Summary of the Diffractive Working Group at DIS98

DIS98

A.Goussiou

DepartmentofPhysicsandAstronomyStateUniversityofNewYorkatStonyBrookStonyBrook,NewYork11794,U.S.A.

E-mail:goussiou@fnal.govM.McDermott

DepartmentofPhysicsandAstronomy,BrunswickSt,

UniversityofManchester,M139PL,England

E-mail:mm@a13.ph.man.ac.uk

N.N.Nikolaev

Institutf.Kernphysik,ForschungszentrumJ¨ulich,D-52425J¨ulich,Germany&L.D.LandauInstituteforTheoreticalPhysics,Kosygina2,117334Moscow,Russia

E-mail:N.Nikolaev@fz-juelich.de

R.Roosen

I.I.H.E,VrijeUniversiteitBrussel,Pleinlaan2,1050Brussels,BelgiumE-mail:roosen@hep.iihe.ac.be

K.Piotrzkowski

DESY,Notkestrasse85,D-22607HamburgGermany

E-mail:krzysztof.piotrzkowski@desy.de

Recentexperimentalandtheoreticaldevelopmentsintheunderstandingofhighenergydiffraction,presentedintheworkinggroupondiffractionatDIS98inBrus-sels,aresummarised.Atemplate,givingthedefinitionofthemostcommonlyusedkinematicalvariablesindiffraction,whichwasprovidedintheworkinggroupsessions,isreproducedasaappendix.Referencestooriginalpapersmaybefoundwithintheindividualcontributions.

1Introduction

1.1

Whyisdiffractioninteresting?

Diffractioncombinesaspectsofparticleandwave-likenatureofhighenergyscatteringandstraddlestheinterfacebetweenshortandlongdistancedomainsofthestronginteraction.Apartfrombeingaveryinterestingprobleminitsownright,itisalsoausefulplacetotrytounderstandthetransitionbetweenreliable,perturbativeQCDcalculationsandtheremarkablysuccessfulstrong

1

interactionphenomenologyofReggetheory.Suchanunderstandingisclearlynecessaryifoneistoeverunderstandthemostdifficultandimportantprobleminstronginteractionphysics:confinement.

Giventhatafundamentalunderstandingofthistransitionisstilllacking,progressinthisareamaybecharacterisedasfollows:oneinvestigateswhatcanbeunderstoodintheregimeofpQCD,extrapolatesthishardQCDwisdomintothesoftdomain,oftenusingexperienceandintuitiongainedfromsoftphysicsphenomenology,andthenconfrontstheresultswiththedata.Thisnecessarilyleadstoastrongpositivefeedbackbetweennewexperimentalresultsindiffrac-tionandthedevelopmentandrefinementofthephenomenologicalmodels.AgreatdealofexperimentalandtheoreticalprogresshasbeenmadesinceDIS97whichwewishtosummarisehere.1.2

Physicalpictureofhighenergydiffraction

Peschanski1remindedusofaverysimplephysicalpicturefordiffractionbasedonanopticalmodel,developedmanyyearsago.Imaginetwohadronsscatter-ingatveryhighenergies.Quantummechanicstellusthateachhadronisacomplicatedevolvingsuperpositionofvirtualstates(atlongdistancesonecanthinkoftheprotonemittingandreabsorbingpions,etc;atshortdistancesoneimaginesfluctuationsofthepartonicstructuredueQCDradiation).Lorentzcontractionoftheseultra-relativisticsystemsensuresthatthissuperpositionisessentiallyfrozenonthe‘snapshot’timescaleoftheinteractionofthetwosystems,thuseachcomponentconstitutesaneigenstateoftheinteraction.Dis-tincteigenstateswillsufferdifferentlevelsofattenuationinthenuclearmediumoftheoppositehadronaccordingtotheirphysicalcharacteristics(numberofconstituents/partons,transversesizeetc).Asaresultthescatteredstateisdifferentfromthebeamstateand,inadditiontoelasticscattering,newex-clusiveandcontinuumstatesare‘diffractedintoexistence’bytheinteraction.Insuchdiffractiveproductionthereisalargerapiditygap(LRG)betweenthebeamexcitationandthetargetrecoilandtheenergydependenceissimilartothatofelasticscattering:intheReggeterminologybothelasticscatteringanddiffractiveexcitationaregovernedbyPomeron(vacuum)exchangeinthet-channel.

IfthePomeronisanisolatedReggepolewiththetrajectoryj=αIP(t)≈

−αIP(t)

.αIP(0)+α′IPt,thendiffractiveamplitudesareexpectedtobehaveasxIP

Itwouldcertainlybeinterestingtorelatethisriseinenergywiththatseenintheprotonstructurefunctionatsmall-x.TheReggephenomenologyofhadronictotalcrosssectionsprovidesausefulreferencevalue

αsoftIP(0)≈1.09.

2

(1)

TheQCDvacuumsingularityseemstobemorecomplexthananisolatedpolewithaneffectivePomerontrajectorythatchangeswiththehardnessoftheprocess.AnyvaluelargerthanthatgiveninEq.(1)maybeconsideredasevidenceforacontributionfromhardscattering.22.1

DiffractionindeepinelasticscatteringInclusivedata

ThetwomeasurementsreportedonbyKowalski&LindemannforZEUS2

D(3)

andbyNichollsforH13,regardingthediffractivestructurefunctionF2,arebasedontwodifferentmethodsandcoverdifferentkinematicranges.TheZEUSdataareanalysedinthekinematicrange7≤Q2≤140GeV2andMX≤15GeVandarebasedonthe1994data.ThediffractivedataareobtainedfromanexcessofeventsovertheextrapolatedinvariantmassdistributionatlargeMXingenericDISevents.TheH1diffractivedataareobtainedfromeventswithalargerapiditygapintheforwarddirection.TheH1diffractivestructurefunctionanalysisisbasedonthe1994data,complementedbythenew1995shifted-vertexdatawhichcovers0.4≤Q2≤5GeV2,0.001≤β≤0.65,therebyextendingthe1994measurementstolowerQ2,βandxIP.A

D(3)

comparisonoftheinclusivexIP.F2dataofH1,ZEUSandoftheZEUSLeadingProtonSpectrometer(LPS)datashowsthatthereisbroadagreement,althoughinthelow-Q2binsdifferencesareobserved.PhenomenologicalReggemodelfitsasusedpreviously,basedonaPomeronandReggeontrajectorydescribetheH1datawell.Theinterceptofthetrajectoriesareconsistentwiththeearlierpublishedvaluesand,giventhelargeerrors,noevidenceisfoundforapossibledependenceofthePomeroninterceptonQ2.Thescalingviolations,

D(3)

observedearlierinxIP.F2(xIP=0.005)ofthe1994dataathigherQ2,arereconfirmedbythenewdataatlowerQ2.TheanalysisofthedataintermsofpartondistributionfunctionssubjectedtoaNLODGLAPevolution,againindicatethatthegluoniccontentofthePomeronisoftheorderof(80-90)%withagluondistributionwhichislargeatβ∼1,incontrasttoamuchsoftergluoncontentintheproton.

FromtheZEUSanalysisaninterceptofαIP(0)isdeducedwhichagreeswiththeH1valueobtainedfromthephenomenologicalfitsofthe1994data.

αIP(0)=1.16±0.01(stat)±0.02(sys)(ZEUS)

αIP(0)=1.203±0.020(stat)±0.013(sys)(H1-‘94data)

(2)(3)

ThisinterceptisclearlylargerthanthatofEq.(1),whereastheReggeoninter-cept,obtainedbyH1,isclosetoαR(0)≈0.5ofstandardReggetheory.The

3

ZEUSresultsforxIP·FD(2)

2indicateaweakβ-dependenceandare,withinerrors,consistentwithscaling.2.2

ModelsofdiffractiveDIS

Diffractionoccursinthesmall-xregimeofDIScorrespondingtothehighen-ergy(Regge)limitoftheγ∗psub-process(W2≫Q2,M2

QCD,themulti-partonFockstatesofthephotonarethep).Intherealmofnaturaldiffractioneigenstates.Atlowestorderinαstheseareqq¯pairs:colourdipolescharac-terisedbytransversesize,orequivalentlyimpactparameter,andmomentum-fractionsharing,z.Thedipolescatteringamplitudesareproportionaltothetransverseareaoccupiedbythedipole,henceitislargesizeconfigurationswhichareprimarilyresponsiblefordiffraction(theyalsoturnouttobeasym-metricconfigurationsz≪1,or1−z≪1).Asthetransversesize,or‘scanningradius’,oftheinteractingdipolesisdecreasedoneexpectsatransitionfromsofttoharddiffraction.Genovese4reviewedmajorapplicationsofthecolourdipolepicturetodiffractiveDIS.

Usingthepredictionsofadipolemodelapproach,basedonleading-logBFKLdynamicsandthelargeNcapproximation,Royon6presentedfitstotheH1diffractivedata,aswellastotheF2data.Boththeprotonandvirtualphotonaretreatedasasuperpositionofdipolesandbothsingleanddoublediffractionareincludedintermsofelasticonium-protonscatteringandasumofinelasticdipole-dipolescattering.Thegrossfeaturesoftheexperimentaldatacanbereproducedwithrelativefewparameters,buttheapplicabilityoftheseapproximationstodiffractiveDISiscertainlyquestionable,duetothelargesoftcontributiontodiffractiveDIS.

Kopeliovich7discussedhowDrell-Yanproduction,whichisusuallytreatedasaqq¯→γ∗annihilation,canbereformulatedinthecolourdipolepictureasasortofdiffractiveexcitationofaFockstateoftheprojectilewhichcontainstheγ∗asaconstituent.Inthisway,thesimilaritybetweenDrell-YanandDISprocessesbecomesapparent.

Itisusefultofocusattentiononthose(relativerare)diffractiveprocesseswhichalsocontainahardscale,inadditiontoQ2,suchasaheavyquarkmassorhigh-ptpair,tobereallysurethatwecantrustourperturbativecalcula-tions.Theknowledgegainedcanthenbeusedtotrytobuildanunderstandingofthewiderpictureofdiffractiveprocesses.TheQCDmodelforthis‘hard’diffractionistheexchangeoftwointeractinggluonsinacolour-singletconfig-urationinthet-channel,whichdominatestheQCDevolutionoftheprotonseastructurefunctionatsmallx.Thediffractiveamplitudesarerelatedtothetargetgluonstructurefunction,G(xIP,

scale

Q2

andalackofoverallReggefactorization

intoanxIP-dependentfluxanda(β,Q2)-dependentstructurefunctionofthePomeron,apartfromtheregionofsmallβ.Furthermore,thevaluesof

the(Regge-factorizationbreaking!)Q2-dependenceofthexIPexponentinthetransverseqq¯term.Inaddition,theH1dataalsoallowasecondsolutionin

whichtheβ-dependenceoftheFoftheβ,QrangeofqT

theq¯gcontributionismuchharderanddominates

overmuch2

data.2.3

Arediffractiveeventsuniversal?

AtthemomenttheRegge(Ingelman-Schlein)factorizationansatzremainstheonlytooltorelatediffractivecrosssectionsinDISandhadroniccollisions.Itisoflimitedapplicabilityandabetterunderstandingoftheconsequencesoftheprocess-dependenthardnessscale

3.1Vectormesonproduction:data

ThestudyofdiffractivevectormesonproductionatHERAremainsaveryac-tiveresearchfieldandisanidealplacetostudythetransitionbetweenhardandsoftdiffraction.Theformerischaracterisedbystrongerenergyrises,broaderdiffractivepeaksandconsiderablylessshrinkagethanthelatter.Thefirstob-servationofthephotoproductionoftheΥ-familywasreportedforZEUSbyBruni11.Across-section(σγp→Υ(nS)p∗BR(Υ(nS)→µ+µ−)forn=1,2,3)of≈15pbhasbeenextractedusingthefull95-97datastatistics,thebranchingratiosΥ(nS)→µ+µ−,anestimateofproton-dissociation,andanassumption

′′′

ofthesamerelativecontributionsofΥ(1S),Υ(2S)andΥ(3S)statesasmea-suredattheTevatron.InspiteofthelargescalegivenbytheΥmass(whichshouldmakepQCDpredictionreliable),eventakingintoaccountthelargeun-certaintiesduetothechoiceofthegluondensity,thescaleitissampledat,andthechoiceoflight-conewavefunctionofthevectormeson,itturnsoutthatthepredictionsofapQCDtwo-gluonexchangemodel,whichsuccessfullydescribestheJ/ψproduction,areaboutanorderofmagnitudebelowthemeasuredcrosssection.Clearlyfurtherdevelopmentsinboththeexperimentalmeasurement(reductionoflargeerrors)andtheoreticalunderstandingareurgentlyrequired.Monteiro12reportedforZEUSonexclusiveandproton-dissociativepho-toproductionofρ0,φandJ/ψmesonsatW≈100GeVand0<|t|<4GeV2.UsingtheReggeformalismandthemeasuredelasticcross-sections,aswellasthelow-WdataandotherHERAmeasurementsatlow|t|,theexchangedPomerontrajectorycouldbedirectlydeterminedupto|t|≈1GeV2.Fortheρ0andφproductionthenominal‘soft’(linear)trajectoryhasbeenmea-suredwithaninterceptcompatiblewithEq.(1).Theslopeofthetrajectoryisnon-zero,butitissignificantlysmallerthan0.25GeV−2.Incontrast,forJ/ψexclusiveproduction,thecorrespondingtrajectoryhasamuchhigherinterceptanditsslopeissmall,compatiblewithzero,indicativeofasmalltransversesizeanda‘hard’diffractivemechanism.

Thompson13reportedstudiesofdiffractiveJ/ψphoto-andelectropro-ductionandalsophotoproductionathigh-|t|forH1.For|t|>1GeVthemeasuredcross-sectionforproton-dissociativediffractioncanbesuccessfullydescribedbyamodelbasedonLOBFKL(seealsoSec.(7)).Newmeasure-mentsofexclusiveelectroproductionofthesmall-sizeJ/ψconfirmthestronglyrisingW-dependencealreadyseeninphotoproduction.Theratioofψ(2S)toJ/ψproductionisfoundtoincreasefromabout0.15inphotoproductiontoabout0.5atQ2≈15GeV2,withlargeerrors.Thisreflectstheincreaseinhardnessoftheproductionscaleofψ(2S)withQ2,whichissimilarinsizetothepion,andmayrevealimportantinformationaboutthelight-conewave-7

functionsoftheseheavyvectormesons.

Thediffractiveelectroproductionofρ0mesonswasreportedbyClerbaux14forH1,Tytgat15forHERMESandKananov16forZEUS(alsoφmesons).AllthreeexperimentsmeasuredtheratioR=σL/σTfromphotoproductionuptolarge-Q2production.TheQ2-dependenceofRisconsistentwithalinearincreaseuptoQ2≈0.5GeV2,beyondwhichthisstrongincreasebecomessignificantlyweaker.Thequantitativedescriptionofthisbehaviour,whichisnowwellestablishedexperimentally,isachallengetothepQCDbasedmodels.

Fredj17reportedonaninterestingcontributiontodiffractivephysicsfromtheL3experimentatLEP-themeasurementoftheγγtotalcrosssection

2(α(0)−1)

extendingtheenergyrangeuptoWγγ≈130GeV.FitstoWγγIPgiveeffectivePomeronintercepts,dependingontheunfoldingmethod,ofαIP(0)≈1.16±0.03(PHOJETMontoCarlo)andαIP(0)≈1.14±0.02(PYTHIAMonteCarlo),inexcessofthevalueinEq.(1).3.2

Vectormesonproduction:theory

Zoller18presentedresultsonexpectationsfortheforwarddiffractiveslope,BD,withintheframeworkofthegBFKLdipolemodel.Threecomponentscanbeidentifiedcomingfromtheproton,theevolutionandfromthescat-teringdipole.AsQ2increasesthedipolesgetsmallerandthelattermakesasmallerandsmallercontributiontoBD,supportingthewell-establishednotionthatthegeometricalsizeofthescatteringobjectsdeterminesBD.Unfortu-natelythecurrentexperimentalerrorsfromHERAaretoobigtoobservethisQ2-dependenceinJ/ψproductionyet,butforlightervectormesonsithasbeenwellestablishedexperimentally.Anapproximateflavourindependenceis

2

observedinthevariableQ2+MV.

Theanalyses14,15,16ofthevectormesonproductiondata,undertheas-sumptionofthes-channelhelicityconservation,giveavalueforR=σL/σTwhichtendstosaturateatlargeQ2,whereasthetheoreticalestimatespredictasteadyrise,albeitslowerthanlinearwithQ2.IntheframeworkofthetwogluonexchangemodelofLow-Nussinov,Royen19discussedthesensitivityofRtomodificationsofthewavefunctionofthevectormesonwiththeconclusionthattheFermimotioneffectsinthewavefunctioncantamethegrowthofRwithoutspoilingotherpredictions,inthekinematicregiondefinedbythedata.3.3

Off-diagonalkinematics

Aparticularlyactiveareaofresearchatpresentconcernsnon-diagonaloroff-forwardpartondistributionswhichariseinexclusivediffractiveprocessessuch

8

asheavyvectormesonproduction,deeplyvirtualComptonscattering(DVCS)andphotoproductionofdijets.

Conventionalpartondistributionsinvolveproductsofoperatorssandwichedbetweenidenticalhadronicstates(e.gincomingandoutgoingprotonsinthesamequantumstate).Thefinitemomentumtransfertotheproton,innon-diagonalkinematics,meansthattheoutgoinghadron(evenifitisaproton)isinadifferentquantumstate.Thisleadstouniversaldistributionswhicharegivenbythequantum-mechanicalinterferencebetweenstatescharacterisedbythedifferenceinthemomentumfractionscarriedbytheoutgoing(x1)andre-turning(x2)partons,xIP=x1−x2,andassuchprobenewnon-perturbativeinformationabouttheproton.Arenormalizationgroupanalysisoftheoper-atorsleadstoevolutionequations,dependentonxIP,whichareknownonlytoleading-loginQ2,atpresent.Forx2>0theyreducetotheDGLAPequationsinthelimitxIP→0.Forx2<0theyobeyERBLequationsforthedistributionamplitudes.Intheleadingln(1/x)approximation,atsmall-x,thenon-diagonaldistributionscoincidewiththeconventional(diagonal)gluondistributions.

Golec-Biernat20presentedinterestingresultsondiffractivedijetproduc-tionwhichshowedthatthenext-to-leadingln(1/x)correctionsforthenon-diagonalityoftheprocessleadstoamarkedenhancementofjetproduction.Itwouldbeinterestingtoseetheimpactofothernon-leadingcorrectionsonthisfinding.

Strikman21presentedananalysisoftherelatedoff-diagonalDVCS,andpointedoutthefeasibilityofmeasuringtherealpartoftheDVCSamplitudeatHERA,which,viadispersionrelations,constrainsthebehaviouroftheimag-inarypartoftheDVCSamplitude,andbyextensionF2,atsmallerx-valuesthanthoseintheHERAkinematicrange.

Inconventionaldefinitionsofpartondistributions,afterfactorizationintohardandsoftphysics,oneexploitstheopticaltheoremandtreatsthe‘softblob’(andthehardblob)asthoughitwereonmass-shell(asaresultofthecut).Byconsideringthesingularitystructureofthefour-pointGreen’sfunctionforthesoftblobinthenon-diagonalcaseDiehl22hasshownthatonemaytreatthesoftpartofthediagramasthoughithadbeencutandexplainssomeoftheimportantphysicalimplicationsofthisresult.4

Diffractivefinalstates

VariousaspectsofdiffractivefinalstateshavebeenreportedbyBuniatian23andWaugh24forH1(energyflow,seagullplot,averagechargedparticlemulti-plicities,meanmultiplicitiesintheforward/backwardhemispheres)andWich-9

mann25forZEUS(thrustandsphericityanalysis)collaborations.Theglobalfeaturesofdiffractivefinalstates,i.e.therapidityandtransversemomentumdistributionsatsmallk⊥,meanmultiplicitiesandmultiplicitydistributions,theseagullplot,aresimilartothoseinhadroniccollisions,hadronicdiffrac-tion,inclusiveDISande+e−annihilation,atthesamemassofthehadronicstates.Non-trivialdifferencesarefoundwhenonelooksatthefinestructureoffinalstates.ThethrustanalysisreportedbyZEUSisperformedonadiffractiveeventsampleselectedbytheLPS.AcomparisonoftheseresultswiththoseobtainedfromtheLRGeventsinH1indicatesthattheaverageeventthrustintheZEUSdataissystematicallyhigheralthough,becauseofthelargeerrors,notinconsistentwiththeH1findings.However,theaveragethrustintheLRGeventsisdefinitelysmallerthaninthee+e−data.

Thestumblingblockintheinterpretationofthesedataisthatthetheoret-icalunderstandingofinitialandfinalstateradiationandoftherelatedvirtualradiativecorrectionstotheformationofdiffractivefinalstates,islaggingbe-hindtherapidexperimentaldevelopment.Theexperimentalistshavetakentheleadand,atthemoment,theRAPGAPMonteCarlo,basedontheIngelman-Schleinapproach,remainstheonlytooltodescribetheresolvedPomeronvia

D(3)

partonicdensitieswhichareobtainedfromfitstotheH1xIP.F2struc-turefunction.TheprincipalfindingisthatthisparticularversionofRAP-GAPdescribesalmostallofthediffractivehadronicfinalstatesrangingfromenergyflowtoparticlecorrelations.Intermsofthismodelalargegluonic

D(2)

Pomeroncontent,asdeterminedfromthexIP.F2analysis,isessentialforagooddescriptionofthedata,althoughitshouldbeemphasizedthatotherMonteCarlo’slikeLEPTO6.5,basedonthesoftcolourinteractionmodelandwhichdoesnotcontainanyspecialmechanismofdiffractiondescribesthedataequallywell.Atpresent,thedatadonotallowadiscriminationbetweentheseconceptuallydifferentmodelstobemade.

FromthetheoreticalpointofviewonealsoshouldtakeintoaccountthatthepresentlyavailableMonteCarlomodelsareassuminganillegitimateReggefactorisation,inwhichhardscaledependenciesonxIPanβasfoundinthe-oreticalQCDanalyses,andwhichcharacterisethefinalstate,areneglected.Forinstance,onetreatsthecharmproductionasentirelyduetothefamiliarphoton-gluonfusion,neglectingthedirectcharm-anticharmexcitationwhichsometheoristsclaimtobesubstantial.Inthisapproximation,inordertore-producethediffractivecharmsignalreportedbyThompson13oneneedsahardglueinthePomeronfits10.ThereforetheconclusionsdrawnfromtheseMonteCarlostudiesastothephysicalpictureunderlyingthediffractivefinalstatesshouldbehandledwithcare.

10

5TheForwardRegion

Inelasticscattering,thetypicalimpactparameterisasumofthesizeofthetarget,theprojectileandoftherangeofinteractionbetweenthetargetandprojectileconstituents.Inthegenericdiffractivereactionap→XY,thediffractiveslopeBDisclosetotheslopeofelastichadronicscattering,Bd∼10

22

GeV−2intheexclusivelimitofsmallmassstates,MX,Y≈O(MP),butthecontributionsfromthea→Xandp→YtransitionverticesareknowntovanishassoonasXorYarehighmasscontinuumstates,soBDdecreaseswiththeincreaseofMX,MY.Bythesametoken,onlythesizeofthescatteredprotonandtheinteractionrangecontributetoBDforsinglediffraction.HenceoneexpectsauniversalvalueforBD∼6-7GeV−2insinglediffractionforallprojectilesaintocontinuumX(includinghadrons,a=p,π,K,aswellasrealandvirtualphotonsa=γ,γ∗)ingoodagreementwiththeobservations.Therelateduniversalityofthe|t|-dependenceistobeexpectedatlarger|t|,andMenghaspresentedempiricalevidenceforthat26.Pronyaev8hasreportedanevaluationofBDfordiffractiveDISep→e′p′Xinthecolourdipolepictureofdiffraction;anontrivialpredictionisasubstantialriseofthediffractionslopeBDfromtheexclusivelimitβ≈1,whenXisthe1Svectormeson,toexcitationofcontinuumatβ∼0.5.

Thecrucialtheoreticalpointaboutleadingnucleonproductionfornon-diffractivez≈1−xIP<∼0.9,andinthefragmentationofprotonsingeneral,isthattheQCDhardnessscaleforsecondaryparticles(h)insemi-inclusiveDIS,ep→e′Xh,graduallydecreasesfromQ2inthevirtualphoton(current)frag-mentationregiontoasoft,hadronic,scaleintheprotonfragmentationregion.Thissuggestsasimilaritybetweentheinclusivespectraofleadingbaryonsinhighenergyhadron-protonandvirtualphoton-proton(DIS)collisions.ThestandardQCDhadronizationmodelsfailinthismanifestlysoftpartofthephasespace,butwereneverreallymeanttodescribeit.

Thenon-perturbativemechanisms-pionexchangefortheneutronproduc-tionandPomeron+pion+Reggeonexchangefortheleadingprotonproduction-havebeendiscussedbyD’Alesio27andNikolaev28,respectively.Ashasbeenunderstoodformanyyears,taggingleadingneutronsselectsDISoffpi-ons.However,theextractionofthepionstructurefunctionatsmallvaluesoftheBjorkenvariablexπ=βrequirestheknowledgeofthefluxofpions.D’Alesiofocusedonthemodeldependencecausedbyabsorptioncorrections,whicharedifferentforleadingneutronproductioninhadroniccollisionsandDISandspoiltheReggefactorizationleadingtoanuncertaintyof20−30%intheassociatednormalizationbetweenprocesses(asimilaranalysishasbeenreportedin28).Theconclusionisthatabsorptioneffectsareunderreasonable

11

control,anddonotprecludetheexperimentaldeterminationsofthegrossfea-turesofthepionstructurefunction.TherelatedabsorptioncorrectionsdefinetheBjorken’sgapsurvivalprobabilityinharddiffractiveppcollisions.Thex,Q2evolutionpropertiesoftheleadingneutronproductionasreportedbyNunnemannforH129andGarfagniniforZEUS30areconsistentwithexpec-tationsoftheDGLAPevolutionofthepionstructurefunction.

ThepQCD-motivatedevaluationofReggeonexchangeindiffractiveDIShasbeenreportedbySch¨afer5.ReggeonexchangeisevaluatedintermsofthevalencequarkdistributionsintheprotonandcomesoutatthesameorderofmagnitudeastheH1evaluations.InthisanalysisthestrongestpossibleconstructiveinterferenceofthePomeron(IP)andReggeonfexchangesap-pears,incontrasttoexpectationsbasedontreatingthePomeronandReggeonashadronicstates.Furthermore,heshowedthatthePomeron,Reggeon,andtheIPfinterferencestructurefunctionsmusthaveasimilarlarge-βbehaviourandthattheβ,Q2evolutionofallthesestructurefunctionsmustbesimilar.Thelatterpointleadstoanapproximatelyx,Q2-independentyieldoflead-ingprotons.Nunnemann29reportedagoodagreementoftheH1dataonleadingprotonswiththePomeron+pion+Reggeonexchangemodel31,whereasLEPTO6.5MonteCarlofailstoreproducetheQ2-dependenceoftheobservedcrosssection.Inprinciple,Reggeonexchangeisconstrainedbythediffrac-tivedata,butmoredetailednumericalevaluationsoftheIPfinterferenceareneededforaunifieddescriptionoftheReggeoneffectsinboththediffractiveregionz>∼0.9,andforz<∼0.9.6Diffractioninproton-protonscattering6.1

NewdatafromtheTevatron

HarddiffractionattheTevatronhasbeenobservedbyboththeDØ(reportedbyRubinov32)andCDF(reportedbyBorras33)collaborations.Diffractiveeventsareselectedbyrequiringalargerapiditygapand/orbyrecordingabeamparticlerecoil.ThehardscaleisseteitherbyjetswithlargeET,orbythemassofadiffractively-producedW-boson(CDF).Inhardsingle-diffractionwithaforwardrapiditygapthegapfraction,definedastheexcessofeventsatlowmultiplicityovertheextrapolatedmultiplicitydistributionfromnon-diffractivedijetevents,hasbeenmeasured.Thedependenceofthegapfractiononηboostandthegaplocationandsizeindicatesthattheseeventsareindeedconsistentwithacoloursingletproductionmechanism.TheDØcollaborationattwodifferentenergies(

√gapfractionsmeasuredbythehardpartonicstructure.Combiningtheratio’sofdiffractivetonon-diffractiveWanddijetproduction,theCDFcollaborationdeterminedafractionofhardgluonsinthePomeronequalto0.7±0.2.ThisvalueentailsamomentumfractionofthehardpartonsinthePomeronwhichisconsistentwithresultsfromtheZEUSexperimentonlyafterintroducingadiscrepancyfactorD=0.18(cf.fluxrenormalization).Bothcollaborationsalsoobservedeventswithtwocentraljetsandtwogapsintheforwardrapidityregions,consistentwithharddoublePomeronexchange.Therate,R(DPE/SD)=0.26±0.05(stat)±0.05(syst.)%,aswellasthekinematicsofthedijetsarewellreproducedbyMonteCarlo,providedarenormalizedIPfluxisused.

ThefractionofdijeteventswithacentralrapiditygaphasbeenbyDØ(reportedbyGoussiou)andCDF(reportedbyBorras35

)at

√measured

34=3.4±1.3;

RfCDF=

JGJ(630)

fJGJ(1800)

mustinvolvepurePomeronexchange.Hence,inthemoderateenergyregionrelevanttotherapiditygapsintheTevatrondiffractivedata,theinterceptofthePomeronmustbeclosetounity,whichremovestherapidgrowthofthetripleReggecrosssectionfromtheFNAL-ISRtoTevatronandresolvesDino’sparadox.Tanhasdiscussedflavouring-theeffectofopeningnewin-elasticchannels-asthemechanismsfortheenergydependentinterceptofthePomeron.Tan’smechanismcanbeconfirmedorruledoutatLHC.

Atpresent,theoryisnotabletomeetthechallengeoftheextremelyin-terestingdataonhardjetproductioninrapiditygapeventsobservedinmanyjetandW-bosonproductionchannels,attheTevatron.Bjorken’spointthatabsorptioneffectsstronglyaffectthegapsurvivalprobabilityhasbeenreit-eratedbyWhitmore10,whohaspresentedevaluationsfordiffractivejetandW-productionfordifferentpartonmodelparameterizationsoftheH1-ZEUSdiffractivestructurefunctionsbasedontheReggefactorizationassumptions.Inallthecasessuchestimatesovershoottheobservedcrosssections,whichtestifiestotheimportanceofabsorption.Whitmore’sresultsshowthatthegapsurvivalprobabilityvariessubstantiallyfromoneharddiffractivereactiontoanother,thetheoreticalunderstandingofthesevariationsis,asyet,lacking.7

SuperharddiffractionandBFKLdynamics

Theevolutionwithenergy(or1/x)ofthecrosssectionforscatteringoftwosmallobjectsofsimilarsize,i.e.Mueller’s“onia”,alsocalledthesingle-hard-scaleproblem,remainsoneofthemostintriguinganddifficultproblemsinperturbativeQCD.Fadin37andLipatovhavepresentedcorrections,next-to-leadinginenergy,totheirfamousBFKLequation;thesesubleadingcorrectionsareverylargeandreducethestrongriseinenergyofhardcrosssections,oftheleading-orderresult.Inviewofthis,itisvitallyimportantthattheexperimentscontinuetheireffortstomeasurehardsmall-xprocesses.

Cox38andForshawhavesuggestedlookingatdoubledissociationinphoto-production(DDP)athigh|t|,asanalternativetothetraditionalgaps-between-jetsmeasurement.Thelatterhasseveraldistinctdisadvantages:thedemand

2

forhighenoughptinthejets(typicallyp2t=25GeV)reducesstatisticsanddiminishestheavailablerapidityspace(thejetsthemselvesoccupyasmuchastwounitsinrapidityeachandmustbeseeninthemaindetectors);onealsoreliesstronglyonbeingabletomeasurethesizeofthegapaccurately(whichinpracticealsorequiresanexperimentaldefinition).IncontrastDDPathigh|t|whichmerelyusesthegaptoseparatethetwosystemsXandY(followingtheH1method),hasamuchwiderreachinrapidity(orenergy)andmayberelevantto|t|valuesaslowas1GeV2.MonteCarlostudies,usingHERWIG,

14

suggestthatthismeasurementisarobustmeasureofwhatevertheenergyriseoftheprocessis.Itwillcertainlybeinterestingtoseethefirstdata.Appendix-DiffractiveDIS:ConventionSummaryInclusiveDIS

Lorentz-invariantvariables

Q2≡−q2=−(k−k′)2

2

W2≡(p+q)2=Mp+2p.q−Q2≈2p.q−Q2x≡

Q2

2W2+Q2−Mp2

W2+Q2−Mp

≈

Q2

2k.p

=

S

≈

Q2

p.q

β≡

Q2

=

2MX+Q2−t

W2+Q2

xIP

=

Q2

2

MY

xIP

22MY=p′2=Mp

•AtHERAt≤1GeV2,andcanbeneglectedintheaboveexpressionsfor

β,xIP

2

•t≈−p⊥withthetransverseplaneperpendiculartothatdefinedbytheincoming(p,γ∗)inthecentre-of-massframe

′

•Theangular-averagedSDdiffractivecrosssectioncanbedecomposedasQyπ

2

d4σ(ep→ep′X)󰀁

y2

(1−y+

2dtdMX

+(1−y)·

d2σL(γ∗p→p′X)

4π2αem

·

󰀁

xIPd2σT(γ∗p→hX)

dxIPdt

=

Q2

dxIPdt

󰀃

D(4)

xIPFL(t,xIP,β,Q2)

•Parameterizingthet-dependencebythediffractiveslopeBD:

F2

D(4)

(t,xIP,x,Q2)≈F2

D(4)

(0,xIP,x,Q2)exp(BDt)

whereBDcandependonxIP,β,Q2.

•Thet-integrateddiffractivestructurefunctions

D(3)

(xIP,β,Q2)xIPFi

=

Q2

dxIPdt

(6)

•Exclusivesingly-dissociativediffractive(ESD)(orelastic)vector

mesonproductionisanexclusivelimitofSDinwhichYisaprotonandXisavectormeson,MX=Mρ,...,MY.

•Exclusivedoubly-dissociativediffractiveprocesses(EDD):Xisavectormeson,MX=Mρ,...,MYandtheprotonexcitesintonucleonresonnancesand/orcontinuumstatesY.

16

e(k)γ(q)(*)e(k’)XSGAPWptY(p’)References

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D

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