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

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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

a_INFN_Bologna,_Bologna,_Italy1

b_University_and_INFN_Bologna,_Bologna,_Italy1

c_{Physikalisches}_Institut_der_Universität_Bonn,_Bonn,_Germany2

d_Panjab_University,_Department_of_Physics,_Chandigarh,_India e_Calabria_University,_Physics_Department_and_INFN,_Cosenza,_Italy1

f_National_Centre_for_Particle_Physics,_Universiti_Malaya,₅₀₆₀₃_Kuala_Lumpur,_Malaysia3

g_The_Henryk_{Niewodniczanski}_Institute_of_Nuclear_Physics,_Polish_Academy_of_Sciences,_Krakow,_Poland4

h_{AGH—University of}_Science_and_Technology,_Faculty_of_Physics_and_Applied_Computer_Science,_Krakow,_Poland4

i_Department_of_Physics,_Jagellonian_University,_Krakow,_Poland j_Deutsches_{Elektronen-Synchrotron}_DESY,_Hamburg,_Germany k_Deutsches_{Elektronen-Synchrotron}_DESY,_Zeuthen,_Germany

l_School_of_Physics_and_Astronomy,_University_of_Glasgow,_Glasgow,_United_Kingdom5

m_Hamburg_University,_Institute_of_Experimental_Physics,_Hamburg,_Germany6

n_Institute_of_Particle_and_Nuclear_Studies,_KEK,_Tsukuba,_Japan7

o_Institute_of_Physics_and_Technology_of_Ministry_of_Education_and_Science_of_Kazakhstan,_Almaty,_Kazakhstan p_Institute_for_Nuclear_Research,_National_Academy_of_Sciences,_Kyiv,_Ukraine

q_Department_of_Nuclear_Physics,_National_Taras_Shevchenko_University_of_Kyiv,_Kyiv,_Ukraine r_Meiji_Gakuin_University,_Faculty_of_General_Education,_Yokohama,_Japan7

s_Lomonosov_Moscow_State_University,_Skobeltsyn_Institute_of_Nuclear_Physics,_Moscow,_Russia8

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

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t_{Max-Planck-Institut}_für_Physik,_München,_Germany

u_Department_of_Physics,_University_of_Oxford,_Oxford,_United_Kingdom5

v_INFN_Padova,_Padova,_Italy1

w_Dipartimento_di_Fisica_e_Astronomia_dell’_Università_and_INFN,_Padova,_Italy1

x_Polytechnic_University,_Tokyo,_Japan7

y_Raymond_and_Beverly_Sackler_Faculty_of_Exact_Sciences,_School_of_Physics,_Tel_Aviv_University,_Tel_Aviv,_Israel9

z_Department_of_Physics,_Tokyo_Institute_of_Technology,_Tokyo,_Japan7

aa_Università_di_Torino_and_INFN,_Torino,_Italy1

ab_Università_del_Piemonte_Orientale,_Novara,_and_INFN,_Torino,_Italy1

ac_Physics_and_Astronomy_Department,_University_College_London,_London,_United_Kingdom5

ad_Faculty_of_Physics,_University_of_Warsaw,_Warsaw,_Poland ae_National_Centre_for_Nuclear_Research,_Warsaw,_Poland

af_Department_of_Particle_Physics_and_{Astrophysics,}_Weizmann_Institute,_Rehovot,_Israel ag_Department_of_Physics,_York_University,_Ontario,_M3J_1P3,_Canada10

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

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_·10−16_cm.

*

Correspondingauthor.

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

1 _{Supported by}_the_Italian_National_Institute_for_Nuclear_Physics_(INFN). 2 _{Supported by}_the_German_Federal_Ministry_of_Education_and_{Research (BMBF),}

undercontractNo.05H09PDF.

3 _{Supported by}_HIR _grant_{UM.C/625/1/HIR/149}_and _UMRG_grants _RU006-2013,

RP012A-13AFRandRP012B-13AFRfromUniversitiMalaya,andERGSgrant ER004-2012AfromtheMinistryofEducation,Malaysia.

4 _{Supported by}_the _National _Science_Centre _under _contract _No._DEC-2012/06/

M/ST2/00428.

5 _{Supported by}_the_Science_and_Technology_Facilities_Council,_UK.

6 _{Supported by}_the_Federal_Ministry _of_Education_and _{Research (BMBF),}_under

contractNo.05h09GUF,andtheSFB676oftheDeutscheForschungsgemeinschaft (DFG).

7 _{Supported by}_the_Japanese_Ministry_of_Education,_Culture,_Sports,_Science,_and

Technology (MEXT)anditsgrantsforScientiﬁcResearch.

8 _{Supported by}_RF_Presidential_grant _N_3042.2014.2 _for _the_Leading _Scientiﬁc

Schools.

9 _{Supported by}_the_Israel_Science_Foundation.

10 _{Supported by}_the_Natural_Sciences_and_Engineering_Research_Council_of_Canada

(NSERC).

11 _{Now at}_INFN_Roma,_Italy.

12 _{Now at}_Sant_Longowal_Institute_of_Engineering_and_Technology,_Longowal,

Pun-jab,India.

13 _{Now at}_Sri_Guru_Granth_Sahib_World_University,_Fatehgarh_Sahib,_India. 14 _{Also at}_Agensi_Nuklear_Malaysia,₄₃₀₀₀_Kajang,_Bangi,_Malaysia.

15 _{Partially supported}_by_the _Polish_National_Science_Centre_projects_DEC-2011/

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

16 _{Now at}_Rockefeller_University,_New_York,_NY_10065,_USA.

17 _{Now at}_European_X-ray_{Free-Electron}_Laser_facility_GmbH,_Hamburg,_Germany. 18 _{Now at}_University_of_Liverpool,_United_Kingdom.

19 _{Now at}_Tel_Aviv_University,_Isreal.

20 _{Now at}_{Physikalisches}_Institut,_Universität_Heidelberg,_Germany. 21 _{Supported by}_the_Alexander_von_Humboldt_Foundation. 22 _{Now at}_CERN,_Geneva,_Switzerland.

23 _Alexander_von_Humboldt_Professor;_also_at_DESY_and_University_of_Oxford. 24 _{Also at}_DESY.

25 _{Also at}_University_of_Tokyo,_Japan. 26 _{Now at}_Kobe_University,_Japan.

27 _{Member of}_National_Technical_University_of_Ukraine,_Kyiv_Polytechnic_Institute,

Kyiv,Ukraine.

28 _{Now at}_DESY_CMS_group. 29 _{Now at}_DESY_ATLAS_group. 30 _{Now at}_LNF,_Frascati,_Italy.

1. Introduction

Precision measurements ofdeepinelastic e±p scattering (DIS) crosssectionsathighvaluesofnegativefour-momentum-transfer squared, Q2_,_allow_searches_for_{contributions}_beyond_the_Standard

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),collectingtogetheratotalintegrated lumi-nosityofabout1 fb−1.Allinclusivedatawere recentlycombined

[1]tocreateoneconsistentsetofneutralcurrent(NC)andcharged current(CC) cross-section measurements fore±p scatteringwith unpolarised beams.The inclusivecross sectionswere used as in-put to a QCD analysis within the DGLAPformalism, resulting in a PDFsetdenoted asHERAPDF2.0. Duetothehighprecision and consistencyoftheinputdata,HERAPDF2.0canbeusedtocalculate SM predictionswithsmalluncertainties.Asearch forBSM contri-butions in the data should take into account thepossibility that the PDF setmay alreadyhave beenbiasedby partially ortotally absorbingpreviouslyunrecognisedBSMcontributions.

31 _{Also at}_Max_Planck_Institute_for_Physics,_Munich,_Germany,_External_Scientiﬁc

Member.

32 _{Also supported}_by_DESY_and_the_Alexander_von_Humboldt_Foundation. 33 _{Also at}_{Łód ´z}_University,_Poland.

34 _{Member of}_{Łód ´z}_University,_Poland. 35 _{Now at}_Polish_Air_Force_Academy_in_Deblin.

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IntheZEUSCIanalysisofHERAIe±p data[2],the uncertain-tiesonthePDFsusedwereadominantsourceofsystematicerror. Estimateduncertaintiesofthepartondensitieswereusedtosmear modelpredictionsinthelimit-settingprocedure.Suchanapproach wasvalidastheCTEQ5Dparameterisation [3,4]usedfor calculat-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 are ﬁt-tedsimultaneously.Resultsofasearchforaﬁnitequarkradiusare presentedwithintheformalismofthequarkform-factormodel[5].

2. QCDanalysis

TheQCD analysispresentedinthispaperwas performed sim-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 withQ2

₃

_.

_{5 GeV}2 _were_used._A_ﬁt_to_the_data,_resulting_in_a_set

ofPDFs, was obtainedby solving the DGLAP evolution equations at NLO in the MS scheme. This was done using the programme QCDNUM[6]withintheHERAFitterframework[7].ForthePDF pa-rameterisation,theapproachadoptedintheHERAPDF2.0 study[1]

was followed. The PDFsof theproton were described ata start-ingscaleof1

.

9 GeV2intermsof14parameters.Theseparameters wereﬁttothedatausinga

χ

2_method,_taking_into_account

statis-ticaluncertainties, aswell asuncorrelatedandcorrelated system-aticuncertaintiesontheexperimentaldata.Thecorresponding

χ

2

formulais:

χ

2

(

m

,

s

)

=

i

mi

₊

j

γ

jimisj

−

μ

i0

2

δ

_i2_,_stat

+ δ

_i2_,_uncor

(

μ

i 0

)

2

+

j s2_j

,

(1) where

μ

i

0 is themeasuredcross-section valueatthepoint i.The

quantities

γ

i

j,

δi

,stat and

δi

,uncor aretherelativecorrelated

system-atic,relativestatisticalandrelativeuncorrelatedsystematic uncer-taintiesoftheinputdata,respectively.Thevector

m represents

the setofpQCDcross-sectionpredictionsmi andthecomponentssjof thevector

s represent

thecorrelatedsystematicshiftsofthecross sections (given in units of

γ

i

j). 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]. Ifthe

ex-pecteddeviations aresmall, theSMpredictions forthe cross sec-tionsaremodiﬁed,approximately,to:

d

σ

d Q2

=

d

σ

SM d Q2

1

−

R 2 e 6 Q 2

2

1

−

R 2 q 6 Q 2

2

,

(2)

where R2e and R2q are the mean-square radii of theelectron and the quark, respectively, relatedto newBSMenergyscales. In the presentanalysis,onlythepossibleﬁnitespatial distributionofthe quark wasconsidered andthe electronwasassumedtobe point-like(R2e

≡

0).BothpositiveandnegativevaluesofR2q were consid-ered.NegativevaluesofR2

qcanbeobtainedifachargedistribution is assumed which changes sign asa function of the radius. The term“quarkradius”isonlyonepossibleinterpretationofBSM ef-fectsparameterisedasformfactors.

The QCD analysis described in the previous section was ex-tended by introducing R2

q as an additional model parameter and modifying all e±p DIS cross-section predictionsaccording to Eq.(2).ValuesforR2qwereextractedusinga

χ

2-minimisation pro-cedure,whereallPDFparameterswerealsosimultaneouslyﬁt;R2

q wastreatedasateststatistictobeusedforlimitsetting.Thevalue ofthisteststatisticforthedataisR2 Data_q

= −

0

.

2

·

10−33cm2.The probability distributions for R2

q 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 ofthe quark-radiussquared, R2 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, R2 True

q .Thevaluesofmi0 werethen

var-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

i 0

·

ri

· ⎛

⎝

1

+

j

γ

i j

·

rj

⎞

⎠ ,

(3)

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

Theapproachadoptedwastogeneratesetsofreplicasthatwere used totestthehypothesis thatthe crosssectionsweremodified by a fixed R2q valueaccordingto Eq.(2).Thevalue of R2 Dataq de-termined by the fit to the data themselves was taken as a test statistic,towhichvaluesfromfitstoreplicas,R2 Fit

q ,couldbe com-pared. Positive(negative) R2 True_q valuesthat, inmorethan95%of

1 _It_was_veriﬁed_that_using_a_Poisson_probability_distribution_for_producing

repli-casathighQ2_,_where_the_event_samples_are_small,_and_using_the_χ2_minimisation

forthesedatadidnotsigniﬁcantlychangetheprobabilitydistributionsfortheﬁtted parametervalues.

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Fig. 1. TheprobabilityofobtainingR2 F it

q valuessmallerthanthatobtainedforthe

actualdata, R2 Data

q ,calculatedfromMonteCarloreplicas,asafunctionofthe

as-sumedvalueforthequark-radiussquared,R2 T rue

q .Pointswithstatisticalerrorbars

representMonteCarloreplicasetsgeneratedfor differentvaluesof R2 T rue q .The

solidcirclescorrespondtotheresultsobtainedfromthesimultaneousﬁtofR2 qand

PDFparameters(PDF+Rq).Forcomparison,theopencirclesrepresentthe

depen-denceobtainedwhenﬁxingthePDFparameterstotheZRqPDFvalues(Rq-only).

Thedashedlineandthedashed-dottedlinerepresentthecumulativeGaussian dis-tributionsﬁttedtothePDF+RqandRq-onlyreplicapoints,respectively.Thevertical

linerepresentsthe95% C.L.upperlimitonR2 q.

thereplicas,resultintheﬁttedradiussquaredvalue,R2 Fit

q ,greater than(lessthan)thatobtainedforthedata, R2 Data

q ,were excluded atthe 95% C.L..The detailsoftheseprocedures aredescribed be-low.

Toset thelimit,a numberofMCreplica cross-sectionsets for eachvalueofR2 True_q wasusedforaQCDﬁtwiththePDF parame-tersandthequarkradiusasfreeparameters,yieldingadistribution oftheﬁttedvaluesofthequark radius, R2 Fit

q .The

χ

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

μ

i

0, in the

nu-meratoroftheﬁrst termreplacedby thegeneratedvaluesofthe replica,

μ

i_,_was_used_for_ﬁtting_R2

q andthePDFparameters. Inalaststep,theprobabilityofobtaininga R2 Fitq valuesmaller thanthat obtained fortheactual data, Prob

(

R2 Fitq

<

R2 Dataq

)

, was plottedasafunctionofR2 True

q ,forpositiveR2 Trueq values,asshown inFig. 1.Theprobabilitydistributionwasinterpolatedtocalculate theR2qvaluecorrespondingtothe95% C.L.upperlimit.About5000 MonteCarloreplicasweregenerated foreachvalue of R2 True

q re-sultinginarelativestatisticaluncertaintyoftheextractedlimitof about0.3%. The corresponding plot fornegative Rq2 True values is showninFig. 2.

As a cross check, the limits on R2_q were also estimated from the simultaneous PDF and R2q ﬁt to the data by looking at the variationofthe

χ

2 _value_minimised _with_respect_to _the_PDF

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. TheprobabilityofobtainingR2 F it

q valueslargerthanthatobtainedforthe

actualdata,R2 Data

q ,calculatedfromMonteCarloreplicas,asafunctionofthe

as-sumedvalueforthequark-radiussquared,R2 T rue

q .OtherdetailsasforFig. 1.

5. Results

Theresultsofthelimit-settingprocedureusingthe simultane-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),correspondingtothe pre-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

·

10−16_cm, _based _on _the _{HERA I} _data _[2]_. _The _present

re-sultimproves the limit set in ep scattering by the H1 collabora-tion [9] (Rq

<

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

(5)

Fig. 3. CombinedHERA(a)e+p and(b)e−p NCDISdatacomparedtothe95% C.L. exclusionlimitsontheeffectivemean-squareradiusofquarks.Alsoshownarethe expectationscalculatedusingtheZRqPDFpartondistributions.Thebandsrepresent thetotaluncertaintyonthe predictions.The insetsshow thecomparisoninthe

Q2_<₁₀4_GeV2

regionwithalinearordinatescale.

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

.

ThisresultiscompetitivewithadeterminationfromLEP2and sub-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.WethanktheDESYdirectoratefortheirstrong sup-portandencouragement.

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