中微子物理(二)

NeutrinoPhysicsIIHitoshiMurayamaTaiwanSpringSchoolMarch28,2002中性微子物理（二）村山斉台湾春期学校二千二年三月二十八日3Outline•SolarNeutrinoOscillations–VacuumOscillation–MatterEffectintheSun–MatterEffectintheEarth–SeasonalEffect•FutureofSolarNeutrinos–Reactorneutrino–Day/NightEffect–SeasonalVariationSolarNeutrinoOscillation5Wedon’tgetenoughWeneedsurvivalprobabilitiesof8B:~1/37Be:1/3pp:~2/3Canwegetthreenumberscorrectlywithtwoparameters?6DarkSideofNeutrinoOscillation•Traditionalparameterizationofneutrinooscillationintermsof(Dm2,sin22q)coversonlyahalfoftheparameterspace(deGouvêa,Friedland,HM)•Convention:n2heavierthann1–Varyqfrom0˚to90˚–sin22qcovers0˚to45˚–Lightside(0to45˚)andDarkSide(45˚to90˚)n1necosqnsinqn2nesinqncosq7DarkSideofNeutrinoOscillation•Tocoverthewholeparameterspace,can’tuse(Dm2,sin22q)but(Dm2,tan2q)instead.(Fogli,Lisi,Montanino;deGouvêa,Friedland,HM)•Invacuum,oscillationprobabilitydependsonlyonsin22q,i.e.,invariantunderq90q•Seenasareflectionsymmetryonthelogscaletan2qcot2q•Orusesin2qonthelinearscalesin2qcos2q8Fittotheratesofsolarneutrinoeventsfromallexperiments(Foglietal)Howdoweunderstandthisplot?9VacuumOscillation•Ga~1/2,Cl~1/3,water~1/3•Onepossibleexplanationisthatneutrinososcillateinthevaccumjustlikeinatmosphericneutrinos•ButoscillationismoreprominentforlowerenergieswhileGaretainsthehalf•Theoscillationlengthneedstobe“justright”sothat8B,7Bearedepletedmorethanaverage7Be:Dm24EL~n12Dm2~n121.61011eV21011MatterEffect•CCinteractioninthepresenceofnon-relativisticelectronLGF2e(15)nene(15)eGF2e(15)ene(15)ne2GFnene0ne•NeutrinoHamiltonianHcommonDm24Ecos2qsin2qsin2qcos2q2GFne1000ElectronneutrinohigherenergyintheSun12ElectronNumberDensityNearlyexponentialformostoftheSun’sinterioroscillationprobabilitycanbesolvedanalyticallywithWhittakerfunctionne(r)ne(0)er/r0ne(0)100NA/cm3r0Rsun/107104km13Propagationofne•Use“instantaneous”eigenstatesn+andn–ne,Earthne,corecosqsinqeim12L/2peim22L/2pab*ba*eiEteiEtcosqMsinqML14SurvivalProbabilityne,Earthne,core2acosqeim12L/2pbsinqeim22L/2pcosqMeiEtb*cosqeim12L/2pa*sinqeim22L/2psinqMeiEt21Pccos2qPcsin2qcos2qMPccos2q1Pcsin2qsin2qMPc1Pcsin2qcosDm22pLEEt~2GFne(0)Rsun/10~1000DecoheresuponAveragingoverProductionregionPcb21Pca2Hoppingprobability15SurvivalProbabilitycont.•ThermaleffectsDE~kT~1keV•Thelasttermaveragesoutif•NowweneedPcne,Earthne,core21Pccos2qPcsin2qcos2qMPccos2q1Pcsin2qsin2qMPc1Pcsin2qcosDm22pLDm2E108eV21MeV16LevelCrossing•Forsmallanglesandq45,neishigheratthecorewhileloweroutside,andhencetwolevelscrossPcesin2qe1e2r0Dm22p1.05Dm2109eV2MeVp1Pc0adiabaticlimit1Pccos2qnon-adiabaticlimit17SurvivalProbability•“MSWtriangle”•100%lostatthecenterofthetriangle,possibleevenforsmallangles•Darksidealwaysbiggerthan50%•ScaleswithenergybecauseofDm2/pdependenceNolevelcrossing18SMALMALOW19SurvivalProbability20MatterEffectintheEarth21MatterEffectintheEarth•WhenneutrinomasseigenstatesgothroughtheEarth,someoflostnestatemayberegeneratedSunmaybebrighterinthenight•Day-nightasymmetry:ADNNDND7Be22Day/NightSpectraatSuperK23•Absenceofday/nighteffectcutsintoLMAADN0.0660.0440.0240.0267Be24SpectrumDistortion•Survivalprobabilitymaybeenergy-dependent•Knowing8Bspectrummeasuredinthelaboratory,onecanlookforspectrumdistortionindata25NospectrumdistortionyetatSuperK26NospectrumdistortionyetatSNO27•AbsenceofspectrumdistortionremovesSMA28SeasonalEffect•Earth’sorbitisslightlyeccentric•TheEarth-Sundistancechanges3.5%frommaxtomin•1/r2lawsays7%changeinneutrinofluxfrommax(summer)tomin(winter)29Sofarnoseasonaleffectin8B30VacuumOscillationagainne,Earthne,core21Pccos2qPcsin2qcos2qMPccos2q1Pcsin2qsin2qMPc1Pcsin2qcosDm22pL1sin22qsin2Dm24p(LRsun)2r0Dm22p0Pcesin2qe1ecos2q31Quasi-Vacuumoscillation•VacuumregionactuallyreachedslowlyasDm2decreased•Transitionregionbetween“MSW”and“vacuum”region:quasi-vacuum•Bothmattereffectandoscillatorytermneedtobekept32•LOWextendsdowntoVAC,especiallyinthedarkside!FutureofSolarNeutrinos34MorefromSNO•NC/CCconfirmationofneutrinoconversionsterileneutrino?•Day/nighteffectLMA•CCspectrumSMA,VAC•SeasonaleffectVAC35WhatNextonSolarNeutrinos?•We’dliketoconvincinglyverifyoscillationwithman-madeneutrinos•HardforlowDm2•NeedlowEn,highFn•Useneutrinosfromnuclearreactors•ToprobeLMA,needL~100km,1ktPsurv1sin22qsin21.27Dm2c4eV2GeVEnLkm36KAMiokaLiquidscintillatorANti-NeutrinoDetector1kt•KamLAND•Detectorselectronanti-neutrinosfromnuclearpowerplantsbyinversebetadecaynepeneenpd(2.2MeV,delayed)37Location,Location,Location38KamLANDsensitivityonLMA•Firstterrestrialexptrelevanttosolarneutrinoproblem•KamLANDwillexcludeorverifyLMAdefinitively•DatatakingsinceNov200139KamLANDfirstneutrinoevent40MeasurementsatKamLAND•CanseethedipwhenDm2210–5eV2(Pierce,HM)•Canmeasuremass&mixingparametersData/theory41IfLMAconfirmed...•Dreamcaseforneutrinooscillati