Slow proton production in semi-inclusive deep inelastic scat

The semi-inclusive cross section for producing slow protons in charged current deep inelastic (anti-) neutrino scattering on protons and neutrons is calculated as a function of the Bjorken $x$ and the proton momentum. The standard hadronization models base

Slowprotonproductioninsemi-inclusivedeepinelasticscatteringandthepioncloudinthe

nucleon

AntoniSzczurek

arXiv:nucl-th/9411035v1 30 Nov 1994InstituteofNuclearPhysics,PL-31-342Cracow,PolandGerardD.BosveldandAlexE.L.DieperinkKernfysischVersnellerInstituut,NL-9747AAGroningen,TheNetherlandsAbstractThesemi-inclusivecrosssectionforproducingslowprotonsinchargedcurrentdeepinelastic(anti-)neutrinoscatteringonprotonsandneutronsiscalculatedasafunctionoftheBjorkenxandtheprotonmomentum.Thestandardhadronizationmodelsbaseduponthecolourneutral-izationmechanismappeartounderestimatetherateofslowprotonproductiononhydrogen.Thepresenceofthevirtualmesons(pions)inthenucleonleadstoanadditionalmechanismforprotonproduction,referredtoasspectatorprocess.Itisfoundthatatlowprotonmo-mentabothmechanismscompete,whereasthespectatormechanismdominatesatverysmallmomenta,whilethecolorneutralizationmechanismdominatesatmomentalargerthan1-2GeV/c.TheresultsofthecalculationsarecomparedwiththeCERNbubblechamber(BEBC)data.Thespectatormodelpredictsasharpincreaseofthesemi-inclusivecrosssectionatsmall

xduetotheseaquarksinvirtualmesons.

PACSnumbers:25.30.Pt,13.85.Hi

The semi-inclusive cross section for producing slow protons in charged current deep inelastic (anti-) neutrino scattering on protons and neutrons is calculated as a function of the Bjorken $x$ and the proton momentum. The standard hadronization models base

1Introduction

Inclusivedeepinelasticleptonscatteringo nucleonsisawellestablishedtoolforinvestigatingthepartondistributions[1].Hadrons,whicharenotmeasuredininclusiveexperiments,areproducedmainlyinthecolourneutralizationprocess;thestringmodelsbeingthestateofart.Itisexpectedthatthemeasurementof nalstatehadronswillleadtoabetterunderstandingofthemechanismofhadronproductionasitcontainsinformationabouthadronizationprocess.Insemi-inclusivedeepinelasticreaction(SIDIS)oneobservesoneormorehadronsinco-incidencewiththescatteredlepton.Inthesimplestapproximationthesemi-inclusivecrosssectionisassumedtofactorizeintoaninclusivecrosssection(proportionaltothedeep-inelasticstructurefunctions)andafragmentationfunction[2,3].

Inthepastthestudyofsemi-inclusivedeep-inelasticleptonscatteringhasbeenrestrictedmainlytothedetectionofhighenergyhadrons,whichoriginatefromthefragmentationoftheleading(struck)quark.Theproductionofslowprotonsincoincidencewithmuonshasbeenstudiedinthe(anti)neutrinoinducedchargedcurrentreactionsatCERN[4,5].InamorerecentanalysisoftheCERNexperimentWA21[5]thefractionofslow(p<0.6GeV/c)protonswasdetermined.InRef.[6]theratefromRef.[5]wasreproducedwithaconstantfragmentationfunction,assumingthatonlyprotons(nootherbaryons)areproduced.Therateofslowprotonproductionstronglydependsonthebehaviourofthefragmentationfunctionatthekinematicallimit,i.e.thelightconemomentumfractionz=p /mcloseto1.Thecountingrules[7]suggestforthediquarkfragmentationfunctionratheralinear,D2q(z)=A(1 z),thanaconstantdependenceonz.Furthermore,otherbaryons(neutrons,isobars,etc.)canbeproducedwhichleadstoasuppressionoftherelativeprotonyield.

InordertoillustratethispointweshowinTable1therelativeyieldofprotonsandneu-tronsincludingbothdirectandsequential(intermediate )productionobtainedfromamorerealistic,yetsimple,quark-diquarkmodel[8].Forcomparisonwegivethenumberofpro-tons/neutronspereventobtainedfromtheLundstringmodel[9].BothargumentsdiscussedabovesuggestthattheagreementwithexperimentalrateinRef.[6]hastobereconsidered.Itwillbediscussedlaterthatamorerealisticcalculationleadstoade citofslowprotonscom-paredtotheexperimentalrate[5].TheviolationoftheGottfriedsumruleobservedbyNMC

[10]stronglysuggeststhe avourasymmetryoftheseaoflightquarksintheproton.Thiscanbenaturallyaccountedforbythepresenceofthepion(meson)cloudinthenucleon[11]–[18].ThepioncloudmodelhasalsobeenusedsuccessfullyininclusiveDIStoexplaintheantiquarkdistributions[18,19].

Thepresenceofthemesoncloudmayleadtoanadditionalmechanismfortheslowprotonproductionindeepinelasticleptonscattering[20,21,22,23].Forinstance,inthe(anti)neutrinoinducedreactionthevirtualbosonWsmashesthevirtualpion(meson)intodebrisandthenucleon(baryon)isproducedasaspectatorofthereaction(seeFig.1).Thepresenceoftheπ Fockcomponentinthenucleonleadstotheproductionofaspectator whichdecaysintoapionandnucleon.

Uptonownofullyconsistenttreatmentofboththestandardfragmentationmechanismandthemesonexchangemechanismexists.Wenotethatitisinconsistenttoaddthecrosssectionsforthetwoprocesses.Inthepresentpaperwediscussinasimplehybridmodelhowthetwomechanismscanbetakenintoaccountinaconsistentmannerwhichensuresbaryon

The semi-inclusive cross section for producing slow protons in charged current deep inelastic (anti-) neutrino scattering on protons and neutrons is calculated as a function of the Bjorken $x$ and the proton momentum. The standard hadronization models base

numberconservation.Itisalsonotfullyconsistenttoreplacethefour-quarkfragmentationbythemesonexchangemechanismduetothefollowingtworeasons.Firstofall,asdiscussedinRef.[16],thevirtualpions(mesons)giverisebothtotheseaandvalencequarkdistributions.Secondly[18,24]theseageneratedbymesonsconstituteonlyafractionofthetotalsea.

Itistheaimofthispapertoquantitativelypredictthecontributionofthemesonexchangemechanismtotheslowprotonproductionratein(anti-)neutrinochargedcurrentdeepinelasticscatteringfromnucleons.Inadditionthemomentumdistributionofprotonsiscalculatedandcomparedwithexistingexperimentaldata[4].Finallythex-dependenceofthecoincidencecrosssectionfortheexperimentalmomentumbinsiscalculatedandcomparedwithexperimentaldatafromRef.[5].

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