Some Properties of a Transient New Coherent Condit

PITHA94/36TTP94{18September1994SomePropertiesofaTransientNewCoherentConditionofMatterFormedinHigh{EnergyHadronicCollisionsSaulBarshaya)andPatrickHeiligerb)a)III.PhysikalischesInstitut(A),RWTHAachenD{52056Aachen,Germanyb)InstitutfurTheoretischeTeilchenphysikUniversitatKarlsruheD{76128Karlsruhe,GermanyAbstractWeinvestigatethedynamicalpossibilityfortheformationofatransientnewcoherentconditionofmatterinhigh{energyhadroniccollisions.Thecoherentbosonicamplitudeischaracterizedbyanon{zeromomentumandissustainedbyP{waveinteractionsofquasi{pionsinadensefermionicmedium.Wemakequantitativeestimatesofseveralessentialproperties:thecondensatemomentumandthefermionicdensity,thesizeofthecoherentamplitudeandthenegativeenergydensitycontributedbythecondensate,acharacteristicpropertimeforthesystemtoexistpriortobreakdownintoafewpions,andacharacteristicextensionofthesystemovertheplaneperpendiculartothecollisionaxis.Thesequantitiesthenallowustomakedeniteestimatesofnewsignals:afewpionswithanomalouslysmalltransversemomenta50MeV/c;andapossibleanomalousbremsstrahlungofverysoftphotonswithcharacteristictransversemomentaaslowasabout4MeV/c.1Thereexistcertaindeniteanomalouseectsincurrenthigh{energyexperimentsinvolvingcollisionsofhadrons[1,2,3,4,5].Theseunusualeectscanbeconnectedthroughthetransientexistenceofanewcoherentconditionofmatter[1].Suchahypothetical,relativelylong{livedsystem,becomingspatiallyextendedoverthe(impact{parameter)planeperpendiculartothecollisionaxiscanbeformedinsomeofthereal,intermediateinelasticstateswhichcontributetothe(imaginary)am-plitudeforthediractiveelasticscatteringofhadrons.Thecoherentsystemcansupportanoscillatorybehaviorofmatterwithafairlydenitenon{zeromomentum[6]inthetransverseplane.TherelevantFourier{Besseltransformofthisspatialos-cillatorybehaviorintothespaceoftransversemomentum{transferpt’ps2(forsmallc.m.scatteringangle),resultsinalocalizedstructureinthedierentialcrosssectiondeldtaroundafairlydenitevalueofpt.Suchalocalizedstructureexists[1]inthedatafromcolliderandxed{targetexperimentsuptothepresenthighestcenter{of{massenergyps=1800GeV.Theremustalsobedirectsignalsfromthetransientcoherentsystemininelasticprocesses.Onesignalthatisageneralconse-quenceoftheextensionofthesystemtoseveralfermisoverthetransverseplaneisthebreakdownintoafewpionswithanomalouslysmalltransversemomenta50MeV/c.Observationofthisunusualeectagainstthebackgroundofmanypionsproducedwiththeusualaveragetransversemomentumof(250350)MeV/cre-quiresmeasurementsonindividualevents,inparticulareventswithlowmultiplicity.Infact,thisunusualphenomenonofsmall{pT,few{particleemissionisthemainnewempiricalfeatureinarecent,detailedstudyofseveralhundredcosmic{rayshowers\intheforwardmostsmall{angularregion[7].Ifchargedcurrentsexistwithinthecoherentsystemduringitsevolution,thenithasbeenshownthatsoftphotonswillbeemitted[8].Theoccurrenceofananomalouslyhighemissionofsoftphotonshasbeenandistoday,anenigmaticfeatureofseveraldierentexperimentsatCERN[2,3,4,5,9].2Inthispaperweattempttocalculateapproximatelysomepropertiesofatran-sientnewcoherentconditionofmatterformedinhigh{energyhadroniccollisions.Weutilizegeneralpropertiesofaphysicalmodelinordertoobtainnumericales-timatesforsomedenitepropertiesofthehypothetical,newcoherentcondition.Themodelispatternedafterthephenomenonofpioncondensationinasucientlydensemediumofnucleons[10,11].Thepionsarereplacedbyquasi{pionswhicharecorrelatedquark{antiquarkpairswithsmall(mass)2.Thedense(\cold)mediumofnucleonsisreplacedbyadensemediumof\dressingquarksandantiquarksformedinthecollision.Inthismediumthequasi{pionspropagateandinteractwiththefermionsviastrong,low{energyP{waveinteractions,justaspionsdoinamediumofnucleons.Inthismodelweexaminethepossibilityfortheoccurrenceofacoher-entconditionwhichcontributesanegativeenergydensityintheextendingmedium.Theessentialdynamicalelementwhichmakesthispossibleistheexistenceofapseu-doscalar(quasi{)bosonwithquitesmall(mass)2andstrong,low{energyP{waveinteractionwithfermions.Thisallowsforthepossibilityofcancellationoftheposi-tive,kineticand(mass)2termsbytheattractivemomentum{dependentinteraction[10,11].Thehypotheticalcoherentconditionwhichisdynamicallyinstigatedfollow-ingthecollision,isevolvingtowardsome(idealized)equilibriumsituation,butitislimitedbytheintrinsic,thoughextendedpropertimeforthesystemtobreakdownintoafewpions.Thereforeonepropertythatweseekareasonforandestimateofistheextendedpropertimeforthesystemtoexistpriortobreakingdown.Ingeneral,thecenterofmassofthedevelopingcoherentsystemcanmoverapidlyalongthecol-lisionaxisinthecollisioncenterofmass(andmorerapidlyalongthebeamdirectioninthelaboratorysystem).ThislongitudinaldimensionisLorentz{contracted;theintrinsictimeintervalisdilated.Asecondpropertythatweestimateistheextensionofthesystemoverthetransverseplaneduringtheintrinsictimeintervalpriortoitsbreakdownintoafewpions.Weestimatethemagnitudeofthemomentumwhich3characterizesthecoherentoscillatorybehaviorofmatteroverthetransverseplane,andweestimatethefermionicdensitywhichsustainsthisbehavior.Wec