Saturation in DIS processes

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

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

Figure4.WdependenceofHERAdataforlogarithmicslopeat xedQ2(inGeV2)comparedwithourcalculationsforscreenedGRV98andtheDLmodel.

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10.Phys.Rev.D60,114023(1999).E.Gotsman,E.Ferreira,E.Levin,U.MaorandE.Naftali,Phys.Lett.B500,87(2001);ibidPhys.Lett.B503,277(2001).A.Zamolodchikov,http://www.77cn.com.cnpidus,JETPL33,595(1981);E.M.LevinandM.G.Ryskin,SJNP45,150(1987);A.H.Mueller,Nucl.Phys.B415,373(1994).E.Gotsman,E.M.Levin,U.MaorandE.Naftali,Nucl.Phys.B539,535(1999)http://www.77cn.com.cnndsho ,Phys.Lett.B437,408(1998);Phys.Lett.B470,243(1999).J.R.Forshaw,G.KerleyandG.ShawPhys.Rev.D60,074012(1999).paper1:submittedtoWorldScienti conFebruary7,20085

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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