Can pions created in high-energy heavy-ion collisi

arXiv:hep-ph/9411329v117Nov1994Canpionscreatedinhigh-energyheavy-ioncollisionsproduceaCentauro-typeeffect?M.Martinis,1V.Mikuta-Martinis,2andJ.ˇCrnugelj3DepartmentofPhysics,TheoryDivision,RudjerBoˇskovi´cInstitute,P.O.B.1016,41001Zagreb,CROATIAAbstractWestudyaCentauro-typephenomenoninhigh-energyheavy-ioncollisionsbyassumingthatpionsareproducedsemiclassicallybothdirectlyandinpairsthroughtheisovectorchannel.Theleading-particleeffectandthefactorizationpropertyofthescatteringamplitudeintheimpact-parameterspaceareusedtodefinetheclassicalpionfield.ByanalyzingthejointprobabilityfunctionPII3(n0,n)forproducingn0neutralandn−negativepionsfromadefiniteisospinstateII3oftheincomingleading-particlesystemweshowthatonlydirectproductionofpionswithoutisovectorpairsfavorsCentauro-typebehavior.Thepresenceofisovectorpairsseemstodestroytheeffect.Ourconclusionissupportedthroughthecalculationoftwopioncorrelationparameters,f0−2andf002,andtheaveragenumberofneutralpions(hn0in)asafunctionofnegativepions(n)produced.PACSnumbers:25.75.+r,12.38.Mh,13.85.Tp,24.60.Ky1e-mailaddress:[e-mail]2e-mailaddress:[e-mail]3e-mailaddress:[e-mail]smic-rayexperiments[1]havereportedevidencefortheexistenceofCentauroeventscharacterizedbyananomalouslylargenumberofchargedpionsincomparisonwiththenumberofneutralpions,indicatingthatthereshouldexistaverystronglong-rangecorrelationbetweentwotypesofthepions.Suchlong-rangecorrelationsarepossibleifpionsareproducedcoherentlyandconstrainedbytheglobalconservationofisospin[2–7].Althoughtheactualdynamicalmechanismoftheproductionofaclassicalpionfieldinthecourseofahigh-energycollisionsisnotknown,thereexistanumberofinterestingtheoreticalspeculations[8–13]thatlocalizedregionsofmisalignedvacuummightoccurinultrahigh-energyhadronicandheavy-ioncollisions.Theseregionsbecomecoherentsourcesofaclassicalpionfield.Inearlymodels[2,3],however,thecoherentproductionofpionsistakenforgrantedandisconsideredtobeadominantmechanism.Thesemodelsalsopredictstrongnegativecorrelationsbetweenthenumberofneutralandchargedpions.Infact,theexactconservationofisospininapionuncorrelatedjetmodelisknown[4,5]togivethesamepatternofneutral/chargedfluctuationsasobservedinCentauroevents.Thisstrongnegativeneutral-chargedcorrelationisbelievedtobeageneralpropertyofthedirectpionemissioninwhichtheclusterformation(ortheshort-rangecorrelationbetweenpions)isnottakenintoaccount[6,7,14].Asimilarconclusionmaybedrawnwhenapropermultipionsymmetrizationcombinedwiththeisospinsingletchannelisconsidered[15].Inthispaperweconsidertheleading-particleeffectasapossiblesourceofaclassicalpionfield[16].Pionsareassumedtobeproducedfromadefiniteisospinstateoftheincomingleading-particlesystembothdirectlyandinisovectorpairs.2Coherentlyemittedisovectorclustersdecaysubsequentlyintopionsoutsidetheregionofinteraction.Wediscussthelimitingbehavioroftheprobabilitydistributionofneutralpions,theneutral-to-chargedratioandthecorrespondingtwo-pioncorrelationfunctionfab2,aswellasthevariationoftheaveragenumberofneutralpions(hn0in)asafunctionofthenumberofnegativepions(n)produced.WeshowthattheCentauroeffectisstronglysuppressedifpionsareproducedinisovectorpairs.Athighenergiesmostofthepionsareproducedinthecen-tralregion.Toisolatethecentralproduction,weadopthigh-energylongitudinallydominatedkinematics,withtwoleadingparticlesretainingalargefractionoftheirincidentmomenta.TheenergyavailableforthehadronproductionisEhad=12√s−Eleading.(1)ItisrelatedtotheinelasticityKofthecollisionsbyEhad=12√sK.(2)Notethatatfixedtotalc.m.energy√s,thehadronicenergyEhadvariesfromeventtoevent.Withasetofindependentvariabless,{~qiT,yi}≡qi,i=1,2,...n,then-pioncontributiontothes-channelunitaritybecomesanintegralovertherelativeimpactparameterbofthetwoincidentleadingparticles:Fn(s)=14sZd2bnYi=1dqi|Tn(s,~b;1...n)|2,(3)wheredq=d2qTdy/2(2π)3.ThenormalizationissuchthatFn(s)=sσn(s),σinel(s)=∞Xn=1σn(s).(4)3Athighenergiesthematterdistributionsofthetwo-leading-particlesystemareLorentz-contracteddisksinthec.m.system.Weassumethat,intheearlystagesofthecollision,ahighlyexcitedlocalizedsystemoccursthatrelaxesthroughthecoherentemissionofpions[17].Accordingto[18],thistypeofcoherentemissionofpionsshouldsaturateclosetothethresholdsince,onceitstarts,theresultingpionemission,intheabsenceofa”resonancecavity”,preventsfurtherbuildupofpionfields.Thebasicassumptionoftheindependentpion-emissionmodel,neglectingtheisospinforamoment,isthefactorizationofthescatteringamplitudeTn(s,~b;1...n)inthebspace:Tn(s,~b;1...n)=2sf(s,~b)in−1√n!nYi=1J(s,~b;qi),(5)where,owingtounitarity,|f(s,~b)|2=e−n(s,~b),(6)andn(s,~b)=Zdq|J(s,~b;q)|2(7)denotestheaveragenumberofemittedpionsatagivenimpactparameterb.Thefunction|J(s,~b;q)|2,aftertheintegrationoverb,controlstheshapeofthesingle-particleinclusivedistribution.Asuitablechoiceofthisfunctionalsoguaranteesthattheenergyandthemomentumareconservedontheaverageduringthecollision.TheaboveparticularfactorizationofTnwasconsideredearlierbyR.Avinetal.[19]inconnectionwiththeconstructionofaunitarymodelofmultiparti