N.Akchurina,L.Berntzona,A.Cardinib,R.Ferraric,G.Gaudioc,J.Hauptmand,H.Kima,L.LaRotondae,M.Livanc,E.Meonie,H.Paarf,A.Penzog,D.Pincih,A.Policicchioe,S.Popescui,1
G.Susinnoe,Y.Roha,W.VandellicandR.Wigmansa,2
a
TexasTechUniversity,Lubbock(TX),USA
bDipartimentodiFisica,Universit`adiCagliariandINFNSezionediCagliari,ItalycDipartimentodiFisicaNucleareeTeorica,Universit`adiPaviaandINFNSezionedi
Pavia,Italy
dIowaStateUniversity,Ames(IA),USA
eDipartimentodiFisica,Universit´adellaCalabriaandINFNCosenza,Italy
fUniversityofCaliforniaatSanDiego,LaJolla(CA),USA
gINFNTrieste,Italy
hDipartimentodiFisica,Universit`adiRoma”LaSapienza”andINFNSezionediRoma
iCERN,Gen`eve,Switzerland
1Introduction
Inrecentyears,therehasbeenagrowinginterestinleadtungstate(PbWO4)crys-talsasdetectorsforhigh-energyparticles.AtCERN’sLargeHadronCollider,boththeCMS[1]andALICE[2]experimentsarecompletingverylargeelectromag-netic(em)calorimetersystemsconsistingofthesecrystals.Smallerdetectorsofthistypeareeitheroperatingorplanned,forexampleforthePANDA[3]andHY-CAL[4]experiments.Leadtungstatecrystalsareattractiveasdetectorsforemshowersbecauseoftheirhighdensity,whichimpliesashortradiationlengthandMoli`ereradius,theirfastsignalsandtheirrelativeinsensitivitytotheeffectsofra-diationdamage.Onthedownside,wementionthesmalllightyield,lessthan1/300ofthelightyieldofthewidelyusedNaI(Tl)andCsI(Tl)crystals[5].Becauseofthissmalllightyield,andthelargeeffectiveZvalue,itisreasonabletoassumethatasignificantfractionofthelightproducedbyPbWO4ofCerenkovˇcrystalsisactuallytheresultradiation,ratherthanmolecularde-excitation.WehaveshownpreviouslythatthecombinedavailabilityofCerenkovˇandscintil-lationsignalsforhadronicshowersmakesitpossibletoeliminatetheeffectsofthedominatingsourceoffluctuationsincalorimetrichadrondetection,andthuscon-siderablyimprovehadroniccalorimeterperformance[6].However,becauseofsmallCerenkovˇthe
lightyield,samplingcalorimetersarelessthanidealfortakingfulladvantageofthis.Ontheotherhand,homogeneouscalorimeterswhoselightnalscouldbesplitintoscintillationandCerenkovˇsig-componentsholdgreatpromise
forhigh-qualityhadroncalorimetry[7].
Forthesereasons,wesetouttomeasurethecompositionofthesignalsproducedbyPbWO4crystals3.InSections2and3,wedescribethemethodsusedtode-terminetheCerenkovˇcomponentofthemeasuredsignals,andtheexperimental
setupinwhichthecrystalsweretested.InSection4,wediscusstheexperimentaldatathatweretakenandthemethodsusedtoanalyzethesedata.InSection5,theexperimentalresultsarepresentedanddiscussed.AsummaryandconclusionsarepresentedinSection6.
2MethodstodistinguishCerenkovˇfromscintillationlight.
IfonewantstodistinguishthecontributionsfromtheCerenkovˇandscintillation
componentstothesignalsfromcrystalsthatgenerateamixtureofthese,suchasPbWO4,onecoulduseoneorseveralofthefollowingcharacteristics:
(1)Directionality.TheCerenkovˇlightisemittedatafixedanglewithrespectto
themomentumvectoroftheparticlethatgeneratesit,whilethescintillationlightisisotropicallyemitted.
(2)Timestructure.TheCerenkovˇlightisprompt,whereasscintillationprocesses
haveoneorseveralcharacteristic(3)Thespectrum.TheCerenkovˇdecaytimes.
lightisemittedwithacharacteristicλ−2spec-trum,whilethescintillationprocesseshavetheir(4)Polarization.Contrarytoscintillationlight,Cerenkovˇowncharacteristicspectra.
lightispolarized.Inthepresentstudy,wehaveexploitedthefirsttwocharacteristics.Itisawell
knownfactthatthelightyieldofPbWO4crystalsisverytemperaturedependent.Itchangesby-2.3%perdegreeCelsius.Thisisobviouslyonlytrueforthelationlight.Therefore,thefractionofthelightthatisproducedbytheCerenkov
ˇscintil-mechanismisexpectedtoincreasewithtemperature.Ourmeasurementshavebeenperformedatroomtemperature.OneshouldkeepthisinmindwhentranslatingourresultstotheALICEexperiment,fromwhichthecrystalswetestedwereborrowed.TheALICEPbWO4calorimeteroperatesatamuchlowertemperature(−wheretherelativecontributionsofCerenkovˇ15◦C),
lighttothesignalsarecorrespond-inglysmaller4.
2.1Directionality
Cerenkovˇlightisemittedbychargedparticlestravelingfasterthanc/n,thespeed
oflightinthemediumwithrefractiveindexninwhichthisprocesstakesplace.Thelightisemittedatacharacteristicangle,θC,definedbycosθC=1/βn.Inthecaseofsufficientyrelativisticparticles(i.e.,β∼1)traversingPbWO4crystals(n=2.2),θC∼63◦.
InordertodetectthecontributionofCerenkovˇlighttothesignalsfromaPbWO4
crystal,weequippedbothendsofthecrystalwithaphotomultipliertube(PMT).Byvaryingthedetectororientationwithrespecttothedirectionoftheincoming
particles,acontributionofCerenkovˇlightwouldthenmanifestitselfasanangle-dependentasymmetry.ThisisillustratedinFigure1,whichshowsthesetupofthe
initialmeasurementsweperformedwithacosmic-raytelescopetotestthisprin-ciple[7].ThePMTgainswereequalizedfortheleftmostgeometry,inwhichthecrystalwasorientedhorizontally.Bytiltingthecrystalthroughanangle(θ)thattheaxisofthecrystalisattheCerenkovˇsuch
angleθCwithrespecttotheparticle
direction,Cerenkovˇlightproducedbythecosmicraystraversingthetriggercoun-terswouldbepreferablydetectedineithertheL(centralgeometry)orR(rightmost
geometry)PMT.Bymeasuringtheresponseasymmetrytionofthetiltangleθ,thecontributionofCerenkovˇ(R−L)/R+L)asafunc-lighttothedetectorsignals
Fig.1.PrincipleoftheasymmetrymeasurementusedtoestablishthecontributionofˇCerenkovlighttothesignalsfromthePbWO4crystals.Dependingontheorientation,thisdirectionallyemittedlightcontributesdifferentlytothesignalsfromtheleftandrightpho-tomultipliertubes.
couldbedetermined.
ˇTheinitialcosmic-raymeasurementsindicatedthatthecontributionofCerenkov
lightwasatthelevelof15-20%[7].Becauseoftheextremelyloweventratesandthetinysignals(typically20-30MeV),wedecidedtoperformsystematicstudiesusingparticlebeams.Theresultsofthesestudiesarethetopicofthepresentpaper.
2.2Timestructure
ThescintillationprocessinPbWO4hasadecayconstantof∼10ns,whereastheˇCerenkovcomponentofthesignalsisprompt.Inthecosmic-raymeasurementsmentionedabove,wealsostudiedthetimestructureofthesignals,usingafastoscilloscopecapableofstoringbothpulseshapessimultaneously.Thesemeasure-mentsqualitativelyconfirmedtheexpecteddifferencesbetweenthesignalsmea-suredintheRandLPMTs[7].However,lowstatisticsandverysmallsignalslimitedthequalityoftheinformationthatcouldbederivedfromthesemeasure-ments.Inthebeammeasurementsdescribedhere,wemeasuredthesignalshapeswithveryfastFlashADCs(effectivesamplingfrequency800MHz).AsisshowninFigure2,thisturnedouttobeawonderfulexperimentaltool.Inaperiodofafewdays,detailedpulseshapeswererecordedformillionsofevents.Thefigureclearlyshowstheadditionalpromptsignalcomponentthatappearswhenthecrystalisro-ˇtatedfromapositioninwhichCerenkovlightdoesnotcontributetothesignals
(θ=−30◦)toapositionwhereitdoes(θ=30◦).ThetrailingedgeofthePMTsignalsisnotaffectedbythisrotationandisindeedingreatdetail(includingthe
4
Fig.2.AveragetimestructureofthesignalsmeasuredwiththePMTreadingoutoneend(R)ofaPbWO4crystaltraversedby10GeVelectrons,fortwodifferentorientationsofcrystal.Atθ=30◦,Cerenkovˇthe
lightcontributestothesignals,atθ=−30◦,itdoesnot.
effectsofreflectionsinthesignalcables)identicalforthesetwopulseshapes.
3Experimentalsetup3.1Detectorandbeamline
ThemeasurementsdescribedinthispaperwereperformedintheH4beamlineof
theSuperProtonSynchrotronatCERN.OurdetectorwasaPbWO4crystalwithalengthof18cmandacrosssectionof2.2×2.2cm2.Thetransversedimen-sion,relevantforourmeasurements,correspondsto2.5radiationlengths.Thelightproducedbyparticlestraversingthiscrystalwasreadoutbytwophotomultipliertubes5,locatedatoppositeends.InordertoreducethelighttrappingeffectsofthelargerefractiveindexofPbWO4,thePMTswerecoupledtothecrystalbymeansofsilicone“cookies”(n=1.403).
Thiscrystalwasmountedonaplatformthatcouldrotatearoundaverticalaxis.Thecrystalwasorientedinthehorizontalplaneandtherotationaxiswentthroughitsgeometricalcenter.Theparticlebeamwasalsosteeredthroughthiscenter,asillustratedinFigure3.Theangleθ,whichisfrequentlyusedinthefollowing,rep-resentstheanglebetweenthecrystalaxisandaplaneperpendiculartothebeamline.TheangleincreaseswhenthecrystalisrotatedsuchthatthecrystalaxisL-Rapproachesthedirectionofthetravelingbeamparticles.ThecrystalorientationsshowninFigures2and3correspondthustoθ>0andθ<0,respectively.
Fig.3.Experimentalsetupinwhichthebeamtestswereperformed.
Twosmallscintillationcountersprovidedthesignalsthatwereusedtotriggerthedataacquisitionsystem.TheseTriggerCounters(TC)were2.5mmthick,andtheareaofoverlapwas6×6cm2.Acoincidencebetweenthelogicsignalsfromthesecountersprovidedthetrigger.
3.2Dataacquisition
Measurementofthetimestructureofthecrystalsignalsformedaveryimportantpartofthetestsdescribedhere.Inordertolimitdistortionofthisstructureasmuchaspossible,weused15mmthickair-corecablestotransportthedetectorsignalstothecountingroom.Suchcableswerealsousedforthesignalsfromthetriggercounters,andthesewereroutedsuchastominimizedelaysintheDAQsystem6.Dependingonthedesiredtypeofinformation,thecrystalsignalswereeithersenttoachargeADC,ortotheFADC.Theresponseasymmetrymeasurementswerebasedonthedigitizedintegratedcharge,thetimestructurewasmeasuredwiththeFlashADC7,whichdigitizedtheamplitudeofthesignalsatarateof200MHz.Duringatimeintervalof80ns,16measurementsoftheamplitudewerethusob-tained.Inordertofurtherincreasethisrate,andthusimprovethetimeresolutionofthismeasurement,weusedseveralinputchannelsforeachsignal.Thecrystalsignalsweresplit(passively,withcorrectimpedancematching)into4equalpartsatthecountingroomend.These4signalsweremeasuredseparatelyin4differentchannelsoftheFADCmodule.Signals2,3and4weredelayedby1.25ns,2.50nsand3.75nswithrespecttosignal1.ByusingtheFADCmoduleinthisway,the
timestructureofthesignalswasthuseffectivelymeasuredwitharesolutionof1.25ns(800MHz).
ThequalityoftheinformationobtainedinthiswayisillustratedinFigure2,whichshowstheaveragetimestructureofthesignalsfrom10GeVelectronstraversingthecrystalforθ=30◦and−30◦,respectively.
Thechargemeasurementswereperformedwith12-bitLeCroy1182ADCs.Thesehadasensitivityof50fC/countandaconversiontimeof16µs.TheADCgatewidthwas100ns,andthecalorimetersignalsarrived∼20nsafterthestartofthegate.
ThedataacquisitionsystemusedVMEelectronics.AsingleVMEcratehostedalltheneededreadoutandcontrolboards.ThetriggerlogicwasimplementedthroughNIMmodulesandthesignalsweresenttoaVMEI/Oregister,whichalsocollectedthespillandtheglobalbusyinformation.TheVMEcratewaslinkedtoaLinuxbasedcomputerthroughanSBS6208opticalVME-PCIinterfacethatallowedmemorymappingoftheVMEresourcesviaanopensourcedriver9.Thecomputerwasequippedwitha2GHzPentium-4CPU,1GBofRAM,andwasrunningaCERNSLC4.3operatingsystem10.
Thedataacquisitionwasbasedonasingle-eventpollingmechanismandperformedbyapairofindependentprogramsthatcommunicatedthroughafirst-in-first-outbuffer,builtontopofa32MBsharedmemory.Onlyexclusiveaccesseswereal-lowedandconcurrentrequestsweresynchronisedwithsemaphores.ThechosenschemeoptimizedtheCPUutilizationandincreasedthedatatakingefficiencybyexploitingthebunchstructureoftheSPS,wherebeamparticleswereprovidedtoourexperimentduringaspillof4.8s,outofatotalcycletimeof16.8s.Duringthespill,thereadoutprogramcollecteddatafromtheVMEmodulesandstoredthemintothesharedmemory,withsmallaccesstimes.DuringtheremainderoftheSPScycle,arecorderprogramdumpedtheeventstothedisk.Moreover,thebufferpresenceallowedlow-prioritymonitoringprogramstorun(off-spill)inspymode.Withthisscheme,wewereabletoreachadataacquisitionrateashighas2kHz,limitedbytheFADCreadouttime.Thetypicaleventsizewas∼1kB.Alldetectorsignalsweremonitoredon-line.
3.3Calibrationofthedetectors
Theabsolutecalibrationofthesignalsgeneratedbythecrystalwasnotamajorconcerninthesetests.Ontheotherhand,itwasabsolutelyessentialthatthegains
ofthe2PMTs,LandR,thatcollectedthelightgeneratedinthecrystalsatthetwooppositeendsofthecrystalwereequalized.Weused10GeVelectronsforthatpurpose.Thecrystalwasorientedsuchthatthebeamenteredthedetectorperpen-ˇdiculartothecrystalaxis(θ=0),sothatanyCerenkovlightgeneratedbythe
beamparticleswouldbeobservedinthesameproportionbybothPMTs.Thehighvoltageswerechosensuchthattheaveragesignalswereabout300ADCcountsabovethepedestalvalue.Off-line,thecalibrationconstantswerefine-tunedsuchastoequalizetheresponsesofthetwoPMTs.
4Experimentaldata
Thecrystalswereexposedtobeamsof150GeVµ+and10GeVelectrons.Theangleθbetweenthecrystalaxisandtheplaneperpendiculartothebeamlinewasvariedfrom−45◦to45◦,instepsof7.5◦.Ateachangle,100000eventswerecollectedfortheresponseasymmetrymeasurements,andanother100000forthetimestructure.
Sincetheparticlestraversedthedetectorperpendiculartothelongitudinalcrys-talaxis,theeffectivethicknessofthecrystalwasonlyafewradiationlengths(2.5X0/cosθ)inthissetup.Inordertoprobetheemshowersatgreaterdepth,wealsoperformedaseriesofmeasurementsinwhichtheelectronstraversed4cmoflead(∼7X0)installeddirectlyupstreamofthecrystal.Inthisway,thelightgeneratedinthecrystalsreflectedtheparticledistributionjustbeyondtheshowermaximum,atadepthof7−10X0.Toavoidintroducingtoolargeachangeinthiseffectivedepth,thelattermeasurementswerelimitedtoanglesθrangingfrom−30◦to30◦.Separatemeasurementswereperformedoftheresponseasymmetryandofthetimestructure.Asbefore,100000eventswerecollectedforeachrun.
5Experimentalresults5.1Left-Rightasymmetry
Wedefinetheresponseasymmetryastheratio(R−L)/(R+L),whereRandLrepresenttheaveragesignalsmeasuredinthePMTsRandLforthesameevents.Sincethesesignalswereequalizedforθ=0,anynon-zerovalueinthisratioisindicativeforanon-isotropiccomponentinthelightgeneratedinthecrystals,
ˇi.e.,Cerenkovlight.Therelationshipbetweenthisresponseasymmetry(tobecalledαinthefollowing)
8
ˇandtherelativecontributionofCerenkovlighttothePMTsignals11canbeseen
ˇasfollows.IfwecalltherelativecontributionsofCerenkovlighttotheRandL
signalsǫRandǫL,respectively(withǫRandǫLnormalizedtothescintillatorsignalsineachchannel),then
ǫR−ǫL
α=
1+ǫR
=
2α
11
ItshouldbeemphasizedthatthisdiscussionconcernsthePMTsignals,andnotthenum-bersofphotonsproducedbythedifferentmechanisms.Forthelatter,differencesinproduc-tionspectraandphotocathodequantumefficiencieswouldhavetobetakenintoaccount.
9
Fig.4.Left-rightresponseasymmetrymeasuredfor10GeVelectronsshoweringina2.5X0thickPbWO4crystal,asafunctionoftheorientationofthecrystal(theangleθ).Resultsareshownfortheearlyandthelatecomponentsoftheshowers.Thelattermeasurementswereobtainedbyplacing4cmofleadupstreamofthecrystal.
ˇtotalacceptanceforCerenkovlightinbothPMTscombinedreachesitsminimum
value.
Theaboveargumentsare,strictlyspeaking,onlyvalidforparticlesthattraversethecrystalinadirectionparalleltothebeam.Upontraversingthecrystal,thebeamelectronslosealargefractionoftheirenergy(typically>80%)radiatingbremsstrahlungphotons.Therelativisticelectronsandpositronsproducedwhenthesephotonsconvertinthecrystaltravelalsopredominantlyinthesamedirection.Forthepurposeofthisexperiment,theearlypartoftheelectromagneticshowersprobedinthismeasurementthusresemblesacollectionofparticlestravelingallapproximatelyinthesamedirection,i.e.,paralleltothebeamline.
However,astheshowerdevelops,sodoesitsisotropiccomponent.ThiscomponentisprimarilyduetoshowerelectronsgeneratedinComptonscatteringorthroughthephotoelectriceffect.Infullycontainedemshowers,thiscomponentisresponsibleforabouthalfofthesignal[8].Itisalsothankstothiscomponentthat0◦quartz-fibercalorimeters,suchastheCMSHF,producemeaningfulsignals[9].
Forthisreason,wealsowantedtomeasuretheeffectofthisincreasedisotropyontheleft/rightresponseasymmetry.Byplacing4cmofleaddirectlyupstreamofthecrystal,theelectronshowersdevelopedinalead/PbWO4combination.For10GeVelectrons,theshowermaximumwaslocatedatadepthof∼5X0,(i.e.,insidethe
10
leadabsorber),andthecrystalprobedthelightproducedatadepthof7−10X0.Figure4alsoshowstheresponseasymmetrymeasuredforthislight.Theasym-metryisconsiderablysmallerthanforthelightproducedintheearlypartoftheshower,byaboutafactorofthree.Yet,thecharacteristicsofthe(R−L)/(R+L)curveindicatethatalsointhiscase,theasymmetryistheresultofthecontribu-ˇtionofCerenkovlighttothesignals.Thereductioninthenetdirectionalityofthe
measuredlightindicatestheimportanceoftheisotropicshowercomponent.Inanotherpaper,wedescribetheresultsofmeasurementsweperformedon(almostfully)containedelectromagneticshowerswithaPbWO4calorimeter.Inthatcase,theasymmetryresultedfromtheintegrationoverthefulllongitudinalshowerpro-file,withtheearlypartcontributingmosttothenetasymmetryandthelatestpartsverylittle,ifanything.Wemeasuredforsuchshowersanoverallresponseasym-metryof0.044[10],i.e.,∼60%oftheasymmetryobservedinthefirst2−3X0reportedhere.
Fig.5.Signaldistributionfor150GeVµ+traversingthe2.5X0thickPbWO4crystalper-pendicularly(θ=0).Theinsertshowstheresultsoffitstothemostprobablesignalregion.Seetextfordetails.
Thesignalsmeasuredintheseexperimentswereverysmall.AccordingtoEGS4simulations,10GeVelectronsdepositedonaverage320MeVinthePbWO4crys-tal,whenitwasplacedperpendiculartothebeamline.However,thiswasstilloneorderofmagnitudelargerthanthesignalsrecordedforthemuons.Figure5showsatypicalsignaldistribution,measuredinoneofthePMTsforθ=0.Basedonacomparisonwiththe10GeVelectronsignals,thisdistributiongaveamostprobableenergydepositof25MeV.
11
Fig.6.Left-rightresponseasymmetrymeasuredfor150GeVmuonstraversinga2.5X0thickPbWO4crystal,asafunctionoftheorientationofthecrystal(theangleθ).Theasym-metryconcernsthemostprobablesignalvaluederivedfromaLandaufit(thetriangles)oraGaussianfit(theclosedcircles),ortheaveragesignalvalue(theopensquares).
Themostprobablesignalvaluewasalsousedfortheresponseasymmetrymeasure-mentfortheseparticles.However,theLandaufitsdidingeneralnotreproducethemeasuredsignaldistributionsverywell.Thisisbecausethebeamspotwaslargerthanthetransversesizeofthecrystal.Asaresult,manybeamparticlesmissedthecrystal(asevidencedbythelargepedestalpeakinFigure5),whereasotherstraverseditclosetotheedge,scatteringout,leadingtosub-mipsignals.Forthisreason,wealsostudiedtheleft-rightasymmetryusingtwoothercharacteristicsofthesignaldistribution:theaveragesignalandtheresultofaGaussianfitaroundthemostprobablevalue(seeinsertFigure5).
Theangulardependenceoftheleft-rightasymmetryformuonstraversingthePbWO4crystalisshowninFigure6,forallthreefigures-of-meritderivedfromthesig-naldistributions.Thiscurveshowsthesamegeneralcharacteristicsastheonemeasuredfortheelectrons(Figure4).Themaximumasymmetryismeasuredforθ≈θC(27◦),inthePMTorientedintheoptimaldirectionfordetectingtheˇCerenkovlight.Themaximumasymmetryis∼0.08,whichtranslatesintoa15%
ˇcontributionofCerenkovlighttothetotalsignalsatthatangle(Equation2).It
alsoseemsthattheasymmetryissomewhatsmallerwhentheaveragedetectorsig-ˇnalisusedinsteadofthemostprobablevalue.ThismightindicatethatCerenkov
lightproducedintheradiativecomponentoftheenergylostbythemuonsissome-whatlessdirectionalthanthatproducedbytheionizingcomponent.Thiswouldbeconsistentwiththeobservationsoftheasymmetryinelectromagneticshowers
12
discussedabove.
Basedonthesignaldistributionsobservedinthesemeasurementsandontheas-sumptionthattheenergydepositionby10GeVelectronsiscalculatedcorrectlybyGEANT4,wecandeterminethespecificenergylossofmuonsinPbWO4.Themostprobableenergylossis11.6MeV/cm,whilethemeasuredaverageenergylostby150GeVµ+is13.2MeV/cm.
Fig.7.Distributionoftheleft-rightresponseasymmetry,measuredfor10GeVelectronstraversingthecrystalatθ=30◦,togetherwiththeresultsofaGaussianfit.
Wecanalsodeterminethe“lightyield”ofthecrystalsandPMTsusedinourstud-ies,orratherthenumberofphotoelectronsmeasured(withthePMTschosenforthesestudies)perunitdepositedenergy.Figure7showstheevent-to-eventdistri-butionoftheleft-rightasymmetrymeasuredfor10GeVelectronstraversingthecrystalatθ=30◦,togetherwiththeresultsofaGaussianfit.Atθ=0◦,thewidthofthedistributionincreasedfrom0.0334to0.0384.Ifweassumethatthewidthisdominatedbystatisticalfluctuationsinthenumberofphotoelectrons,thenaσof0.0384translatesintoanaveragenumberofphotoelectronsof∼340perPMT,or∼1photoelectronperMeVdepositedenergy.Atθ=0◦,thewidthofthe(R−L)/(R+L)distributionforthe150GeVµ+was0.1274,whichtranslatesintoanaveragesignalof31photoelectronsperPMT.
Theaveragesignalfromthe10GeVelectronsincreasedby47%whenthecrystalwasrotatedfrom0◦to30◦.Thisreflectstheonsetoftheshowerdevelopment,sinceasimpleincreaseinpathlength(∼cos−1θ)wouldonlyleadtoa15%increase.Themeasuredwidthoftheasymmetrydistributionat30◦(σ=0.0334)correspondstothestatisticalfluctuationsin448photoelectrons/PMT,anincreaseofonly32%withrespecttothe0◦case.Thefactthatthedecreasingwidthdoesnotmatchtheincreasedsignalindicatesthatotherfactors(e.g.,temperatureeffects,responsenon-uniformities)didcontributetothemeasuredwidthandthat,therefore,theestimated
13
lightyieldisinfactalowerlimit.
ThedistributionshowninFigure7illustratesoneotherimportantaspectoftheseexperimentaldata.Allthemeasurementresultsreportedinthispaperconcernav-erages.Boththeobservedleft/rightasymmetries,andalsotheangulardependenceofthetimestructurediscussedinthenextsubsection,concerntheaveragecharac-teristicsofalargenumberofevents,typically100000.Thequestionariseshow
ˇaccuratelyonecandeterminetheCerenkovcontentofthesignalfromoneparticu-lareventonthebasisofthesecharacteristics.Figure7providesananswertothat
question,forwhatconcernstheleft/rightasymmetry.Itshowsthat,ifforaparticu-lar10GeVelectrontraversingthiscrystal,anasymmetryismeasuredof0.080,theexperimentaluncertaintyonthisnumberis0.033(1standarddeviation).Inother
ˇwords,thatparticularsignalcontains14.8±5.9%Cerenkovlight(Equation2).Of
course,thiserrorbarisstronglydeterminedbyphotoelectronstatistics,especiallyattheselowenergies(∼0.4GeV).
Wewanttore-emphasizethatalltheseresultsconcernsoneparticularcrystal,op-eratedatroomtemperature.Noattemptsweremadetocontrolthetemperature,ortomeasureatemperaturedependenceoftheobservedeffects.5.2Timestructureofthesignals
ˇAsecondvaluabletoolforrecognizingthecontributionsofCerenkovlighttothe
calorimetersignalsisderivedfromthetimestructureoftheevents.Thisisillus-tratedinFigure8,whichshowstheaveragetimestructureofthe10GeVshowersignalsrecordedwiththesamePMTatdifferentanglesofincidence,namelyθ=30◦andθ=−30◦.ThediagramsonthelefthandsiteofthisfigureconcernPMTR.ˇCerenkovlightproducedbythetraversingelectronandbytheparticlesproducedintheearlyshowercomponentareexpectedtobedetectedbythisPMTwhenthecrystalisorientedatθ=30◦,whileverylittle,ifanything,willreachthisPMTatθ=−30◦.Thefigureshowsthatthetrailingedgesofbothtimestructuresarealmostcompletelyidentical.Thispartofthetimestructureofthepulsesiscom-pletelydeterminedbythedecaycharacteristicsofthescintillationprocessesinthePbWO4crystalsandshouldthusindeedbeindependentofthedetectororientation.However,thereisaverysignificantdifferenceintheleadingedgeofthepulses.Theonesmeasuredforθ=30◦exhibitasteeperrisethantheonesforθ=−30◦.Thetopgraphsshowtheresultofsubtractingthelatterpulseshapefromthe“30◦”one:Thepulsesrecordedatθ=30◦containanadditional“prompt”componentof
ˇthetypeonewouldexpectfromCerenkovlight.ThereversesituationisobservedintheotherPMT(L).Here,thepromptadditional
componentisobservedinthetimestructureofthepulsesrecordedwhenthecrys-talwasorientedatθ=−30◦.AlsointhisPMT,thetimestructurebeyondthe
14
Fig.8.Averagetimestructuresofthesignalsmeasuredintheleft(L)andright(R)photo-multipliertubesthatdetectthelightproducedby10GeVelectronsina2.2X0thickPbWO4crystal.Thebottomplotsshowthesesignalsforanglesθ=±30◦,forPMTsRandL,re-spectively.Thetopplotsshowthedifferencebetweenthetwoorientations,i.e.,thePMT’s
ˇresponsefunctiontoapromptCerenkovcomponentinthesignal.
amplitudeofthesignalswasfoundtobeindependentofthecrystalorientation.Theseresultsconfirmthepromptnatureoftheadditionallightcomponentob-servedintheleft/rightasymmetrymeasurements,andprovidemoreevidencefor
ˇtheCerenkovmechanismbeingresponsiblefortheobservedphenomena.ThefigureshowsminordifferencesbetweentheshapesofthepromptcomponentsobservedinthetwoPMTs.Thesearemostlikelyduetodifferencesinthecharac-teristcsofthesetubes.PMTL,whichoperatedataslightlyhigherhighvoltage,respondedtoaδ-functionwithaσrmsof2.3ns,vs.2.8nsforPMTR.Asaresult,
ˇtheresponsetotheCerenkovcomponenthadaslightlydifferenttimestructurein
thesePMTs.
TheaveragepulseshapesshowninFigure8makeitalsopossibletodeterminethe
ˇcontributionofCerenkovlighttothecrystalsignals.Inthecaseofthe10GeVelec-trons,theadditionalcomponentrepresented∼12%ofthetotalsignalinPMTR
and13%inPMTL.Forcomparison,werecallthattheleft/rightasymmetrymea-ˇsurementsledustoconcludethat,attheCerenkovangle,thesesignalscontained,
ˇonaverage,∼13%ofCerenkovlight12.Wehavealsostudiedtheangulardependenceoftheaveragepulseshape.Sincethe
ˇCerenkovcontributionmanifestsitselfintheleadingedgeofthetimestructure,wehavedevelopedseveralmethodstocharacterizethepropertiesofthatpartofthepulseshapeinaquantitativemanner.TwoofthesemethodsareillustratedinFigure9.Inthefirstmethod(Figure9a),weusedanappropriatefunctiontodescribethe
Fig.9.Thecharacteristicsofthetimestructureofthesignalsaredeterminedwithtwodifferentmethods.Inmethoda,theleadingedgeisfittedtoEquation3,andthefitted
ˇparameterstLandτLdeterminetheCerenkovcontentofthesignal.Inmethodb,thetime
atwhichthepulseheightexceedsacertainthresholdlevelisusedforthispurpose.Seetextfordetails.
timestructure.Itturnsoutthattheleadingedgeofthepulseshape,V(t),iswelldescribedbyafunctionofthefollowingtype:
V(t)=|A|
1
pulseheightexceedsacertainfixedthresholdlevel,e.g.,-50mV.AnincreaseintheˇCerenkovcontentofthesignalwillshiftthatpointtoanearliermoment.SomeresultsoftheseanalysesareshowninFigures10and11.Figure10showsthe
Fig.10.Averageleadconstant,τL(seeEquation3),ofthepulsesrecordedbyPMTR,asafunctionoftheorientationofthecrystal,i.e.,theangleθ.Datafor10GeVelectrons.
valueoftheleadconstant,τL,measuredforthe10GeVelectronsignalsfromPMT
ˇR,asafunctionoftheangleθ.Fornegativevaluesofθ,Cerenkovlightproduced
bytheelectronswasnotdetectedbythisPMT.Thepulseshapeisindependentofθ,withaτLvalueof1.20ns.However,whenthecrystalwasrotatedtowardsvalues
ˇofθ>0,Cerenkovlightproducedbytheshoweringparticlesbecameasignificant
componentofthesignalsmeasuredbyPMTR,andtheleadingedgeofthepulseshapesteepened(τLbecamesmaller).ThisprocesscontinueduntilθreachedtheˇCerenkovangle(∼30◦),atwhichpointτLreachedaminimumvalueof∼1.09ns.
ˇForlargerangles,theacceptanceofCerenkovlightdecreasedagainandtheleading
edgebecamelesssteep,τLincreased.TheτLvaluemeasuredforthesignalsfromPMTLshowsasimilarbehavior:Itisconstantforθ>0,decreasesforθ<0,reachesaminimumvalueforθ=−30◦andincreasesagainforlargerangles.Figure11showstheresultsofananalysisofthethresholdcrossingtime,forsignalsgeneratedby150GeVµ+.ThedifferencebetweenthecrossingtimesofthesignalsrecordedbyPMTsRandLisgivenasafunctionoftheangleθ,fortwodifferentthresholdlevels.Thisdifferenceissettozeroforθ=0.Thefigureshowsthatthedifferenceisnegativeforθ>0.AsaresultoftheincreasingcontributionofˇCerenkovlighttothesignalsfromPMTR,thethresholdwascrossedearlierinthis
ˇPMT,andthereforetheplottedquantityisnegative.Whenθ<0,Cerenkovlight
contributedtothesignalsfromPMTL,andtheplottedquantityispositive.Asinthecaseoftheresponseasymmetry,themaximumdifferenceisobservedforan-ˇglesneartheCerenkovangle,∼30◦.Theresultsarequalitativelynotsignificantly
differentforthetwodifferentthresholdlevels,buttheydoindicateaslightlylarger
17
Fig.11.AveragedifferencebetweenthetimesthetwoPMTsreadingoutthetwosidesofthecrystalneededtoreachacertainthresholdlevel,asafunctionoftheorientationofthecrystal(i.e.,theangleθ).Datafor150GeVµ+,andtwodifferentthresholdvalues.
effectforthehigherthreshold.
Asinthecaseoftheleft/rightasymmetry,theresultsshowninFigures10and11concerntheaveragebehaviorobservedforlargenumbersofevents(100000).Theerrorbarsinthesefiguresindicatetheprecisionwithwhichtheparameterinquestionisdeterminedforindividualevents.Thesizeoftheseerrorbars,whichforthesesmallsignalsiscompletelydominatedbyphotoelectronstatistics,issuchthatthevalueoftheleadconstant(τL)orthethresholdcrossingtimedoesnotprovide
ˇstatisticallysignificantinformationaboutthe(sizeofthe)contributionofCerenkov
lighttothesignalinquestion.
6Conclusions
ˇWehavemeasuredthecontributionofCerenkovlighttothesignalsfromelec-tronsandmuonsinleadtungstatecrystals.Inthechosengeometry,whichwas
optimizedfordetectingthiscomponent,informationaboutthiscontributionwasobtainedfromtheleft/rightresponseasymmetryandfromthetimestructureofthesignals.Forsingleparticlestraversingthecalorimeter(muons),themaximumˇCerenkovcontributiontothesignalswasmeasuredtobe15−20%.Themeasure-mentsforelectronshowersindicatedsomewhatlowervalues,becauseofthecon-tributionsofisotropicallydistributedshowerparticlestothesignals.Thisreducedthemeasuredasymmetriesintheresponseandtimestructureofthesignals.Thiseffectwasmeasuredtoincreaseinimportanceastheshowerdeveloped.Theasym-metriesmeasuredfor10GeVelectronsinthefirst2-3radiationlengthswereaboutthreetimeslargerthanthosemeasuredatadepthof7−10X0,i.e.,justbeyondthe
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showermaximum.
Acknowledgments
ThestudiesreportedinthispaperwerecarriedoutwithPbWO4crystalsmadeavailabletousbythePHOSgroupoftheALICECollaboration.WesincerelythankDrs.MikhailIppolitovandHansMullerfortheirhelpandgenerosityinthiscontext.WethankCERNformakingparticlebeamsofexcellentqualityavailable.ThisstudywascarriedoutwithfinancialsupportoftheUnitedStatesDepartmentofEnergy,undercontractDE-FG02-95ER40938.
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