Limits on the effective quark radius from inclusive ep scattering at HERA

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Limits on the effective quark radius from inclusive ep scattering at HERA

ZEUS Collaboration

H. Abramowicz

^y,31

, I. Abt

^t

, L. Adamczyk

^h

, M. Adamus

^ae

, S. Antonelli

^b

, V. Aushev

^q

, O. Behnke

^j

, U. Behrens

^j

, A. Bertolin

^v

, S. Bhadra

^ag

, I. Bloch

^k

, E.G. Boos

^o

, I. Brock

^c

, N.H. Brook

^ac

, R. Brugnera

^w

, A. Bruni

^a

, P.J. Bussey

^l

, A. Caldwell

^t

, M. Capua

^e

,

C.D. Catterall

^ag

, J. Chwastowski

^g

, J. Ciborowski

^ad,33

, R. Ciesielski

^j,16

, A.M. Cooper-Sarkar

^u

, M. Corradi

^a,11

, R.K. Dementiev

^s

, R.C.E. Devenish

^u

, S. Dusini

^v

, B. Foster

^m,23

, G. Gach

^h

, E. Gallo

^m,24

, A. Garfagnini

^w

, A. Geiser

^j

, A. Gizhko

^j

, L.K. Gladilin

^s

, Yu.A. Golubkov

^s

, G. Grzelak

^ad

, M. Guzik

^h

, C. Gwenlan

^u

, W. Hain

^j

, O. Hlushchenko

^q

, D. Hochman

^af

,

R. Hori

ⁿ

, Z.A. Ibrahim

^f

, Y. Iga

^x

, M. Ishitsuka

^z

, F. Januschek

^j,17

, N.Z. Jomhari

^f

, I. Kadenko

^q

, S. Kananov

^y

, U. Karshon

^af

, P. Kaur

^d,12

, D. Kisielewska

^h

, R. Klanner

^m

, U. Klein

^j,18

,

I.A. Korzhavina

^s

, A. Kota ´nski

ⁱ

, U. Kötz

^j

, N. Kovalchuk

^m

, H. Kowalski

^j

, B. Krupa

^g

, O. Kuprash

^j,19

, M. Kuze

^z

, B.B. Levchenko

^s

, A. Levy

^y

, S. Limentani

^w

, M. Lisovyi

^j,20

, E. Lobodzinska

^j

, B. Löhr

^j

, E. Lohrmann

^m

, A. Longhin

^v,30

, D. Lontkovskyi

^j

, O.Yu. Lukina

^s

, I. Makarenko

^j

, J. Malka

^j

, A. Mastroberardino

^e

, F. Mohamad Idris

^f,14

,

N. Mohammad Nasir

^f

, V. Myronenko

^j,21

, K. Nagano

ⁿ

, T. Nobe

^z

, R.J. Nowak

^ad

,

Yu. Onishchuk

^q

, E. Paul

^c

, W. Perla ´nski

^ad,34

, N.S. Pokrovskiy

^o

, A. Polini

^a

, M. Przybycie ´n

^h

, P. Roloff

^j,22

, M. Ruspa

^ab

, D.H. Saxon

^l

, M. Schioppa

^e

, U. Schneekloth

^j

,

T. Schörner-Sadenius

^j

, L.M. Shcheglova

^s

, R. Shevchenko

^q,27,28

, O. Shkola

^q

, Yu. Shyrma

^p

, I. Singh

^d,13

, I.O. Skillicorn

^l

, W. Słomi ´nski

^i,15

, A. Solano

^aa

, L. Stanco

^v

, N. Stefaniuk

^j

, A. Stern

^y

, P. Stopa

^g

, D. Sukhonos

^q

, J. Sztuk-Dambietz

^m,17

, E. Tassi

^e

, K. Tokushuku

^n,25

, J. Tomaszewska

^ad,35

, T. Tsurugai

^r

, M. Turcato

^m,17

, O. Turkot

^j,21

, T. Tymieniecka

^ae

, A. Verbytskyi

^t

, W.A.T. Wan Abdullah

^f

, K. Wichmann

^j,21

, M. Wing

^ac,∗,32

, S. Yamada

ⁿ

, Y. Yamazaki

^n,26

, N. Zakharchuk

^q,29

, A.F. ˙Zarnecki

^ad

, L. Zawiejski

^g

, O. Zenaiev

^j

, B.O. Zhautykov

^o

, D.S. Zotkin

^s

aINFNBologna,Bologna,Italy¹

bUniversityandINFNBologna,Bologna,Italy¹

cPhysikalischesInstitutderUniversitätBonn,Bonn,Germany² dPanjabUniversity,DepartmentofPhysics,Chandigarh,India eCalabriaUniversity,PhysicsDepartmentandINFN,Cosenza,Italy¹

fNationalCentreforParticlePhysics,UniversitiMalaya,50603KualaLumpur,Malaysia³

gTheHenrykNiewodniczanskiInstituteofNuclearPhysics,PolishAcademyofSciences,Krakow,Poland⁴ hAGH—University ofScienceandTechnology,FacultyofPhysicsandAppliedComputerScience,Krakow,Poland⁴ iDepartmentofPhysics,JagellonianUniversity,Krakow,Poland

jDeutschesElektronen-SynchrotronDESY,Hamburg,Germany kDeutschesElektronen-SynchrotronDESY,Zeuthen,Germany

lSchoolofPhysicsandAstronomy,UniversityofGlasgow,Glasgow,UnitedKingdom⁵ mHamburgUniversity,InstituteofExperimentalPhysics,Hamburg,Germany⁶ nInstituteofParticleandNuclearStudies,KEK,Tsukuba,Japan⁷

oInstituteofPhysicsandTechnologyofMinistryofEducationandScienceofKazakhstan,Almaty,Kazakhstan pInstituteforNuclearResearch,NationalAcademyofSciences,Kyiv,Ukraine

qDepartmentofNuclearPhysics,NationalTarasShevchenkoUniversityofKyiv,Kyiv,Ukraine rMeijiGakuinUniversity,FacultyofGeneralEducation,Yokohama,Japan⁷

sLomonosovMoscowStateUniversity,SkobeltsynInstituteofNuclearPhysics,Moscow,Russia⁸

http://dx.doi.org/10.1016/j.physletb.2016.04.007

0370-2693/©^{2016CERNforthebenefitoftheZEUS}Collaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

tMax-Planck-InstitutfürPhysik,München,Germany

uDepartmentofPhysics,UniversityofOxford,Oxford,UnitedKingdom⁵ vINFNPadova,Padova,Italy¹

wDipartimentodiFisicaeAstronomiadell’UniversitàandINFN,Padova,Italy¹ xPolytechnicUniversity,Tokyo,Japan⁷

yRaymondandBeverlySacklerFacultyofExactSciences,SchoolofPhysics,TelAvivUniversity,TelAviv,Israel⁹ zDepartmentofPhysics,TokyoInstituteofTechnology,Tokyo,Japan⁷

aaUniversitàdiTorinoandINFN,Torino,Italy¹

abUniversitàdelPiemonteOrientale,Novara,andINFN,Torino,Italy¹

acPhysicsandAstronomyDepartment,UniversityCollegeLondon,London,UnitedKingdom⁵ adFacultyofPhysics,UniversityofWarsaw,Warsaw,Poland

aeNationalCentreforNuclearResearch,Warsaw,Poland

afDepartmentofParticlePhysicsandAstrophysics,WeizmannInstitute,Rehovot,Israel agDepartmentofPhysics,YorkUniversity,Ontario,M3J1P3,Canada¹⁰

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received23February2016

Receivedinrevisedform31March2016 Accepted2April2016

Availableonline12April2016 Editor:L.Rolandi

The high-precision HERA data allows searches up to TeV scales for beyond the Standard Model contributionstoelectron–quarkscattering.Combinedmeasurementsoftheinclusivedeepinelasticcross sectionsinneutralandchargedcurrentep scatteringcorrespondingtoaluminosityofaround1 fb⁻¹have beenusedinthisanalysis.AnewapproachtothebeyondtheStandardModelanalysisoftheinclusive ep data ispresented;simultaneousfits ofpartondistributionfunctions togetherwithcontributionsof

“new physics” processeswere performed. Results are presented considering afinite radius ofquarks withinthequarkform-factormodel.Theresulting95% C.L.upper limitontheeffectivequarkradiusis 0.43·^10−16cm.

©^{2016CERNforthebenefitoftheZEUS}Collaboration.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

*

Correspondingauthor.

E-mailaddress:m.wing@ucl.ac.uk(M. Wing).

1 Supported bytheItalianNationalInstituteforNuclearPhysics(INFN).

2 Supported bytheGermanFederalMinistryofEducationandResearch (BMBF), undercontractNo.05H09PDF.

3 Supported byHIR grantUM.C/625/1/HIR/149and UMRGgrants RU006-2013, RP012A-13AFRandRP012B-13AFRfromUniversitiMalaya,andERGSgrantER004- 2012AfromtheMinistryofEducation,Malaysia.

4 Supported bythe National ScienceCentre under contract No.DEC-2012/06/

M/ST2/00428.

5 Supported bytheScienceandTechnologyFacilitiesCouncil,UK.

6 Supported bytheFederalMinistry ofEducationand Research (BMBF),under contractNo.05h09GUF,andtheSFB676oftheDeutscheForschungsgemeinschaft (DFG).

7 Supported bytheJapaneseMinistryofEducation,Culture,Sports,Science,and Technology (MEXT)anditsgrantsforScientificResearch.

8 Supported byRFPresidentialgrant N3042.2014.2 for theLeading Scientific Schools.

9 Supported bytheIsraelScienceFoundation.

10 Supported bytheNaturalSciencesandEngineeringResearchCouncilofCanada (NSERC).

11 Now atINFNRoma,Italy.

12 Now atSantLongowalInstituteofEngineeringandTechnology,Longowal,Pun- jab,India.

13 Now atSriGuruGranthSahibWorldUniversity,FatehgarhSahib,India.

14 Also atAgensiNuklearMalaysia,43000Kajang,Bangi,Malaysia.

15 Partially supportedbythe PolishNationalScienceCentreprojectsDEC-2011/

01/B/ST2/03643andDEC-2011/03/B/ST2/00220.

16 Now atRockefellerUniversity,NewYork,NY10065,USA.

17 Now atEuropeanX-rayFree-ElectronLaserfacilityGmbH,Hamburg,Germany.

18 Now atUniversityofLiverpool,UnitedKingdom.

19 Now atTelAvivUniversity,Isreal.

20 Now atPhysikalischesInstitut,UniversitätHeidelberg,Germany.

21 Supported bytheAlexandervonHumboldtFoundation.

22 Now atCERN,Geneva,Switzerland.

23 AlexandervonHumboldtProfessor;alsoatDESYandUniversityofOxford.

24 Also atDESY.

25 Also atUniversityofTokyo,Japan.

26 Now atKobeUniversity,Japan.

27 Member ofNationalTechnicalUniversityofUkraine,KyivPolytechnicInstitute, Kyiv,Ukraine.

28 Now atDESYCMSgroup.

29 Now atDESYATLASgroup.

30 Now atLNF,Frascati,Italy.

1. Introduction

Precision measurements ofdeepinelastic e^±p scattering (DIS) crosssectionsathighvaluesofnegativefour-momentum-transfer squared, Q²,allowsearchesforcontributionsbeyondtheStandard Model (BSM), even far beyond the centre-of-mass energy of the e^±p interactions.Formany“newphysics”scenarios,crosssections canbeaffectedbynewkindsofinteractionsinwhichvirtualBSM particles are exchanged. The cross sections would also be influ- encedwerequarkstohaveafiniteradius.AstheHERAkinematic rangeisassumedtobefarbelowthescaleofthenewphysics,all suchBSMinteractionscanbeapproximatedascontactinteractions (CI).Inallcases,deviationsoftheobservedcrosssectionfromthe Standard Model(SM) predictionare searchedforin ep scattering at thehighest available Q². The predictions are calculated using partondistributionfunction(PDF)parameterisationsoftheproton.

The H1andZEUScollaborations measuredinclusivee^±p scat- teringcrosssectionsatHERAfrom1994to2000(HERAI)andfrom 2002to2007(HERAII),collectingtogetheratotalintegratedlumi- nosityofabout1 fb⁻¹.Allinclusivedatawere recentlycombined [1]tocreateoneconsistentsetofneutralcurrent(NC)andcharged current(CC) cross-section measurements fore^±p scatteringwith unpolarised beams.The inclusivecross sectionswere used asin- put to a QCD analysis within the DGLAPformalism, resulting in a PDFsetdenoted asHERAPDF2.0. Duetothehighprecision and consistencyoftheinputdata,HERAPDF2.0canbeusedtocalculate SM predictionswithsmalluncertainties.Asearch forBSMcontri- butions in the data should take into account thepossibility that the PDF setmay alreadyhave beenbiasedby partially ortotally absorbingpreviouslyunrecognisedBSMcontributions.

31 Also atMaxPlanckInstituteforPhysics,Munich,Germany,ExternalScientific Member.

32 Also supportedbyDESYandtheAlexandervonHumboldtFoundation.

33 Also atŁód ´zUniversity,Poland.

34 Member ofŁód ´zUniversity,Poland.

35 Now atPolishAirForceAcademyinDeblin.

IntheZEUSCIanalysisofHERAIe^±p data[2],theuncertain- tiesonthePDFsusedwereadominantsourceofsystematicerror.

Estimateduncertaintiesofthepartondensitieswereusedtosmear modelpredictionsinthelimit-settingprocedure.Suchanapproach wasvalidastheCTEQ5Dparameterisation [3,4]usedforcalculat- ing modelpredictions included only1994 HERAdata inaddition tomanyother datasets.The limitswere dominatedby statistical uncertainties.FortheCIanalysispresentedhere,inwhichthedata areidenticaltothoseusedfortheHERAPDF2.0 determinationand the statistical uncertainties are no longer dominant, a new pro- cedure to setlimitson the BSMmodelcontributions is required.

InthisanalysisBSMcontributions andthe QCDevolution arefit- tedsimultaneously.Resultsofasearchforafinitequarkradiusare presentedwithintheformalismofthequarkform-factormodel[5].

2. QCDanalysis

TheQCD analysispresentedinthispaperwas performedsim- ilarly to that for the HERAPDF2.0determination [1]. It was used to predict cross sections without BSM contributions. The HERA combined data on inclusive e^±p scattering [1]were used as in- putto the perturbative QCD (pQCD) analysis. Onlycross sections withQ²³.5 GeV² wereused.Afittothedata,resultinginaset ofPDFs, was obtainedby solving the DGLAP evolution equations at NLO in the MS scheme. This was done using the programme QCDNUM[6]withintheHERAFitterframework[7].ForthePDFpa- rameterisation,theapproachadoptedintheHERAPDF2.0 study[1]

was followed. The PDFsof theproton were described ata start- ingscaleof1.9 GeV²intermsof14parameters.Theseparameters werefittothedatausinga

χ

²method,takingintoaccountstatis- ticaluncertainties, aswell asuncorrelatedandcorrelatedsystem- aticuncertaintiesontheexperimentaldata.Thecorresponding

χ

²

formulais:

χ

²

(

m

,

s

) = 

i



mⁱ

+ 

j

γ

_jⁱmⁱs_j

− μ

ⁱ₀

^

²



δ

_i²_,stat

+ δ

_i²_,uncor

 ( μ

ⁱ₀

)

²

+ 

j

s²_j

,

(1)

where

μ

ⁱ₀ is themeasuredcross-section valueatthepoint i.The quantities

γ

ⁱ_j,δi,stat andδi,uncor aretherelativecorrelatedsystem- atic,relativestatisticalandrelativeuncorrelatedsystematicuncer- taintiesoftheinputdata,respectively.Thevectorm representsthe setofpQCDcross-sectionpredictionsmⁱ andthecomponentssjof thevector s representthecorrelatedsystematicshiftsofthecross sections (given in units of

γ

_jⁱ). The summations extend over all datapointsi andallcorrelatedsystematicuncertainties j.

The

χ

² formula used in this analysis differs from that of HERAPDF2.0 study[1]inordertofacilitatetheproductionofdata replicaswithin the HERAFitter framework [7], see Section 4.The resultingsetsofPDFs,referred toasZRqPDFinthefollowing,are neverthelessingoodagreementwithHERAPDF2.0.

TheexperimentaluncertaintiesonthepredictionsfromZRqPDF were determined with the criterion 

χ

²₌1. The uncertainties dueto the choice ofmodel settingsand theform ofthe param- eterisationwereevaluatedasforHERAPDF2.0.

3. Quarkformfactor

One of the possible parameterisations of deviations from SM predictions in ep scatteringis achieved by assigning an effective finite radius to electrons and/or quarks while assuming the SM gauge bosons remain point-like and their couplings unchanged.

The expected modification of the SM cross section can be de- scribedusinga semi-classical form-factorapproach [5]. Iftheex-

pecteddeviations aresmall, theSMpredictions forthe crosssec- tionsaremodified,approximately,to:

d

σ

d Q²

=

^d

σ

^SM

d Q²



1

−

^R2e

6 Q²

2

1

−

^R

2q

6 Q²



2

,

(2)

where R²_e and R²_q are the mean-square radii of theelectron and the quark, respectively, relatedto newBSMenergyscales. In the presentanalysis,onlythepossiblefinitespatial distributionofthe quark wasconsidered andthe electronwasassumedtobe point- like(R²_e≡^{0).BothpositiveandnegativevaluesofR2}q wereconsid- ered.NegativevaluesofR²_qcanbeobtainedifachargedistribution is assumed which changes sign asa function of the radius. The term“quarkradius”isonlyonepossibleinterpretationofBSMef- fectsparameterisedasformfactors.

The QCD analysis described in the previous section was ex- tended by introducing R_q² as an additional model parameter and modifying all e^±p DIS cross-section predictionsaccording to Eq.(2).ValuesforR²_qwereextractedusinga

χ

²-minimisationpro- cedure,whereallPDFparameterswerealsosimultaneouslyfit;R²_q wastreatedasateststatistictobeusedforlimitsetting.Thevalue ofthisteststatisticforthedataisR^{2 Data}_q = −⁰.2·^{10−33cm2.The} probability distributions for R_q² were determined as described in thenextsection.

4. Limit-settingprocedure

The limit ontheeffective quark-radiussquared, R_q²,isderived inafrequentistapproach[8]usingthetechniqueofreplicas.Repli- cas are setsofcross-section valuesthat aregenerated byvarying all cross sections randomly according to their known uncertain- ties. For the analysis presented here, multiple replica sets were used,eachcoveringcross-sectionvaluesonallpointsofthex, Q² gridusedintheQCDfit.Foran assumedtruevalue ofthequark- radiussquared, R^{2 True}_q ,replicadatasetswerecreatedbytakingthe reduced cross sections calculated from the ZRqPDF fit and scal- ing them with the quark form factor, Eq. (2), with R²_q=^{R2 True}q . This results in a set ofcross-section valuesmⁱ₀ for the assumed truequark-radiussquared, R^{2 True}_q .Thevaluesofmⁱ₀ werethenvar- iedrandomly withinstatisticalandsystematicuncertaintiestaken from the data, taking correlations into account. All uncertainties wereassumedtofollowaGaussiandistribution.¹ Foreachreplica, the generated value of the cross section at the point i,

μ

ⁱ, was calculatedas:

μ

ⁱ

₌ 

mⁱ₀

+

δ

²_i,stat

+ δ

_i²_,uncor

· μ

ⁱ₀

_·

r_i



·

⎛

⎝

1

+ 

j

γ

ⁱ_j

_·

r_j

⎞

⎠ ,

(3)

wherevariables ri andrj representrandomnumbers froma nor- maldistribution foreach datapoint i andforeachsourceofcor- relatedsystematicuncertainty j,respectively.

Theapproachadoptedwastogeneratesetsofreplicasthatwere used totestthehypothesis thatthe crosssectionsweremodified by a fixed R²_q valueaccordingto Eq.(2).Thevalue of R^{2 Data}_q de- termined by the fit to the data themselves was taken as a test statistic,towhichvaluesfromfitstoreplicas,R^{2 Fit}_q ,couldbecom- pared. Positive(negative) R^{2 True}_q valuesthat, inmorethan95%of

1 ItwasverifiedthatusingaPoissonprobabilitydistributionforproducingrepli- casathighQ²,wheretheeventsamplesaresmall,andusingtheχ²minimisation forthesedatadidnotsignificantlychangetheprobabilitydistributionsforthefitted parametervalues.

Fig. 1. TheprobabilityofobtainingR^{2 F it}q valuessmallerthanthatobtainedforthe actualdata, R^{2 Data}_q ,calculatedfromMonteCarloreplicas,asafunctionoftheas- sumedvalueforthequark-radiussquared,R^{2 T rue}_q .Pointswithstatisticalerrorbars representMonteCarloreplicasetsgeneratedfor differentvaluesof R^{2 T rue}_q .The solidcirclescorrespondtotheresultsobtainedfromthesimultaneousfitofR²_qand PDFparameters(PDF+^Rq).Forcomparison,theopencirclesrepresentthedepen- denceobtainedwhenfixingthePDFparameterstotheZRqPDFvalues(Rq-only).

Thedashedlineandthedashed-dottedlinerepresentthecumulativeGaussiandis- tributionsfittedtothePDF+RqandRq-onlyreplicapoints,respectively.Thevertical linerepresentsthe95% C.L.upperlimitonR²q.

thereplicas,resultinthefittedradiussquaredvalue,R^{2 Fit}_q ,greater than(lessthan)thatobtainedforthedata, R^{2 Data}_q ,were excluded atthe 95% C.L..The detailsoftheseprocedures aredescribed be- low.

Toset thelimit,a numberofMCreplica cross-sectionsets for eachvalueofR^{2 True}_q wasusedforaQCDfitwiththePDFparame- tersandthequarkradiusasfreeparameters,yieldingadistribution ofthefittedvaluesofthequark radius, R^{2 Fit}_q .The

χ

² formulaof Eq. (1), with the measured cross-section values,

μ

ⁱ₀, in the nu- meratorofthefirst termreplacedby thegeneratedvaluesofthe replica,

μ

ⁱ,wasusedforfittingR²_q andthePDFparameters.

Inalaststep,theprobabilityofobtaininga R^{2 Fit}_q valuesmaller thanthat obtained fortheactual data, Prob(R^{2 Fit}_q <R^{2 Data}_q ), was plottedasafunctionofR_q^{2 True},forpositiveR^{2 True}_q values,asshown inFig. 1.Theprobabilitydistributionwasinterpolatedtocalculate theR²_qvaluecorrespondingtothe95% C.L.upperlimit.About5000 MonteCarloreplicasweregenerated foreachvalue of R^{2 True}_q re- sultinginarelativestatisticaluncertaintyoftheextractedlimitof about0.3%. The corresponding plot fornegative R_q^{2 True} values is showninFig. 2.

As a cross check, the limits on R²_q were also estimated from the simultaneous PDF and R²_q fit to the data by looking at the variationofthe

χ

² valueminimised withrespectto thePDF pa- rameters when changing the R²_q value. Both limits are in good agreement with the results based on the Monte Carlo replicas.

Thelimit-settingprocedurewas alsorepeatedfordifferentmodel and parameter settings, considered as systematic checks in the HERAPDF2.0 analysis[1].The resultingvariations ofthelimitson R²_q arenegligible.

Fig. 2. TheprobabilityofobtainingR^{2 F it}q valueslargerthanthatobtainedforthe actualdata,R_q^{2 Data},calculatedfromMonteCarloreplicas,asafunctionoftheas- sumedvalueforthequark-radiussquared,R^{2 T rue}_q .OtherdetailsasforFig. 1.

5. Results

Theresultsofthelimit-settingprocedureusingthesimultane- ous fit to PDF parameters and R²_q,based on sets ofMonte Carlo replicas testingthe possible cross-section modifications dueto a quark formfactor,yieldthe95% C.L. limitsontheeffectivequark radiusof

−(

⁰

.

47

·

^10−16cm

)

²

<

R²_q

< (

0

.

43

·

^10−16cm

)

²

.

Taking into account the possible influence of quark radii on the PDF parameters is necessary as demonstrated in Figs. 1 and 2, because the limitsthat wouldbe obtained for fixed PDF param- eters aretoo strongby about10%.The limitsareconsistent with the estimated experimental sensitivity, calculated as the median of the limit distribution for the SM replicas, corresponding to a quarkradiusof0.45·^{10−16cm (forbothpositiveandnegative R2}q).

Cross-sectiondeviationsgivenbyEq.(2),correspondingtothepre- sented 95% C.L. exclusion limits, are compared to the combined HERAhigh- Q² NCandCCDISdatainFigs. 3 and4,respectively.

The 95% C.L. upperlimit forthe quark radius presented here is almost a factor of two better than the previous ZEUS limit of 0.85·^{10−16cm, based on the HERA I data [2]. The present re-} sultimproves the limit set in ep scattering by the H1collabora- tion [9] (R_q<0.65·^{10−16 cm) and is similar to the limit pre-} sented by the L3 collaboration (Rq<0.42·^{10−16 cm), based on} quark-pair production atLEP2 [10]. It is important to remember thatthepossibleBSMphysicsparameterisedbytheRq atLEPand HERA canbe very different, sothat the LEP andHERAlimitsare largelycomplementary.Thelimitonnegative R²_q valuespresented hereisanimprovementcomparedtothe publishedZEUS limitof R²_q > −(¹.06·^10−16cm)².

6. Conclusions

The HERA combined measurement of inclusivedeep inelastic crosssections inneutralandchargedcurrent e^±p scattering was

Fig. 3. CombinedHERA(a)e⁺p and(b)e⁻p NCDISdatacomparedtothe95% C.L.

exclusionlimitsontheeffectivemean-squareradiusofquarks.Alsoshownarethe expectationscalculatedusingtheZRqPDFpartondistributions.Thebandsrepresent thetotaluncertaintyonthe predictions.The insetsshow thecomparisoninthe Q²<10⁴GeV²regionwithalinearordinatescale.

usedtosetlimitsonpossibledeviationsfromtheStandardModel due to a finite radius of the quarks. The limit-setting procedure wasbasedonasimultaneousfitofPDF parametersandthequark radius.Theresulting95% C.L.limitsforthequarkradiusare

−(

0

.

47

·

10⁻¹⁶cm

)

²

<

R²_q

< (

0

.

43

·

10⁻¹⁶cm

)

²

.

ThisresultiscompetitivewithadeterminationfromLEP2andsub- stantiallyimprovespreviousHERAlimits.

Acknowledgements

We appreciate the contributions to the construction, mainte- nance and operation of the ZEUS detector of many people who

Fig. 4. CombinedHERA(a)e⁺p and(b)e⁻p CCDISdatacomparedtothe95% C.L.

exclusionlimitsontheeffectivemean-squareradiusofquarks.Otherdetailsasfor Fig. 3.

are notlistedasauthors.TheHERA machinegroupandtheDESY computing staff are especially acknowledged fortheir success in providingexcellent operationofthecolliderandthedata-analysis environment.WethanktheDESYdirectoratefortheirstrongsup- portandencouragement.

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