Decays of the [gamma](1S) into a photon and two charged hadrons

2004·5 MB·English

by  Breva-Newell, Luis

DECAYSOFTHET(1S)INTOAPHOTONANDTWOCHARGEDHADRONS
By
LUISBREVA-NEVVELL
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
2004
TomyParents.
ACKNOWLEDGMENTS
Iowemygratitudetomanypeoplewithoutwhomthisworkwouldnothave
beenpossible. Firstofall,Iwouldliketothankmysupervisor,Dr. Yelton. His
officedoorwasalwaysopenforme,andhespentlonghoursofhistimelistening
tomyideaseventhoughonlyafewofthemeverworked. Hegavemefreedomto
exploreandbranchoffindifferentdirectionswhilesteadilyguidingmeforwardat
thesametime. AftertheseyearsofworkingtogetherIconsiderhimmorethana
mentor,andathinkofhimasaclosefriend.
DuringmystayattheUniversityofFloridaIhavemetmanypeopleinside
andoutsidethephysicsworld. Iwouldliketothankmyfirstyeargraduateteachers
Dr. SikivieandDr. Woodardwhowereasourceofinspirationforme. Mythanks
alsogotomyfellowgraduatestudentsVijayPotlia,RukshanaPatel,Necula
Valentin,JenniferSippel,SuzetteAtienza,G.Suhas,andmanymoreforallourfun
physicsdiscussionsandlatehomeworksessions. Iwouldalsoliketothankthegood
friends1madeoutsidethephysicsbuilding,JamesPower,YaseenAfzal(Paki),
RamjiKamakoti(Ramjizzle),DanDeKee(DoubleDown),andFernandoZamit
(Fernizzle)whoalwaysremindedmethatthereismoretolifethanPhysics.
ThemostimportantpersonIhavemetduringmygraduatecareerismywife,
Jennifer. IthankherforenduringallthoseendlessdayswhenIwouldanswerher
questionswithonlygruntsandnodswhilemyattentionremainedfixedonthe
computerscreen. Herloveandsupportareinvaluabletome.
Finally,IwouldliketothankmyparentsManuelandCharlene,mysister
Teresa,andmybrotherGaizka. Theyhavealwaysbeenthereforme.
in
TABLEOFCONTENTS
page
ACKNOWLEDGMENTS "*
ABSTRACT vi
CHAPTER
1 THEORY 1
1.1 ParticlePhysics 1
1.1.1 TheStandardModel 1
1.1.2 QuantumChromodynamics 3
1.1.3 IntroductiontotheRadiativeDecaysoftheT(1S) .... 6
1.2 RadiativeDecaysofQuarkoniaOverview 14
2 EXPERIMENTALAPPARATUS 17
2.1 TheCornellElectronStorageRing 17
2.2 TheCLEOIIIDetector 20
2.2.1 SuperconductingCoil 21
2.2.2 TrackingSystem 21
2.2.3 CrystalCalorimeter 24
2.2.4 RingImagingCherenkovDetector 25
2.2.5 MuonDetectors 28
3 ANALYSISOFTHEDATA 31
3.1 DataSample 31
3.1.1 ContinuumSubtractedDistributions 32
3.2 EventSelection 34
3.2.1 SkimCuts 35
3.2.2 AnalysisCuts 37
3.2.3 CutSummary,Efficiencies,andFakeRates 43
4 EXCLUSIVERADIATIVEDECAYT(LS)->^+n' 48
4.1 RobustnessofTheMassDistribution 48
4.2 StatisticalFitoftheInvariantMassDistribution: SignalAreas
andTheirSignificance 49
4.3 AngularDistributionofTheSignal : . . . 50
4.3.1 OptimumMassInterval 51
4.3.2 BackgroundSubtraction 53
iv
4.3.3 StatisticalFitoftheHelicityAngularDistribution: JAs-
signmentsandtheirProbabilityDistribution 55
5 EXCLUSIVERADIATIVEDECAYT(15)-»yK+K~ 66
5.1 StatisticalFitoftheInvariantMassDistribution: SignalAreas
andTheirSignificance 66
5.2 AngularDistributionofTheSignal 67
6 EXCLUSIVERADIATIVEDECAYT(15)-ipp 80
7 SYSTEMATICUNCERTAINTIES 86
7.1 Cuts 86
7.1.1 JustificationoftheDPTHMUCut 87
7.2 AngularDistributionofSignal 88
7.3 DifferentHadronicFakeRatesBetweenISand4S 97
7.4 OtherSystematicSources 97
7.5 OverallSystematicUncertainties 99
8 RESULTSANDCONCLUSION 100
APPENDIX HELICITYFORMALISMFORTWOBODYDECAYS .... 103
REFERENCES 119
BIOGRAPHICALSKETCH 121
AbstractofDissertationPresentedtotheGraduateSchool
oftheUniversityofFloridainPartialFulfillmentofthe
RequirementsfortheDegreeofDoctorofPhilosophy
DECAYSOFTHET(1S)INTOAPHOTONANDTWOCHARGEDHADRONS
By
LuisBreva-Newell
December2004
Chair: JohnYelton
MajorDepartment: Physics
UsingtheCLEOIIIdetectorwereportonanewstudyofexclusiveradiative
T(15)decaysintothefinalstates77r+7r~,~/K+K~andjpp. Wepresentbranching
ratiosforthedecaymodesT(15) ->7/2(1270),T(15) -»7/2(1525),T(15) -*
7/o(1710)with/(1710)-*K+K~andT(15)-*7/4(2050).
vi
CHAPTER1
THEORY
1.1 ParticlePhysics
Particlephysicsisthebranchofphysicsdedicatedtothestudyofmatter
a.ndenergyatthemostfundamentallevel. Thismeansthatthejobofaparticle
physicististoidentifythesmallestconstituentsofmatteranddescribehowthey
interactwitheachother.
Humankindhasbeeninterestedinthissubjectsinceancienttimes. Twoofthe
firstparticlephysicistsinrecordedhistoryaretheGreekthinkersEmpedoclesand
DemocritusfromthefifthcenturyBC.Empedoclesstatedthatourcomplexworld
wasmadefromcombiningfourfundamentalelements(earth,air,fireandwater)in
differentproportions. Democritusontheotherhand,believedthattheapparently
continuousobjectsinthenaturalworldwerenotreallycontinuous,butmadefrom
voidsandindivisibleparticlescalledatoms.
OverthelasthalfcenturyParticlephysicshasadvancedtremendouslyandwe
nowhaveabeautiful,butincomplete,theoryfirmlygroundedonexperimentthat
describesthefundamentalconstituentsofmatterandhowtheyinteractwitheach
other. Thistheoryiscalled "TheStandardModel."
1.1.1 TheStandardModel
AccordingtotheStandardModel,thefundamentalbuildingblocksofmatter
arepointlikeparticleswhichinteractwitheachotherinasmanyasthreedifferent
ways. Eachtypeofinteraction,orforce,isitselfcarriedbypointlikeparticles
calledforcecarriers. Theparticleswhichareforcecarriersarebosons1 andare
collectivelycalledgaugebosonsbecausetheyareneededforthetheorytobegauge
invariant. Thenon-forcecarryingparticlesarefermions.2
ThethreeinteractionsdescribedbytheStandardModelarecalledthe
electromagneticforce,theweakforce,andthestrongforce. Theforceofgravityis
notincludedintheStandardModel,andthisisoneofthereasonstheStandard
Modelisnotyetcomplete. Theelectromagneticforcecarriersarephotons,the
weakforcecarriersaretheZ°,W+,andW~particles,andfinally,thestrongforce
iscarriedbyeightkindsofgluons. Table1-1summarizesthesituation.
Table1-1: Gaugebosonsandtheforcetheycarry.
Symbol Name ForceCarried
7 Photon Electromagnetic
Z° Z° Weak
w+ w+ Weak
w~ w~ Weak
9 gluon Strong
Particleswhichinteractthroughaparticularforcearesaidtocoupletoit
andtocarryanassociatedcharge. Thenomenclatureisasfollows,particlesthat
interactthroughtheelectromagneticforcehaveanelectromagneticchargecalled
electriccharge,thosewhichinteractthroughtheweakforcehaveaweakcharge
calledweakisospin,andthosewhichinteractstronglyhaveastrongchargecalled
color.
TherestoftheparticlesintheStandardModelwhicharenotforcecarriers,
thefermions,aresubdividedintodifferentgroupsdependingontheirproperties
(Seetable1-2),reminiscentofthewaychemistsorganizedtheelementsinto
1Bosonsaredefinedasparticleswithintegerspininquantummechanics.
2Fermionsaredefinedasparticleswithhalfoddfractionalspin.
theperiodictableduringthesecondhalfofthenineteenthcentury. Fermionsare
dividedintoquarks(genericallyrepresentedbythesymbolq)andleptons. The
maindifferencebetweenthesetwogroupsisthatquarksinteractthroughthestrong
forcewhileleptonsdonot. Therearesixtypesofleptonsandsixtypesofquarks
(alsocalledthesixquarkflavors)whicharegroupedintothreegenerations. Each
generationconsistoftwoquarksandtwoleptons. Allthreegenerationsreplicate
thesamesetofforcecharges,themaindifferencebetweengenerationsisthemass
oftheparticles(forexample,theratioofthemassesofe:/i:Tis1:200:3500).
Foreachfermionthereisananti-fermionwithequalmassandspinandopposite
charge.
Table1-2: Fermionsymbolsclassifiedintoquarks,leptons,andthethreegenera-
tionsalongwiththegenerationalcommoncharges.
First Second Third Electric Weak Has
Generation Generation Generation Charge Charge Color
Quarks ud cs tb +-21//33 +-11//22 YYeess
+1/2 No
Leptons e T -1 -1/2 No
1.1.2 QuantumChromodynamics
Quantumchromodynamics(QCD)isthepartoftheStandardModelthat
describesthestrongforce. QCDisbasedonlocalgaugeinvarianceandcolor
symmetry. Therearethreepossiblecolorchargesforquarkscalledr(red),b(blue),
andg(green). Anti-quarkshaveoppositecolorscalledf,b,g. Thestrongforce
betweenquarksonlydependsontheircolorsandisindependentoftheirflavor.
Averyimportantcharacteristicofthestrongforceisthatgluonsthemselves
carryacolorchargeandananti-colorchargesotheycaninteractwithotherquarks
throughthestrongforceandchangetheircolor. Sincetherearethreecolorsand
threeanti-colorsonemightthinkthatthereareninedifferentgluons. However,
thereisonelinearcombinationofcoloranti-colorstatesthathasnonetcolorand
leavesaquarkunchanged. Therearetherefore9-1=8gluons. The8individual
gluoncolorstatescanbewrittenasfollows,
|1>=-={rb+bf)
v2
12>=^{rb-bf)
|3>=-=[rf-bb)
V2
|4>= -^{rg+gf)
V2 (i.i)
|5>=--Urg-gf)
|6>= -f={bg+gb)
V2
|7>=~(bg-gb)
\S>=-={rf+gg-2bb)
vo
andrepresenttheeightdifferentgluonsthatexistinnature. Thesingleandunique
colorstateleftoutiscalledacolorsinglet,
|9>=-^(^+66+gg) (1-2)
v3
whichisinvariantunderaredefinitionofthecolor(arotationincolorspace). In
grouptheorythisdecompositionofthecolorstatesintoanoctetandasingletis
denotedby3<g>3=8©1. Itisworthnotingherethatacolorlesssate,suchas|3>
or18>,isnotnecessarilyacolorsingletstate.
Thissituationisanalogoustotheperhapsmorefamiliarexampleoftwospin
1/2particles. Eachparticlecanhavetheirspinup(t)ordown(|)correspondingto
fourpossiblecombinations,eachgivingatotalspinS= or1. TheS=1states