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,cdxedxpdzFa/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