for strong supp ort and encouragement. 19

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ZEUS 1994-1996

min

x 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85

max

x 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95

0:95