, J.C.,

ISSN0418-9833

MeasurementofDeeplyVirtualComptonScattering

atHERA

H1Collaboration

Abstract

AmeasurementispresentedofelasticDeeplyVirtualComptonScattering

atHERAusingdatatakenwiththeH1detector.Thecrosssectionismeasured

system,inasafunctionofthephotonvirtuality,,andtheinvariantmass,,ofthe

thekinematicrange,and,whereisthesquaredmomentumtransfertotheproton.ThemeasurementiscomparedtoQCDbasedcalculations.

TobesubmittedtoPhysicsLettersB

C.Adloff,V.Andreev,B.Andrieu,T.Anthonis,V.Arkadov,A.Astvatsatourov,A.Babaev,J.B¨ahr,P.Baranov,E.Barrelet,W.Bartel,P.Bate,A.Beglarian,O.Behnke,C.Beier,A.Belousov,T.Benisch,Ch.Berger,T.Berndt,J.C.Bizot,V.Boudry,W.Braunschweig,V.Brisson,H.-B.Br¨oker,D.P.Brown,W.Br¨uckner,D.Bruncko,J.B¨urger,F.W.B¨usser,A.Bunyatyan,A.Burrage,G.Buschhorn,L.Bystritskaya,A.J.Campbell,J.Cao,S.Caron,D.Clarke,B.Clerbaux,C.Collard,J.G.Contreras,Y.R.Coppens,J.A.Coughlan,M.-C.Cousinou,B.E.Cox,G.Cozzika,J.Cvach,J.B.Dainton,W.D.Dau,K.Daum,M.Davidsson,B.Delcourt,N.Delerue,R.Demirchyan,A.DeRoeck,E.A.DeWolf,

C.Diaconu,J.Dingfelder,P.Dixon,V.Dodonov,J.D.Dowell,A.Droutskoi,

A.Dubak,C.Duprel,G.Eckerlin,D.Eckstein,V.Efremenko,S.Egli,R.Eichler,F.Eisele,E.Eisenhandler,M.Ellerbrock,E.Elsen,M.Erdmann,W.Erdmann,P.J.W.Faulkner,L.Favart,A.Fedotov,R.Felst,J.Ferencei,S.Ferron,M.Fleischer,Y.H.Fleming,G.Fl¨ugge,A.Fomenko,I.Foresti,J.Form´anek,J.M.Foster,G.Franke,E.Gabathuler,K.Gabathuler,J.Garvey,J.Gassner,J.Gayler,R.Gerhards,C.Gerlich,S.Ghazaryan,L.Goerlich,N.Gogitidze,M.Goldberg,C.Goodwin,C.Grab,H.Gr¨assler,T.Greenshaw,G.Grindhammer,T.Hadig,D.Haidt,L.Hajduk,W.J.Haynes,B.Heinemann,G.Heinzelmann,R.C.W.Henderson,S.Hengstmann,H.Henschel,R.Heremans,G.Herrera,I.Herynek,M.Hildebrandt,M.Hilgers,K.H.Hiller,J.Hladk´y,P.H¨oting,D.Hoffmann,R.Horisberger,S.Hurling,M.Ibbotson,C¸.˙Is¸sever,M.Jacquet,M.Jaffre,L.Janauschek,X.Janssen,V.Jemanov,L.J¨onsson,D.P.Johnson,M.A.S.Jones,H.Jung,H.K.K¨astli,D.Kant,M.Kapichine,M.Karlsson,O.Karschnick,F.Keil,N.Keller,J.Kennedy,I.R.Kenyon,S.Kermiche,

C.Kiesling,P.Kjellberg,M.Klein,C.Kleinwort,T.Kluge,G.Knies,B.Koblitz,S.D.Kolya,V.Korbel,P.Kostka,S.K.Kotelnikov,R.Koutouev,A.Koutov,H.Krehbiel,J.Kroseberg,K.Kr¨uger,A.K¨upper,T.Kuhr,T.Kurˇca,R.Lahmann,D.Lamb,M.P.J.Landon,W.Lange,T.Laˇstoviˇcka,P.Laycock,E.Lebailly,A.Lebedev,B.Leißner,R.Lemrani,V.Lendermann,S.Levonian,M.Lindstroem,B.List,E.Lobodzinska,B.Lobodzinski,A.Loginov,N.Loktionova,V.Lubimov,S.L¨uders,D.L¨uke,L.Lytkin,H.Mahlke-Kr¨uger,N.Malden,E.Malinovski,I.Malinovski,R.Maraˇcek,P.Marage,J.Marks,R.Marshall,H.-U.Martyn,J.Martyniak,S.J.Maxfield,D.Meer,A.Mehta,

K.Meier,A.B.Meyer,H.Meyer,J.Meyer,P.-O.Meyer,S.Mikocki,D.Milstead,T.Mkrtchyan,R.Mohr,S.Mohrdieck,M.N.Mondragon,F.Moreau,A.Morozov,J.V.Morris,K.M¨uller,P.Mur´ın,V.Nagovizin,B.Naroska,J.Naumann,

Th.Naumann,G.Nellen,P.R.Newman,T.C.Nicholls,F.Niebergall,C.Niebuhr,O.Nix,G.Nowak,J.E.Olsson,D.Ozerov,V.Panassik,C.Pascaud,G.D.Patel,M.Peez,E.Perez,J.P.Phillips,D.Pitzl,R.P¨oschl,I.Potachnikova,B.Povh,K.Rabbertz,G.R¨adel,J.Rauschenberger,P.Reimer,B.Reisert,D.Reyna,

C.Risler,E.Rizvi,P.Robmann,R.Roosen,A.Rostovtsev,S.Rusakov,K.Rybicki,D.P.C.Sankey,J.Scheins,F.-P.Schilling,P.Schleper,D.Schmidt,D.Schmidt,S.Schmidt,S.Schmitt,M.Schneider,L.Schoeffel,A.Sch¨oning,T.Sch¨orner,V.Schr¨oder,H.-C.Schultz-Coulon,C.Schwanenberger,K.Sedl´ak,F.Sefkow,V.Shekelyan,I.Sheviakov,L.N.Shtarkov,Y.Sirois,T.Sloan,P.Smirnov,Y.Soloviev,D.South,V.Spaskov,A.Specka,H.Spitzer,R.Stamen,B.Stella,

1

J.Stiewe,U.Straumann,M.Swart,M.Taˇsevsk´y,V.Tchernyshov,

S.Tchetchelnitski,G.Thompson,P.D.Thompson,N.Tobien,D.Traynor,P.Tru¨ol,G.Tsipolitis,I.Tsurin,J.Turnau,J.E.Turney,E.Tzamariudaki,S.Udluft,M.Urban,A.Usik,S.Valk´ar,A.Valk´arov´a,C.Vall´ee,P.VanMechelen,

S.Vassiliev,Y.Vazdik,A.Vichnevski,K.Wacker,R.Wallny,B.Waugh,G.Weber,M.Weber,D.Wegener,C.Werner,M.Werner,N.Werner,G.White,S.Wiesand,T.Wilksen,M.Winde,G.-G.Winter,Ch.Wissing,M.Wobisch,E.W¨unsch,

ˇacA.C.Wyatt,J.Z´ˇek,J.Z´aleˇsa´k,Z.Zhang,A.Zhokin,F.Zomer,J.Zsembery,and

M.zurNedden

I.PhysikalischesInstitutderRWTH,Aachen,GermanyIII.PhysikalischesInstitutderRWTH,Aachen,Germany

SchoolofPhysicsandSpaceResearch,UniversityofBirmingham,Birmingham,UKInter-UniversityInstituteforHighEnergiesULB-VUB,Brussels;UniversitaireInstellingAntwerpen,Wilrijk;Belgium

RutherfordAppletonLaboratory,Chilton,Didcot,UKInstituteforNuclearPhysics,Cracow,PolandInstitutf¨urPhysik,Universit¨atDortmund,Dortmund,GermanyJointInstituteforNuclearResearch,Dubna,RussiaCEA,DSM/DAPNIA,CE-Saclay,Gif-sur-Yvette,FranceDESY,Hamburg,GermanyII.Institutf¨urExperimentalphysik,Universit¨atHamburg,Hamburg,GermanyMax-Planck-Institutf¨urKernphysik,Heidelberg,GermanyPhysikalischesInstitut,Universit¨atHeidelberg,Heidelberg,GermanyKirchhoff-Institutf¨urPhysik,Universit¨atHeidelberg,Heidelberg,GermanyInstitutf¨urexperimentelleundAngewandtePhysik,Universit¨atKiel,Kiel,GermanyInstituteofExperimentalPhysics,SlovakAcademyofSciences,Koˇsice,SlovakRepublicSchoolofPhysicsandChemistry,UniversityofLancaster,Lancaster,UKDepartmentofPhysics,UniversityofLiverpool,Liverpool,UKQueenMaryandWestfieldCollege,London,UK

PhysicsDepartment,UniversityofLund,Lund,Sweden

PhysicsDepartment,UniversityofManchester,Manchester,UKCPPM,CNRS/IN2P3-UnivMediterranee,Marseille-France

InstituteforTheoreticalandExperimentalPhysics,Moscow,RussiaLebedevPhysicalInstitute,Moscow,RussiaMax-Planck-Institutf¨urPhysik,M¨unchen,GermanyLAL,Universit´edeParis-Sud,IN2P3-CNRS,Orsay,FranceLPNHE,EcolePolytechnique,IN2P3-CNRS,Palaiseau,FranceLPNHE,Universit´esParisVIandVII,IN2P3-CNRS,Paris,France

InstituteofPhysics,AcademyofSciencesoftheCzechRepublic,Praha,CzechRepublicFacultyofMathematicsandPhysics,CharlesUniversity,Praha,CzechRepublicDipartimentodiFisicaUniversit`adiRomaTreandINFNRoma3,Roma,ItalyPaulScherrerInstitut,Villigen,SwitzerlandFachbereichPhysik,BergischeUniversit¨atGesamthochschuleWuppertal,Wuppertal,Germany

YerevanPhysicsInstitute,Yerevan,Armenia

2

DESY,Zeuthen,GermanyInstitutf¨urTeilchenphysik,ETH,Z¨urich,SwitzerlandPhysik-InstitutderUniversit¨atZ¨urich,Z¨urich,Switzerland

AlsoatPhysicsDepartment,NationalTechnicalUniversity,ZografouCampus,GR-15773Athens,Greece

AlsoatRechenzentrum,BergischeUniversit¨atGesamthochschuleWuppertal,GermanyAlsoatInstitutf¨urExperimentelleKernphysik,Universit¨atKarlsruhe,Karlsruhe,GermanyAlsoatDept.Fis.Ap.CINVESTAV,M´erida,Yucat´an,M´exico

ˇarik,KoˇAlsoatUniversityofP.J.Saf´sice,SlovakRepublic

AlsoatCERN,Geneva,SwitzerlandAlsoatDept.Fis.CINVESTAV,M´exicoCity,M´exicoSupportedbytheBundesministeriumf¨urBildung,Wissenschaft,ForschungundTechnologie,FRG,undercontractnumbers7AC17P,7AC47P,7DO55P,7HH17I,7HH27P,7HD17P,7HD27P,7KI17I,6MP17Iand7WT87P

SupportedbytheUKParticlePhysicsandAstronomyResearchCouncil,andformerlybytheUKScienceandEngineeringResearchCouncilSupportedbyFNRS-NFWO,IISN-IIKW

PartiallySupportedbythePolishStateCommitteeforScientificResearch,grantno.

2P0310318andSPUB/DESY/P03/DZ-1/99,andbytheGermanFederalMinistryofEducationandScience,ResearchandTechnology(BMBF)

SupportedbytheDeutscheForschungsgemeinschaftSupportedbyVEGASRgrantno.2/5167/98

SupportedbytheSwedishNaturalScienceResearchCouncil

SupportedbyRussianFoundationforBasicResearchgrantno.96-02-00019SupportedbytheMinistryofEducationoftheCzechRepublicundertheprojects

ˇgrantnoB1010005INGO-LA116/2000andLN00A006,andbyGAAVCR

SupportedbytheSwissNationalScienceFoundationSupportedbyCONACyT

PartiallySupportedbyRussianFoundationforBasicResearch,grantno.00-15-96584

3

1Introduction

ThispaperpresentsthefirstmeasurementoftheelasticcrosssectionforDeeplyVirtualComptonScattering(DVCS)(Fig.1a)i.e.thediffractivescatteringofavirtualphotonoffaproton[1–6]bystudyingthereaction:

(1)

Theinterestofthisprocess,becauseofitsapparentsimplicity,residesintheparticularinsightitgivesfortheapplicabilityofperturbativeQuantumChromoDynamics(QCD)inthefieldofdiffractiveinteractions.Thewidekinematicrangeinthephotonvirtuality,,accessibleatHERA,providesapowerfulprobefortheinterplaybetweenperturbativeandnon-perturbativeregimesinQCD.FurthermoretheDVCSprocessgivesaccesstoanewclassofpartondistri-butionfunctions,theskewedpartondistributions(SPD)[7–9]whicharegeneralisationsofthefamiliarpartondistributionsandincludepartonmomentumcorrelations.

ThereactionstudiedreceivescontributionsfromboththeDVCSprocesswhoseoriginliesinthestronginteraction,andthepurelyelectromagneticBethe-Heitler(BH)process(Fig.1bandc)wherethephotonisemittedfromthepositronline.TheBHprocessispreciselyknownasitdependsonlyonQEDcalculationsandprotonelasticformfactors.TheDVCScrosssectionisextractedbysubtractingtheBHcontributionfromthetotalcrosssection,whichispossiblesincetheinterferencecontributionvanisheswhenaveragedoverthefullazimuthalangleofthefinalstateparticles.Arecentmeasurementofthesinglespinasymmetryinalongitudinallypolarisedelectronbeam[10]complementsthismeasurement.

e󰀀e󰀀γ󰀀*󰀀e󰀀γ󰀀

e󰀀*󰀀γ󰀀γ󰀀

e󰀀e󰀀

*󰀀γ󰀀e󰀀γ󰀀

p󰀀a)󰀀p󰀀p󰀀b)󰀀

p󰀀p󰀀c)󰀀

p󰀀

Figure1:TheDVCS(a)andtheBethe-Heitler(bandc)processes.TheQCDinterpretationofDVCSisbasedonthetwodiagramsshowninFig.2.Inthepresenceofahardscale,theDVCSscatteringamplitudefactorises[2,3,9]intoahardscatteringpartcalculableinperturbativeQCDandpartondistributionswhichcontainthenon-perturbativeeffectsduetotheprotonstructure.TheDVCSprocessissimilartodiffractivevectormesonelectro-production,arealphotonreplacingthefinalstatevectormeson.RecentmeasurementsofdiffractivevectormesonproductionatHERA[11–15]indicatethatisrelevantforthehardscaleoftheinteractioninQCDcalculation.Incomparisontovectormesonproduction,DVCSavoidsthetheoreticalcomplicationsanduncertaintiesassociatedwiththeunknownvectorme-sonwavefunction.However,evenatvaluesaboveafewGeV,nonperturbativeeffects

4

e󰀀e󰀀e󰀀e󰀀γ󰀀*󰀀γ󰀀γ󰀀

*󰀀γ󰀀

p󰀀a)󰀀p󰀀p󰀀b)󰀀p󰀀Figure2:ThetwoleadingDVCSdiagramsinaQCDpicture.influencethepredictionsandhavetobemodeled.TheDVCScrosssectionissuppressedrela-tivetothatofvectormesonproductionbytheadditionalelectromagneticcoupling.

CalculationsoftheDVCScrosssectionhavebeenpublishedbyFrankfurt,FreundandStrikman(FFS)[16]andbyDonnachieandDosch(DD)[17].Bothcontain“soft”(non-perturbative)and“hard”contributions.ThesoftpartintheFFSpredictionisbasedonthealignedjetmodel[18],whereasreggeonandsoftpomeronexchangesareconsideredintheDDprediction.ThehardcontributioninFFSiscalculatedinperturbativeQCD.ThehardcontributioninDDisbasedonadipolemodelwhereallparametersaredeterminedfromandcrosssectionmeasurements.Thesepredictionsonlyprovidethescatteringamplitude

,whereisthesquaredmomentumtransfertotheproton,at

theprotonmassandtheinvariantmassofthesystem.Inbothcasesanexponential-dependence,,isassumed.

FortheDVCSprocessaswellasforthevectormesonproduction,thetransitionfromavir-tualphotontoanonshellparticleforcesthefractionalmomentaofthetwopartonsinvolvedtobeunequalandimposesacorrelation.Therefore,thecrosssectioncalculationnecessitatestheuseofskewedpartondistributions[7–9].Thedifferenceinfractionalmomenta,theskewedness,becomesimportantathighvaluesorhighvectormesonmasses.InparticularSPDshavebeenintroducedinordertoreconcileQCDcalculationswiththediffractivephoto-productionmeasurementsatHERA[19,20].ForvectormesonproductionSPDsappearquadraticallyinthecrosssectionexpression.AuniquefeatureofDVCSisthattheyappearlinearlyintheinterferencetermwiththeBethe-Heitlerprocess.ThereforetheDVCSmeasurement,incon-trasttovectormesonproduction,offersaparticularlysuitablechanneltoextractskewedpartondistributions[16,21–23].

Inthispaper,theelasticDVCScrosssectionmeasurementatHERAispresenteddifferen-tiallyinandintherangefromtoGeV,fromtoGeVandbelowGeV.

5

2H1Detector,KinematicsandMonteCarloSimulation

AdetaileddescriptionoftheH1detectorcanbefoundin[24].Hereonlythedetectorcompo-nentsrelevantforthepresentanalysisareshortlydescribed.TheSPACAL[25],alead–scin-tillatingfibrecalorimetercoversthebackward1regionoftheH1detector().Itsenergyresolutionforelectromagneticshowersis

asobtainedfromtestbeammeasurements[26].Themajorcom-ponentsofthecentraltrackingdetectoraretwo2mlongcoaxialcylindricaldriftchambers,theCJC,withwiresparalleltothebeamdirection.Themeasurementofchargedparticletransverse

T,uniformoverthefulltrackervolume.Themomentaisperformedinamagneticfieldof

forwardcomponentsofthedetector,usedheretotaghadronicactivityathighpseudo-rapidity(),aretheforwardmuonspectrometer(FMD)andtheprotonremnanttagger(PRT).TheFMD,designedtoidentifyandmeasurethemomentumofmuonsemittedintheforwarddirection,containssixactivelayers,eachmadeofapairofplanesofdriftcells.Thethreelayersbetweenthemaincalorimeterandthetoroidalmagnetcanbereachedbysecondaryparticlesarisingfromtheinteractionofparticlesscatteredundersmallangleshittingthebeamcollima-torsorthebeampipewalls.SecondaryparticlesorthescatteredprotonatlargecanalsobedetectedbythePRT,locatedatmfromtheinteractionpointandconsistingofdoublelayersofscintillatorsurroundingthebeampipe.ThetriggerusedisbasedonthedetectionofaclusterintheelectromagneticsectionoftheSpaCalcalorimeterwithanenergygreaterthan6GeV.

ThedatawereobtainedwiththeH1detectorinthe1997runningperiodwhentheHERAcolliderwasoperatedwithGeVprotonsandGeVpositrons.Thesamplecorrespondstoanintegratedluminosityof.

Thereconstructionmethodforthekinematicvariablesand-Bjorkenreliesonthepolaranglemeasurementsofthefinalstateelectron,,andphoton,,(doubleanglemethod):

(4)

whereandaretheelectronandtheprotonbeamenergies,respectively.Incaseavertexcannotbereconstructed,thenominalpositionoftheinteractionsistaken.Thevariable,thesquareofthefour-momentumtransfertotheproton,isverywellapproximatedbythenegativesquareofthetransversemomentumoftheoutgoingproton.Thelatteriscomputedasthevectorsumofthetransversemomentaofthefinalstatephotonandofthescatteredpositron:

(5)

MonteCarlosimulationsareusedtoestimatethecorrectionstobeappliedtothedatafortheacceptanceandresolutionsofthedetector.ThegeneratedeventsarepassedthroughadetailedsimulationoftheH1detectorandaresubjecttothesamereconstructionandanalysischainasthedata.TheDVCSprocessissimulated(formoredetailssee[27])accordingtothepredictedcrosssectionofFFS[16],whichincludestheDVCSprocess,theBethe-Heitlerprocessandtheirinterference2.Photonradiationfromtheincomingpositronhasbeenincludedinthesimulationinthecollinearapproximation.TheMonteCarlogeneratorCOMPTON2.0[30]isusedtosimulateBethe-Heitlerevents.Tosimulatethebackgroundsources(seesection3),diffractive,andmesoneventsaregeneratedwiththeDIFFVMMonteCarlo[31],dileptonproductionthroughaphoton-photoninteractionissimulatedusingtheGRAPEprogram[32].

3EventSelection

ThecrosssectionoftheBethe-Heitlerprocess,proceedingviaBremsstrahlungfromthepositronlines,isthelargestwhenthepositronandthephotonarebothproducedinthebackwarddirec-tion.IntheDVCScase,thefinalstatephotondoesnotoriginatefromthepositronandthereforetheratioofDVCSoverBHprocessisexpectedtoincreasewhenthephotonisfoundintheforwarddirection.Theanalysisisthusrestrictedtothecasewherethephotonisdetectedinthecentralorintheforwardpartsofthedetector,i.e.intheLArcalorimeter.Adatasam-ple,dominatedbyBethe-Heitlerevents,isusedasareferencesampletomonitorthedetectorperformanceanditssimulation.Twoeventsamplesareselected.

EnrichedDVCSsample:ThephotoncandidateisdetectedintheLArcalorimeterandthepositroncandidateintheSpaCalcalorimeter.BothDVCSandBethe-Heitlerprocessesareexpectedtocontributetothissamplewithsimilarmagnitudes.

Controlsample:ThephotoncandidateisdetectedintheSpaCalcalorimeterandthepositroncandidateintheLArcalorimeter.ThecontributionofDVCStothissampleisnegligible.

Theeventselectionisbasedonthedetectionofexactlytwoelectromagneticclusters,cor-respondingtothefinalstatephotonandpositron.OneclusterisrequiredtobedetectedintheSpaCalcalorimeterwithenergylargerthanandtheotheroneintheLArcalorimeter()withatransversemomentum.Eventswithmorethanonetrackarerejected.Eventswithonetrackareonlykeptifthetrackisassociatedtooneoftheclusterswhichhenceidentifiesthepositroncandidate.Ifnotrackisreconstructed,theSpaCalclusterisassumedtobethepositron.Inordertorejectinelasticandprotondissociationevents,nofurtherclusterintheLArcalorimeterwithenergyaboveisallowedandtheabsenceofactivityabovethenoiselevelinforwarddetectorsPRTandFMDisrequired.Theinfluenceof

theskewednessofthepartondensitiesdata[29]hasbeenused.

[28]andthesensitivityto

[16].TheprotonstructurefunctionasextractedfromtheH1

7

QEDradiativecorrectionsisreducedbyrequirementsonthelongitudinalmomentumbalance3.ToenhancetheDVCSsignalwithrespecttotheBethe-Heitlercontribution,andtomaintainalargedetectoracceptance,thekinematicdomainisexplicitlyrestrictedto:,

and.IthastobenotedthatfortheBHprocess,theand

variablescannotbeassociatedwiththephotonvirtualityandthecenterofmassenergy,respectively.

3.1Controlsample

Thissampleof338eventsisdominatedbytheBethe-Heitlerprocess.Duetothelargescatter-ingangleofthepositron,theDVCSprocessissuppressedtonegligiblelevels.InordertohaveacontrolofthedetectorresponseinthesameenergyandangularrangesasfortheenrichedDVCSsample,thekinematiccutsinandareappliedtothissample,treatingthephotoncandidateinSpaCalasthescatteredpositronandthepositroncandidateintheLArcalorime-terasthephoton.BackgroundcontributionsfrominelasticBethe-Heitlerevents,diffractivemesonproductionandelectronpairproductionhavetobeconsidered.Thecontributionofin-elasticBethe-Heitlereventsisestimatedtobe.Thediffractiveelectroproductionofmesonsconstitutesabackgroundwhenoneofthedecaypionsismis-identifiedasapositroninthecalorimeterandtheotherpionisundetected,whilethepositronscatteredintotheSpaCalcalorimeteristakentobethephoton.Theelasticproductionofelectronpairsbyphoton-photonprocessescontributestothebackgroundwhenonlytwoofthethreeleptonsaredetected.TheseprocesseshavebeensimulatedusingtheMonteCarloprogramsCOMPTON2.0(bothforelasticandinelasticBH),DIFFVMandGRAPErespectively.IntheleftcolumnofFig.3,eventdistributionsofthecontrolsampleareshown.ThedataarecomparedtothesumoftheabsoluteMCpredictionswhichincludestheBethe-Heitlerprocess,elasticproductionandelasticdileptonproduction,allnormalisedtoluminosity.AgooddescriptionofthedatabythesumofthedifferentMCsamplesisachieved,showingthatthedetectorresponseiswelldescribedbythesimulation.

3.2EnrichedDVCSsample

Thissample(172events)isfoundtobedominatedbytheDVCScontributionalthoughthecontributionoftheBethe-Heitlerprocessisnonnegligible.AnimportantcontaminationtoDVCSelasticcandidatesisduetotheDVCSprocesswithprotondissociation:

(6)

whenthedecayproductsofthebaryonicsystemarenotdetectedintheforwarddetectors.ThesumofnonelasticDVCSandBHcontributionshasbeenestimatedtobeofthefi-nalsample[27],basedonthefractionofeventswithprotondissociationtaggedbytheforwarddetectorsandthedetectionefficiencyoftheforwarddetectorsforprotondissociationeventsusingtheDIFFVMMonteCarlo.Theothersourcesofbackgroundtobeconsideredaredue

ControlsampleEnrichedDVCSsample

# events󰀀# events󰀀150󰀀100󰀀50󰀀0󰀀0󰀀a)H1󰀀BH󰀀dilepton󰀀diff. 󰀀ρ󰀀80󰀀60󰀀40󰀀20󰀀

b)H1󰀀DVCS󰀀BH󰀀diff. 󰀀ω 󰀀󰀀φ󰀀2󰀀4󰀀6󰀀8󰀀10󰀀0󰀀

0󰀀2󰀀4󰀀6󰀀8󰀀10󰀀E󰀀 [ GeV ]󰀀e󰀀

# events󰀀c)100󰀀50󰀀0󰀀

E󰀀 [ GeV ]󰀀γ󰀀

# events󰀀60󰀀40󰀀20󰀀

d)0󰀀50󰀀100󰀀150󰀀o󰀀

0󰀀

0󰀀50󰀀θ󰀀 [ 󰀀 ]󰀀e󰀀

# events󰀀e)200󰀀100󰀀0󰀀

o󰀀

θ󰀀 [ 󰀀 ]󰀀γ󰀀

100󰀀150󰀀# events󰀀60󰀀40󰀀20󰀀

f)170󰀀180󰀀190󰀀0󰀀

o󰀀

170󰀀180󰀀190󰀀Coplanarity [ 󰀀 ]󰀀Coplanarity [ 󰀀 ]󰀀

o󰀀

Figure3:Eventdistributionsofthecontrolsample(left)andoftheenrichedDVCSsample(right).a-b)energyoftheclusterintheLArcalorimeter,c-d)polarangleoftheclusterintheLArcalorimeter,e-f)coplanarity,i.e.differenceoftheazimuthalangleofthepositronandphotoncandidates.Theerrorbarsondatapointsarestatistical.Controlsample:theclusterintheLArcalorimetercorrespondstothepositroncandidate.ThedataarecomparedtothesumofthepredictionsfortheBethe-Heitlerprocess,elasticdileptonproductionanddiffractiveproduction.Allpredictionsarenormalisedtoluminosity.EnrichedDVCSsample:theclusterintheLArcalorimetercorrespondstothephotoncandidate.ThedataarecomparedtothesumofthepredictionsforthereactionaccordingtoFFS,addedtoanddiffractivebackgrounds.ThebackgroundsandtheBHcontribution(shownontopofthebackgrounds)arenormalisedtoluminositywhereastheDVCSpredictionisnormalisedinsuchawaythatthesumofallcontributionsisequaltothetotalnumberofevents.9

todiffractiveandproduction,withdecaymodestofinalstatesincludingphotons(directlyorfromdecay)or.Themaincontributionsoriginatefromandfollowedby.Thebackgroundarisingfromproduction,withthedecayphotonsreconstructedinasinglecluster,inlowmultiplicityDIS,isestimatedfromdata.AccordingtotheMCsimulationthetwodecayphotonsarerecognised,inthisenergyrange,inoftheeventsinseparateclusters.TheselectionhasthusbeenextendedtoeventswithatleasttwoclustersintheLArcalorimeterofenergiesexceeding.Thetwophotoninvariantmassspectrumisinagreementwithexpectationfromdiffractiveandproduction.Backgroundfromproductionisthereforeinferredtobenegligible.Figure3showsdatadistributionsincomparisontothesumofthepredictionsaccordingtotheFFScalculationandthediffractiveandbackgrounds.TheBHcontributionintheFFSpredictionandtheandbackgroundsarenormalisedtoluminosity.TheDVCScontributionintheFFSpredictionisherenormalisedsuchthatthesumofallcontributionsisequaltothetotalnumberofeventsinthedata.ThepureBethe-Heitlercontributionisalsoshown.TheDVCSsignalexhibitsdifferentkinematicdistri-butionsfromtheBethe-Heitlercontributions,inparticularinthepolarangleoftheLArcluster(Fig.3c-d)andincoplanarity(Fig.3e-f),whichisdefinedasthedifferenceoftheazimuthalanglesofthetwoclustersandisrelatedtothe-balanceofthepositron-photonsystem.Thecoplanaritydistributionisfoundtobebroader()forthesumofthecontributionintheenrichedDVCSsamplethanfortheBethe-Heitlerdominatedcontrolsample().ThisisattributedtotheelectromagneticnatureoftheBHprocesswhichimpliesasteeperdistributionthantheDVCSsignal.

4Crosssectionmeasurementandmodelcomparison

Toextractthecrosssection,thedataoftheenrichedDVCSsamplehavebeencorrectedfordetectoreffects,acceptanceandforinitialstateradiationofrealphotonsfromthepositronlineusingtheMonteCarlosimulation.Thebinsizehasbeenchosenaccordingtothestatisticalaccuracyandislargewithrespecttoresolutionsin()and().ThecontaminationofinelasticBHandDVCSeventswithprotondissociation()issubtractedstatistically.Thebackgroundcontributionsfromdiffractiveandproduction,estimatedtobeonaverageandbelowinallbins,havebeensubtractedbinbybin.

ThecrosssectionispresentedinFig.4andinTable1differentiallyinand.ThedataarecomparedtotheestimateofthepureBethe-Heitlercontribution.ThetotalcrosssectionisdominatedbytheDVCSprocessatsmallvaluesandtheBethe-Heitlerprocessatlargevalues.Withthepresentprecision,theslopesofthetwoprocessesappearsimilar.Thelimitedresolutionandstatisticsdonotallowthecrosssectionmeasurementdifferentiallyinandtheextractionoftheslopefromthepresentdata.Themaincontribution,of,tothesystematicerrorarisesfromdetectoreffectsandisduetotheuncertaintyonthemeasurementoftheangleofthescatteredpositron.Otherdetectorrelatederrorsareestimatedtobearoundorbelow.ThesecondlargestsystematicerrorarisesfromtheestimateofthecontaminationofnonelasticBHandDVCS().Thetotalsystematicerrorisfoundtobearound.

Intheleadingtwistapproximationthecontributionoftheinterferencetermtothecross

10

d󰀀σ󰀀/dQ󰀀 [ pb/GeV󰀀 ]󰀀 H1󰀀Bethe-Heitler󰀀a)d󰀀σ󰀀/dW [ pb/GeV ]󰀀2󰀀10󰀀

2󰀀3󰀀

H1󰀀Bethe-Heitler󰀀b)2󰀀10󰀀

30 < W < 120 GeV󰀀2󰀀|󰀀 t 󰀀|󰀀 < 1 GeV󰀀2 < Q󰀀 < 20 GeV󰀀2󰀀

2󰀀2󰀀 󰀀|󰀀 t 󰀀|󰀀 < 1 GeV󰀀2󰀀1󰀀

1󰀀

10󰀀

-1󰀀5󰀀10󰀀Q󰀀 [ GeV󰀀 ]󰀀

2󰀀

15󰀀2󰀀

20󰀀0󰀀

40󰀀60󰀀80󰀀100󰀀120󰀀W [ GeV ]󰀀

Figure4:Differentialcrosssectionmeasurementsforthereactionasafunctionof(a)and(b).Theinnererrorbarsarestatisticalandthefullerrorbarsincludethesystematicerrorsaddedinquadrature.ThehatchedhistogramshowsthecontributionoftheBethe-Heitlerprocesstothereaction,where,however,anddonotcorrespondtothephotonvirtualityandthecenterofmassenergy,respectively.sectionisproportionaltothecosineofthephotonazimuthalangle4.Sincethepresentmeasure-mentisintegratedoverthisangle,theoverallcontributionoftheinterferencetermisnegligible.ThereforetheBethe-HeitlercrosssectioncanbesubtractedfromthetotalcrosssectioninordertoobtaintheDVCScrosssection.TheDVCScrosssectionisthenconvertedtoaDVCScrosssectionusingtheequivalentphotonapproximation(asin[11]).

Table1:Differentialcrosssectionsforthereaction:inthekinematicdomain,errorsarestatistical,thesecondsystematic.,asafunctionofand,and.ThefirstThecrosssectionfortheDVCSprocessisshowninFig.5andgiveninTable2asa

functionofforGeV,andasafunctionofforGeV.Thesystematicerrorsonthecrosssectionareduetothepropagationofthesystematicerrorsonthecrosssectioncombinedwiththebincentercorrectionserror().ThedataarecomparedwiththepredictionsbyFFSandDD.Theshapeofthedataiswelldescribedbybothcalculationsbothinand.Theabsenceofpredictionsforthe-slopeleavesanuncertaintyonthe

σγp→ γp [nb] H1DVCS (FFS)[nb]a)20

H115

2b)10

DVCS (DD)γ∗p→ γp DVCS (FFS)DVCS (DD)σ W = 75 GeV2 | t | < 1 GeV Q = 4.5 GeV2 | t | < 1 GeV2∗10

1

5

-1

10

05102

152

200

255075100125Q [ GeV ]

󰀀

W [ GeV ]

DVCSprocessasafunctionofFigure5:Crosssectionmeasurementsforthe(a)and(b).ThedataarecomparedtothetheoreticalpredictionsofFFS[16]andDD[17].Thebandassociatedtoeachpredictioncorrespondstoavariationoftheassumed-slopefrom(upperbound)to(lowerbound).Theinnererrorbarsarestatisticalandthefullerrorbarsincludethesystematicerrorsaddedinquadrature.normalisationofthetheoreticalmodels.Thebandassociatedtoeachpredictioncorrespondstoavariationofthe-slopeof,coveringthemeasuredrangeforlightvectormesonproduction[11,14].Bothpredictionsareconsistentwiththedatawithinthisuncertainty.ItisnotedthatthesedataprovideconstraintsalsoforrecentNLOcalculations,whichinvokeskewedpartondistributions[33].

Table2:MeasuredcrosssectionfortheelasticDVCSprocessforandasafunctionoffor,bothforerrorsarestatistical,thesecondsystematic.asafunctionof.Thefirst5Conclusion

TheDVCSprocesshasbeenstudiedinthekinematicregionGeV,

GeVandGeVusingadatasampletakenbytheH1detectorandcorrespondingtoanintegratedluminosityof.Thecrosssectionforthereactionhasbeenmeasuredforthefirsttimeandpresenteddifferentiallyinand.TheDVCSprocessis

12

observedtodominateovertheBethe-HeitlerprocessforGeV.TheDVCScrosssectionhasbeenextractedandcomparedtotheQCDbasedpredictions[16,17]whichbothdescribethemeasuredanddistributionswithinerrors.

Acknowledgements

WearegratefultotheHERAmachinegroupwhoseoutstandingeffortshavemadeandcontinuetomakethisexperimentpossible.WethanktheengineersandtechniciansfortheirworkinconstructingandnowmaintainingtheH1detector,ourfundingagenciesforfinancialsupport,theDESYtechnicalstaffforcontinualassistanceandtheDESYdirectorateforthehospitalitywhichtheyextendtothenonDESYmembersofthecollaboration.WearegratefultoM.DiehlandA.Freundforvaluablediscussions.

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