Saturation in DIS processes
时间:2025-04-02
时间:2025-04-02
We examine HERA data with a view of determining whether unique signs of saturation can be identified. Concentrating on two channels the logarithmic slope of $F_{2}$, and the production of $J/\Psi$, which are sensitive to the behaviour of $xG(x,Q^{2})$ the
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iXraSATURATIONINDISPROCESSESERROLGOTSMAN[incollaborationwithE.Levin,U.MaorandE.Naftali]SchoolofPhysicsandAstronomy,TelAvivUniversity,TelAviv69978IsraelE-mail:gotsman@post.tau.ac.ilWeexamineHERAdatawithaviewofdeterminingwhetheruniquesignsofsat-urationcanbeidenti ed.ConcentratingontwochannelsthelogarithmicslopeofF2,andtheproductionofJ/Ψ,whicharesensitivetothebehaviourofxG(x,Q2)thegluondensitydistributionintheproton,weshowthatourmodelincorporat-ingscreeningcorrectionsandalternativemodelscomprisingasumofa”soft”and”hard”componentprovidegood tstothedata.1IntroductionTheweaddress,iswhethertheexperimentalresultseminatingfromHERAcontainclearevidenceforthepresenceofsaturatione ects,orwhethertheyareconsistentwithorthodoxpQCDevolution.Toquantifysaturationitisinstructivetointroducetheconceptofapack-ingfactor(PF)whichisrelatedtothedensityofthepartonsinapartoncascade.PF≡κ=3π2αSπR2(1)ThesaturationscaleQ2sisde nedbyκ=1,forwhichQ2=Q2Inthediluteregion(κ<1)thepartonsaredistantfroms.(see g.1)oneanother(andhavenointeractioninthepartoncascade),sopQCD(i.e.DGLAPandBFKL)evolutionholds,andthedominantprocessistheemissionofgluons.Inthehighdensityphase(κ>1)thepartonsinthepartoncascadeinteract,theseinteractionsgiverisetoscreeningcorrections(SC),whichslowdownthegrowthofthepartondensitydistributions.Thecorrectdescriptionofparton
evolutioninthehighdensityphaseisgivenbyanon-linearevolutionequationofthetype rstsuggestedbyGribov,LevinandRyskin3,whichincorporatespartonrecombonationaswellasemission.
Therehavebeennumerousattemptsto ndbothapproximateanalyticalnumericalsolutionstothenon-linearequation(forarecentreviewsee4).ThesesolutionssuggestthatthesaturationscaleQS(x)≈1 2GeV2,intheHERAkinematicregion.verysuccessfulphenomenologicalmodelofGolec-BiernatandWuesto 5,whichprovidesanexcellentdescriptionofpaper1:submittedtoWorldScienti conFebruary7,20081
We examine HERA data with a view of determining whether unique signs of saturation can be identified. Concentrating on two channels the logarithmic slope of $F_{2}$, and the production of $J/\Psi$, which are sensitive to the behaviour of $xG(x,Q^{2})$ the
s(x) )2
Q2
Figure1.Partondistributioninthetransverseplane.
HERAdatabasedonthepremisethatthesaturationregionhasbeenreachedatHERA,isadditionalevidencesupportingthesaturationhypothesis.2TheGLMNmodel
Inaseriesofpapers,thelatestofwhicharelistedin6,wehaveappliedscreen-ing(unitarity)correctionstoanumberofinclusiveandexclusivechannels.WefollowtheGlauber-Mueller(eikonal)approach7incalculatingscreening(uni-tarity)correctionstopQCDevolution.ThetechniqueusedforevaluatingtheSCinthequarkandgluonsectorsaregiveninreference8.
AstheSCaremuchlargerforthegluonsectorthanforthequarksector,wequoteresultsherefortwochannelsthatinLLAofpQCDaredirectlyproportionaltoxG(x,Q2),thegluondistributionintheproton.
1)ThelogarithmicslopeofF2:
F2(x,Q2)
9πxGDGLAP(x,Q2),(2)
2)ThecrosssectionfortheexclusiveproductionofthevectormesonJ/Ψ.ForwhichthecontributionofpQCDtotheimaginarypartofthet=0di erentialcrosssectionisgivenby
paper1:submittedtoWorldScienti conFebruary7,20082
We examine HERA data with a view of determining whether unique signs of saturation can be identified. Concentrating on two channels the logarithmic slope of $F_{2}$, and the production of $J/\Psi$, which are sensitive to the behaviour of $xG(x,Q^{2})$ the
(dσ(γ p→Vp)α2S(Q¯2)
48αM2),
V
herexGDGLAPdenotesthegluondistributionfunctionasobtainedfromtheDGLAPanalysis.
Ourresults.seeFig.2andFig.3,suggestthatalreadyatHERAenergiestheSCareconsiderablefortsetwochannels.
Figure2.LogarithmicderivativeofF2withoutandwithSC.
3AlternateModels
Although,theresultspresentedaboveareconsistentwiththehypothesisthatsignsofsaturationhavebeenseenatHERA,theyarenotconclusive.Sincemodelsbasedonthesumofthecontributionsofa”hard”andasoft”Pomeron”e.g.9and10,provideafairdescriptionoftheHERAdata.ThesemodelstonotincorporatepQCDevolution,buthaveacommonfeatureinthattheybothrequirethe”soft”Pomeroncomponenttobeappreciableatfairlysmallscales≈0.3-0.5fm.
InFig.4wecomparetheDLpredictionsfor F2(x,Q2)
We examine HERA data with a view of determining whether unique signs of saturation can be identified. Concentrating on two channels the logarithmic slope of $F_{2}$, and the production of $J/\Psi$, which are sensitive to the behaviour of $xG(x,Q^{2})$ the
Figure3.J/ΨphotoproductionwithandwithoutSC.
4Conclusions
Although,HERAdataisconsistentwiththehypothesisthatwearedealingwithpartondensitiesthataresu cientlydense(κ≈1),thatSCareneces-sary.The ndingsarenotconclusiveasanalternativeexplanationisalsovalidi.e.thatofamatchingbetweena”soft”anda”hard”process(e.g.theDLmodel)wherethe”soft”componentdominatesatrelativelyshortdistancesof0.3-0.5fm.
References
1.seeexperimentalpaperspresentedbyH1andZEUScollaborationat
HEP2001(thisvolume).
2.A.H.Mueller,Nucl.Phys.B355,115(1990).
3.L.V.Gribov,E.M.LevinandM.G.Ryskin,Phys.Rep.100,1(1983);
Nucl.Phys.B188,555(1981).
4.M.Lublinsky,”ScalingPhenomenafromNon-LinearEvolutioninhigh
energyDIS”hep-ph/0106112.
5.K.Golec-BiernatandM.Wuestho ,Phys.Rev.D59,014017(1999);paper1:submittedtoWorldScienti conFebruary7,20084
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