$pi to pipi$ results in nuclei

1002 peS 11 1v7009010/ex-lcu:nviXraP.Camerinia,b,E.Fragiacomoa,b,N.Griona,1,R.Ruia,b,J.T.Brackc,E.F.Gibsond,G.J.Hofmane,E.L.Mathief,R.Meierg,K.Raywoode,M.E.Seviorh,G.R.Smithe,2andR.

Tacikf.

a

IstitutoNazionalediFisicaNucleare,34127Trieste,Italy

bDipartimentodiFisicadell’Universita’diTrieste,34127Trieste,Italy

cUniversityofColorado,BoulderCO80309-0446,USAdCaliforniaStateUniversity,SacramentoCA95819,USA

eTRIUMF,Vancouver,B.C.,CanadaV6T2A3

fUniversityofRegina,Regina,Saskatchewan,CanadaS4S0A2gPhysikalischesInstitut,Universit¨atT¨ubingen,72076T¨ubingen,GermanyhSchoolofPhysics,UniversityofMelbourne,Parkville,Vic.,3052,Australia

oftheTheπ−CrystalA→+π0Ballπ0A(′CB)collaborationatBNLhasrecentlypresentedresultsregardingastudybutfortheπA→π+reactionπ±A′onH,D,C,AlandCu,usinganearly4πdetector.Similarresults,thereactionon2H,12C,40Ca,and208Pb,havebeenpublishedearlierbytwoCHAOSfeatures.measurementscollaborationInparticular,ismade,attheincreasewhichTRIUMFshows.instrengththatInthistheBriefasaCHAOSReportfunctionandaofACBcomparisonseendataoftheresultsoftheinthesharenear-thresholdrelevantcommonπ+π−invariantthetwofrommassexperiments.

thespectratwogroupsreportedarebycomparedtheCHAOSinawaygroup,whichisalsoaccountsseeninforthetheπ0π0resultsdifferentCBdata,acceptanceswhentheofPACS:25.80Hp

Thephenomenonofnuclearmediummodificationofππpropertieshasbeenthefocusofagrowingnumberofrecentstudies.AselectionofthemostrecenttheoreticalarticlescanbefoundinRef.[1].TheauthorsthereinhavereanalysedthemodificationscausedbynuclearmatteratfinitedensityfortheππinteractionintheI=J=0channel(theσ-mesonchannel),andfoundadramaticreshapingoftheππinteractionstrengthfunctionataroundthe2mπthreshold.Thereshapingresultsinastrongenhancementofthestrengthfunctionaround2mπ,whichisdeterminedbythecombinedeffectofcollectivepionicmodesandpartialrestorationofchiralsymmetry.ThefirsteffectisexplainedintermsofstandardP−wavecouplingofpionstoparticle−holeand∆−holecorrelatedstates.Theeffectofpartialrestorationofchiralsymmetryinnuclearmatterrelatestothemodificationofthebasic(ππ)I=J=0interaction:inthescalar-isoscalarchannel,pionpairsstronglyinteract

withthenucleonsgivingrisetotheelusiveσ−meson,evenatdensitiesbelowthenuclearsaturationdensity.SuchapictureofππdynamicsinnuclearmatterissupportedbytheexperimentalresultsoftheCHAOScollaboration.Theseresults,however,seeminparttobecontradictedbytherecentlypublisheddatafromtheCBcollaboration.ThepurposeofthisBriefReportistomakeamorecarefulcomparisonwhichaccountsforthedifferentacceptanceofthetwoexperiments.Suchacomparisonrevealsthatinfactthemainresultsoftheexperimentsareingoodagreementwitheachother.

TheTRIUMFpionproductionprogrammeasuredtheπ+A→π+π±A′reactionon2H,12

C,40Ca,and208Pbatpπ+=399MeV/c,usingtheCHAOSspectrometer[2].CHAOSconsistsofadipolemagnetproducingaverticalfieldandfourringsofcylindricalwirechambersforthetrackingofchargedparticles.Theoutermostwirechamberissurroundedbyasegmentedtelescopeforparticleidentification.Particlesfromapionproductionreaction(π,2π)aremeasuredinthehorizontalplane(360◦),and±7◦outofthisplaneforasolidangleof∼10%of4πsr.TheCBcollaborationreportedresultsfromastudyoftheπ−A→π0π0A′reactiononH,2H,C,AlandCuatpπ−=408MeV/c,usingaNaI(Tl)crystalballwhichcovered93%of4πsr[3].Thedetectorisamultiphotonspectrometer,thuscapableofdetectingπ◦’sinthefinalstate.Chargedparticlesarevetoedbyaplasticscintillatorbarrelwhichsurroundsthetarget.Table1reportsthequantitieswhicharerelevanttothefurtherdiscussion.SincetheCBdetectorhasalargersolidanglecoverage,theCBdatacouldinprinciplebeanalysedandreducedtotheCHAOSsolidangle.Inthismanner,theresultsofthetwomeasurementscouldbedirectlycompared.Thisapproach,unfortunately,isimpracticalbecauseofthelowstatisticsoftheCBdata.InthecaseofH(Fig.2ofRef.[3]),thelow-energyyieldat∼284MeVnearlyequalsthestandarddeviationthusimplyingthatthebincontentis∼1.Aboutthesameamountisaccumulatedinthe∼293MeVbin.Aswell,thedeuteriuminvariantmass(Mππ)spectrum(Fig.3)displaysthesamefeatures.Thecomparisonwillthereforebeaddressedtothebulkofthe(π,2π)results.

AnalysesoftheCHAOSworkfocusedonstudiesoftheA-dependenceofthereactionatthreshold[4],thereactionmechanism[5],thepropertiesoftheππsysteminvacuum[6,7]andinnuclearmatter[8,9].SomeofthepreviouslypublishedCHAOSresultsmostrelevanttothisBriefReportaresummarisedinthefollowing.

Table1:RelevantquantitiesintheCBandCHAOSmeasurements.ThenotationsTπandMππindicatethesinglepionkineticenergyandtheππinvariantmass,respectively.

CB0.093%∼03.3−7.1π−→π0π0CHAOS0.510%∼111.1−2.1π+→π+π±

Theπ→ππreactioninnucleiisaquasifreeprocess,whichinvolvesasinglenucleonandproceedsviaπN→ππN[5].

Nearthe2mπthreshold,theπ+π−interactingsystempredominantlycouplesinS-wave(∼95%),whileP-wavecouplingisnegligible[4,9].TogetherwiththeargumentspresentedinRef.[10],thispermitsthequantumnumbersI=J=0tobeassignedtotheπ+π−system.Thesamequantumnumbersarereadilyreachedbythepureisospin0π0π0systemintheCBmeasurement.Therefore,theπ+π−systemcanbedirectlycomparedtotheπ0π0system.ThemoststrikingphysicsresultfromtheCHAOSdataistheremarkableA-dependenceobservedintheπ+π−invariantmass(Mππ)distributionsataroundthe2mπthreshold[9].Unfortunatelythedataalsoexhibitapeakinthissameregionwhichisanartifactofthelimitedout-of-planeacceptanceofthespectrometer.TheMππresolution(1.1-2.1MeV)doesnotexceedtheMππbinning(8.7MeV),soresolutiondoesnotaffecttheshapeoftheMππdistributions.ThephysicsisintheobservedA-dependenceofthenearthresholdMππdistributions,notinthepeakitself.Furthermore,thepeakisalsoobservedinthesimulta-neouslymeasuredisospin2π+π+invariantmassdistributions,whichexhibitnoremarkableA-dependence,andappearsinthephase-spacesimulations.Thishasbeenconsistentlyex-plainedineachoftheCHAOSarticles.

TheobservableCAππwasdefinedinRef.[8]preciselyinordertodisentangletheaccep-tanceissuefromthephysicsobservedintheA-dependence,andthereforefocusexclusively

AMππAN

onmediumeffects.CA,whereσ(σ)isthemeasuredisthecompositeratioNTTππσT

totalcrosssectionofthe(π,2π)processinnuclei(nucleon).Thisobservablewasshowntoyieldtheneteffectofnuclearmatterontheππinteractingsystem,regardlessofthereac-tionmechanismusedtoproducethepionpair,andtobenearlyunrelatedtotheCHAOSacceptance.ThesetraitsandthepointsdiscussedaboveensurethatthecompositeratioCAππshouldbenearlythesamefortheCHAOSandtheCBmeasurements,despitethedifferentsolidanglessubtendedbythetwoexperiments.

BeforeusingtheacceptanceindependentCAππtomakeameaningfulcomparisonoftheCB[3]andtheCHAOS[4−9]results,somecommentsontheCBresultsareneeded.Theexperimentaldataforthe2π0invariantmassdistributions(Figs.2and3ofRef.[3])areingeneralcharacterisedbylowstatistics.Onlyafew(π,2π)eventswereaccumulatedinthelow-energyyieldforHand2H.Thisisveryunfortunate,sincethesepoorstatisticsoccurexactlyinthemostinterestingregionoftheinvariantmassdistribution,whereCAππdepartsfromaflatbehaviour[8].

Fig.3ofRef.[3]showstheexperimental2π0invariantmassdistributionsforthestudiednucleicorrectedfortheCBacceptance.TheCBdata(inarbitraryunits)arecomparedtothemodelcalculationofVicente-Vacas[11],dashedline,andRapp[12],fullline.ForH

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(and2H,seeRef.[9]),thecurvesareabletoreproducetheshapeoftheMππexperimentaldistribution.InthecaseofC,thewideningofthedistributiontowardhighenergiesreflectstheFermimotionofthestrucknucleon,π−p[A−1]→π0π0n[A−1].ForAlandCu,thesefeaturesseemcontradictedbytheshrinkingofthedistributions.TheMππhigh-energytailappearsdepletedratherthanfurtherexpandedeventhoughthemodels,whichincludetheFermimotion,predictanon-negligibleyield20-30MeVabovetheCBdata.

The2π0invariantmassesaregiveninarbitraryunitsinRef.[3],whichprecludescom-parisontoanabsoluteprediction.Normalizingsimulations(Fig.2)andmodelpredictions(Fig.3)todatacanleadtoambiguousinterpretations.Forinstance,theCu-targetdatainFig.3arepoorlydescribedbythecurvesofVicente-Vacas(dashedline)andRapp(fullline),thusanyanalysisisinconclusive.IfthecurveswerenormalisedtotheMππhigh-energytail,thenthedatawouldhaveexplicitlydisplayedanaccumulationofstrengthatthreshold.Ontheotherhand,ifthecurveswerenormalizedtolow-energyinvariantmasses,thenthecomparisonwouldhavedisclosedaratherstrongdepletionoftheMππhigh-energyyield.Thecaseforthehydrogentargetisdifferent:thetheoreticalpredictionsseemtobenormalizedtotheexperimentaldata.ThecalculationbyVicente-Vacasagreesalmostperfectlywiththedata,whichreflectsthedetailedmicroscopicdescriptionoftheelementaryπN→ππNreaction.ThemodelofRapp,whichmissessomeimportantdiagrams,overestimatestheMππyields(from2to3times)inthelow-energyinterval.ThesamequantitativeconclusionforthehydrogentargetisalsoreachedusingtheCHAOSdata[9].

Finally,theresultsofCHAOSarecomparedtotheresultsfromtheCBCollaboration.TheauthorsofRef.[3]repeatedlymakethepointthattheydonotobservethepeakinthenearthresholdinvariantmassthatisobservedbyCHAOS.Asnotedabove,thisismerelyanexpectedconsequenceofthedifferentacceptancesofthetwodetectors.

TheresultsshowninFig.4ofRef.[3]leadtotheconclusionthatthenuclearmediumasrepresentedbynucleiD,C,AlandCuchangestheπ−πinteractioninsuchawaythattheπ0π0invariantmassdistributionfromcomplextargetsisclosertothephase-spacedistributionthanisthesamedistributionfromH.ThesebroadfeaturescanalsobefoundintheCHAOSdata:thephase-spacesimulationsfortheπA→ππN[A−1]reactionreportedinFig.9ofRef.[9](shadedregions)shouldjustbecomparedtotheπ+π−invariantmassdistributions(diamonds).ThehigherAπ+π−resultsclearlymatchthephasespacecalculationsbetterthanthelowerAπ+π−resultsdo.Thesefindings,however,donotdisclosethenatureofthethresholdenhancementoftheπ+π−invariantmassdistributions.Aspointedoutbythe

AA

CHAOSresults,comparisonofMπ+π−withMπ+π+providesusefulinsightintoππdynamics

A

innuclearmatter.Fig.9ofRef.[9]showsthattheMπ+π+distributionsareaccountedforwellbytheπA→ππN[A−1]phase-spacefrom2Hto12Cto40Caandto208Pb,andthemaximuminvariantmassincreaseswiththeincreaseofthenucleonFermimomentum

A

(i.e.,A),asonewouldexpect.Incontrast,theMπ+π−strengthnearthresholdisnegligiblefor2H,andstronglyincreasesasAincreases.Thisenhancementisattributedtomedium

4

diamonds,theCCπ0π0

C

theCHAOSCπ+π−

Figure1:ThecompositeratiosCAππasafunctionoftheππinvariantmassforthe

Ctarget.Full

distributiondeducedfromthedataofRef.[3]asexplainedinthetext;opendiamonds,distributiontakenfrom[9].

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modificationsinthe(ππ)I=J=0interactingsystem[8].

A

IntheI=J=0channel,boththeCBandCHAOSmeasurementsfindtheMππyieldtobeclosetozeronearthe2mπthresholdforA=(1or)2,whileitincreaseswithincreasingA.ThecompositeratioCAπ+π−discussedinRefs.[8,9]canbederivedfromtheCBdataby

AHA

dividingtheMπ0π0bytheMπ0π0yields.Cπ0π0fortheC-target(theonlynucleusincommontothetwoexperiments)isshowninFig.1withfulldiamonds.Asdiscussedabove,CCπ0π0

A

canbedirectlycomparedwithCCπ+π−.SincetheMπ0π0distributionsweregiveninarbitrary

C

units,CCπ0π0isnormalizedtoCπ+π−intheenergyrangeabove350MeV,wherethetwodistributionsareflat.ThelargeerrorbarsassociatedwithCCπ0π0reflectthepoorstatistical

H

contentofMπ0π0aroundthreshold.ItisworthwhilecomparingtheCBandCHAOSratiosforCsincetheyconveyrelevantcommonfeatures:theybothareflatat∼350MeV,arepeakedatthresholdandarecomparableinstrength.Infacttheagreementbetweenthetwoexperimentsisremarkablygood.ThecuriousdepletionoftheinvariantmassyieldforAlandCuobservedinRef.[3]makesaclosecomparisonbetweenCs’forthesetwotargetsof

C

questionablesignificance.TheirCAπ0π0distributions,however,resembletheCπ0π0one.

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Insummary,thenumberofcurrentinternationalworkshops[13]devotedtothestudyofhadronicpropertiesinnuclearmatterrevealstheincreasingimportanceofthisfieldofnuclearphysics.Inthisrealm,thecorrelatedsystemoftwopionsintheI=J=0channelembodiesaspecialrole:(ππ)I=J=0isthelighterobjectcarryingthequantumnumbersoftheQCDvacuum.Ontheotherhand,experimentalstudiesofthebehaviourofpionpairsinnuclearmatterarefairlyrecent.TheCBmeasurementexaminedtheA-dependenceofpion-inducedpionproductionat408MeV/cintheπ0π0neutralchannel.AnearlierstudyundertakenbytheCHAOScollaborationreportedontheπ+π±channelsatanincidentpionmomentumof399MeV/c.Asfarasthe(ππ)I=J=0interactingsystemisconcerned,theCBresultssharerelevantcommonfeatureswiththeCHAOSresults.Whenthetwoexperimentsarecomparedusinganobservabledesignedtomitigateacceptancedifferences,theresultsagreewitheachotherverywell,althoughthestatisticalqualityoftheCBdatainthemostinteresting,near-thresholdregionismarginal.ThisagreementmaybeinterpretedasanindipendentconfirmationbytheCBmeasurementofthenuclearmattermodificationsintheI=J=0ππsystem,firstreportedbyCHAOS.

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