Photoproduction of prompt photons at NLO

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arXiv:hep-ph/0105135v1 15 May 2001LPT–Orsay01–46

PHOTOPRODUCTIONOFPROMPTPHOTONSATNLOa

G.HEINRICHLaboratoiredePhysiqueTh´eoriqueLPT,Universit´edeParisXI,Bˆatiment210,F-91405Orsay,France

Anumericalprogramtocalculatethephotoproductionofpromptphotonsispresented.Thecodeincludesfullnext-to-leadingordercorrectionstoallsubprocesses.Theresultsarecom-paredtorecentZEUSdata.

1Introduction

Highenergyelectron–protonscatteringisdominatedbyphotoproductionprocesses,wherethe

electronactsasasourceofquasi-realphotonswhichinteractwiththepartonsintheproton.

Theseprocessesareofspecialinterestsincetheyaresensitivetoboththepartonicstructureof

theprotonaswellasofthephoton.Inparticular,theyofferthepossibilitytoconstrainthe

gluondistributioninthephoton,sincethesubprocessqg→γq,wherethegluonisstemming

fromaresolvedphoton,iscontributingalreadyatleadingorder.

Thefirstcalculations2−4ofhigherordercorrectionstotheComptonprocessγq→γqcon-

sideronlythefullyinclusivecrosssectionwithoutthepossibilitytodealwithisolatedphotons.

MorerecentcalculationsdonebyGordon/Vogelsang5andKrawczyk/Zembrzuski6takeisolation

intoaccount,butonlybyaddingasubtractiontermevaluatedinthecollinearapproximation

tothefullyinclusivecrosssection.Moreover,thecodeof6doesdonotcontainthefullsetof

NLOcorrections.

ThecalculationpresentedheretakesintoaccountthefullNLOcorrectionstodirectaswell

asresolvedandfragmentationparts.Inaddition,itincludestheboxcontributiongγ→gγ

whichisformallyanO(α2s)correction,butknowntobeimportant3.Amajoradvantageofthepresentcodeisalsogivenbythefactthatitisconstructedasa”partoniceventgenerator”and

assuchisveryflexible.ItproducesN-tuplesofpartonicfinalstateconfigurationswhichcanbe

generatedonceandforall.BasedontheseN-tuples,suitableobservablesmatchingaparticular

experimentcanbedefinedandhistogrammed.

2Theoreticalformalism

Theinclusivecrosssectionforep→γXcansymbolicallybewrittenasaconvolutionofthe

partondensitiesoftheincidentparticles(resp.fragmentationfunctionforanoutgoingparton

fragmentingintoaphoton)withthepartoniccrosssectionˆσ

dσep→γX(Pp,Pe,Pγ)=󰀁

a,b,c󰀂dxe󰀂dxp󰀂dzFa/e(xe,M)Fb/p(xp,Mp)

dˆσab→cX(xpPp,xePe,Pγ/z,µ,M,Mp,MF)Dγ/c(z,MF)(1)

whereM,Mparetheinitialstatefactorizationscales,MFthefinalstatefactorizationscaleandµ

therenormalizationscale.Thesubprocessescontributingtothepartonicreactionab→cXcan

bedividedintofourcategorieswhichwillbedenotedby1.directdirect2.directfragmentation

3.resolveddirect4.resolvedfragmentation.Thecases1.and3.correspondtoc=γand

Dγ/c(z,MF)=δcγδ(1−z)in(1),thatis,thepromptbphotonisproduceddirectlyinthehard

subprocess.Thecases1.and2.correspondtoa=γ,withFγ/eapproximatedbytheWeizs¨acker-

Williamsformulaforthespectrumofthequasi-realphotons

feγ(y)=αemylnQ2max(1−y)

y󰀄

.(2)

Fortheresolvedcontributions(3.and4.)apartonstemmingfromthephotoninsteadofthe

photonitselfparticipatesinthehardsubprocess,suchthatFa/e(xe,M)isgivenbyaconvolution

oftheWeizs¨acker-Williamsspectrumwiththepartondistributionsinthephoton:

Fa/e(xe,M)=󰀂1

0dydxγfeγ(y)Fa/γ(xγ,M)δ(xγy−xe).(3)

Atnext-to-leadingorder,theO(αs)correctionstothecorrespondingsubprocessesaretaken

intoaccount.TheinitialstatecollinearsingularitiesareabsorbedintothefunctionsFa/γ(xγ,M)

resp.Fb/p(xp,Mp)atthefactorizationscalesM,Mp,thefinalstatesingularitiesareabsorbed

intothefragmentationfunctionsDγ/c(z,MF)atthefragmentationscaleMF.Asaconsequence,

thefoursubpartsseparatelydependstronglyonM,Mp,MFandonlythesumofallfourparts,

wheretheleadingscaledependencecancels,hasaphysicalmeaning.

Fromatechnicalpointofview,therearebasicallytwomethodstoisolatetheinfrared

singularitiesappearinginthecalculationatNLO:Thephasespaceslicingmethodandthe

subtractionmethod.Themethodusedhereisbasicallyaphasespaceslicingmethod.For

furtherdetailssee12.

Inordertosingleoutthepromptphotoneventsfromthehugebackgroundofsecondary

photonsproducedbythedecaysofπ0,η,ωmesons,isolationcutshavetobeimposedonthe

photonsignalsintheexperiment.Acommonlyusedisolationcriterionisthefollowing:A

photonisisolatedif,insideaconecenteredaroundthephotondirectionintherapidityand

azimuthalangleplane,theamountofdepositedhadronictransverseenergyEhadTissmallerthan

somevalueEmaxTfixedbytheexperiment:

(η−ηγ)2+(φ−φγ)2≤R2exp,EhadT≤EmaxT(4)FollowingtheconventionsoftheZEUScollaboration7,weusedEmaxT=0.1pγTandRexp=

1.Isolationnotonlyreducesthebackgroundfromsecondaryphotons,butalsosubstantially

reducesthefragmentationcomponents.

3NumericalresultsandcomparisontoZEUSdata

Thenumericalresultscanbepresentedonlybrieflyhere,forfurtherdetailsthereaderisreferred

to12.ForthepartondistributionsintheprotontheMRST2parametrization8istaken.The

defaultchoiceforthepartondistributionsinthephotonisAFG9,forcomparisonswealsoused

theGRV10distributionstransformedtothe