Differential Distributions for Heavy Flavour Produ

arXiv:hep-ph/9506226v25Jun1995CERN-TH/95-143GEF-TH-5/1995IFUM506/FThep-ph/yymmxxxDifferentialDistributionsforHeavyFlavourProductionatHERAStefanoFrixione1Dip.diFisica,Universit`adiGenova,Genoa,ItalyPaoloNason2CERNTH-Division,CH-1211Geneva23,SwitzerlandGiovanniRidolfiINFN,SezionediGenova,Genoa,Italy.AbstractWecomputepseudorapidityandtransversemomentumdistributionsforcharmandbottomproductionatHERA.Weexaminetheeffectofnext-to-leadingorderQCDcorrections,theeffectofpossibleintrinsictransversemo-mentaoftheincomingpartons,andoffragmentation.WecompareourresultswiththoseofafullMonteCarlosimulationusingHERWIG.Theimportanceofthehadroniccomponentofthephotonisalsostudied.Weexaminethepossibilityofdistinguishingbetweendifferentparametrizationsofthephotonpartondensitiesusingcharmproductiondata,andthepossibilityofextractinginformationaboutthesmall-xbehaviourofthegluondensityoftheproton.WealsogiveapredictionforthetransversemomentumandpseudorapiditydistributionsforbottomproductionatHERA.CERN-TH/95-143/95May19951AddressafterJune1:ETH,Zurich,Switzerland2OnleaveofabsencefromINFN,SezionediMilano,Milan,Italy.–1–1.IntroductionExperimentalresultsoncharmphotoproductionatHERAhaverecentlybecomeavailable[1].Itislikelythatmoredetailedresultsonthedifferentialdistributionswillappearinthenearfuture.Withrespecttopreviousphotoproductionexperiments(ref.[2])HERAoffersthenewopportunityofahigherenergyregime.Atheoreticalstudyofthetotalphotoproductioncrosssectionhasalreadybeengiveninref.[3].Inthepresentworkweextendtheanalysisofref.[3](towhichwereferthereaderforageneralintroductionandfornotation)byconsideringsingleinclusivedistributionsforheavyflavourproductionatHERA.Ouranalysisisbasedonthenext-to-leadingordercalculationofheavy-quarkphotoproductionandhadroproductioncrosssectionsper-formedinrefs.[4,5],asimplementedinacomputerprogramdevelopedinrefs.[6,7].Wewillconsidercrosssectionsatfixedphotonenergies.Whennecessary,adiscus-sionoftheenergydependenceofthedistributionswillbegiven.Wewillalsoconsiderelectroproductionforsmallphotonvirtuality,intheWeizs¨acker-Williamsapproxima-tion,whichisappropriateforthebulkofthephotoproductioncrosssection.Wewillnotconsidertheproductionofheavyflavoursindeeplyinelasticevents,i.e.eventsinwhichhighphotonvirtualityisrequired(seerefs.[8]).Thepaperisorganizedasfollows.Insection2westudythepoint-likecontributionofthetransversemo-mentumandpseudorapiditydistributionsinphotoproduction.Section3isdevotedtothestudyofthehadroniccomponent,consideringthepossibilityofseparatingitfromthepoint-likecomponentwithappropriatecuts.Insections4and5weconsiderelectroproductionofcharmandbottom,intheWeizs¨acker-Williamsapproximation.Insection6wecompareourfixed-orderresultswiththoseoftheMonteCarloHER-WIG[9],andinsection7wegiveourconclusions.Sometechnicaldetailsonthefactorizationschemes,thescaledependence,andthemodifiedWeizs¨acker-WilliamsapproximationusedherearegivenintheAppendix.2.point-likecomponentUnlessspecificallystated,wewilluseinthefollowingthesetofpartondensitiesMRSA,ref.[10],withΛ5=151MeV.Thissetofdistributionfunctionshasbeenrecentlyupdated(MRSG,ref.[11]),toincludenewHERAdeepinelasticscatteringdata,allowingadifferentsmall-xbehaviourofthegluonandseaquarkdensities.Wehavecheckedthattheshapesofthesingle-inclusivedistributionsweareconsidering–2–arenotsignificantlydifferentwhenthenewparametrizationisused.Thedefaultvalueofthecharmquarkmasswillbemc=1.5GeV.TherenormalizationscalewillbetakenasμR=μ0,andthefactorizationscalefortheprotonandforthephotonwillbetakenasμF=μγ=2μ0,whereμ0=qp2T+m2c.Webeginbyshowingthetransversemomentumdistributionforthecharmquarkinfig.1,forEγ=25GeV(theprotonenergyEpwillbefixedinthefollowingtobe820GeV).WealsoshowFigure1:Charmtransversemomentumdistributioninphoton-protoncolli-sions,withandwithoutapseudorapiditycut.TheeffectofapplyingaPetersonfragmentationfunctiontothefinal-statequarkisalsoshown.theeffectofapplyingthePetersonfragmentationfunction[12]D(x)=1x(1−1/x−ǫ/(1−x))2(2.1)tothefinalstatequark.Weusethevalueǫ=0.06,whichisthecentralvaluequotedinref.[13]forcharmquarks.AscanbeexpectedthissoftensconsiderablythepTspectrum.Asdiscussedinref.[14],inthecaseoffixedtargetphotoproductionexperiments,theinclusionofPetersonfragmentationcorrectlyreproducestheshapeofthemeasuredpTdistribution.TheeffectofapseudorapiditycutsimilartotheoneappliedbytheZEUScollaboration[1]isalsoshown.AtlowtomoderatepTthiscutconsiderablylowersthecrosssection,whileathigherpTithasanegligibleeffect.Infig.2wecomparethepTdistributionsatdifferentphotonenergies.Wealsoillustrate–3–theeffectofapplyinganintrinsictransversemomentumkTtotheincomingparton(seeref.[14]).Wefindthatevenwiththeverylargevalueofhk2Ti=2GeV2theeffectissmall.Therefore,inthefollowing,wewillneglecttheeffectofanintrinsictransversemomentumoftheincomingpartons.Figure2:Charmtransversemomentumdistributioninphoton-protoncolli-sions,fortwovaluesofthephotonenergy.Theeffectofapplyinganintrinsictransversemomentumtotheincomingpartonisalsoshown.Pseudorapiditydistributionsforcharmareshowninfig.3forEγ=25GeV.Weobservethatthepoint-likecontributiontothecrosssecti