Matter Effects on Neutrino Oscillations in Long Ba

arXiv:hep-ph/0002149v219May2000MatterEffectsonNeutrinoOscillationsinLongBaselineExperimentsIrinaMocioiu∗(a)andRobertShrock†(a,b)(a)C.N.YangInstituteforTheoreticalPhysicsStateUniversityofNewYorkStonyBrook,NY11794-3840(b)PhysicsDepartmentBrookhavenNationalLaboratoryUpton,NY11973Wecalculatemattereffectsonneutrinooscillationsrelevantforlongbase-lineexperiments.Inparticular,wecomparetheresultsobtainedwithconstantdensityalongtheneutrinopathversusresultsobtainedbyincorporatingtheactualdensityprofilesintheEarth.Westudythedependenceoftheoscilla-tionsignalonbothE/Δm2atmandontheanglesintheleptonicmixingmatrix.WealsocommentontheinfluenceofΔm2solontheoscillations.Theresultsshowquantitativelyhow,asafunctionoftheseinputparameters,matteref-fectscancausesignificant(25%)changesintheoscillationprobabilities.AnimportantconclusionisthatmattereffectscanbeusefulinamplifyingcertainneutrinooscillationsignalsandhelpingonetoobtainmeasurementsofmixingparametersandthemagnitudeandsignofΔm2atm.PACS:13.15.+g,14.60.Pq∗email:[e-mail]†email:[e-mail]oreticalcontext,onegenerallyexpectsnonzeroneutrinomassesandasso-ciatedleptonmixing.Experimentally,therehasbeenaccumulatingevidenceforsuchmassesandmixing.Allsolarneutrinoexperiments(Homestake,Kamiokande,SuperKamiokande,SAGE,andGALLEX)showasignificantdeficitintheneutrinofluxescomingfromtheSun[1].Thisdeficitcanbeexplainedbyoscillationsoftheνe’sintootherweakeigenstate(s),withΔm2soloftheorder10−5eV2forsolutionsinvolvingtheMikheev-Smirnov-Wolfenstein(MSW)resonantmatteroscillations[2,3]oroftheorderof10−10eV2forvacuumoscillations.Accountingforthedatawithvacuumoscillations(VO)requiresalmostmaximalmixing.TheMSWsolutionsincludeoneforsmallmixingangle(SMA)andonewithessentiallymaximalmixing(LMA).Anotherpieceofevidenceforneutrinooscillationsistheatmosphericneutrinoanomaly,observedbyKamiokande[4],IMB[5],SuperKamiokande[6]withthehigheststatistics,andbySoudan[7]andMACRO[8].Thisdatacanbefitbytheinferenceofνμ→νxoscillationswithΔm2atm∼3.5×10−3eV2andmaximalmixingsin22θatm=1[6].Theidentificationνx=ντispreferredoverνx=νsterileataboutthe2.5σlevel[9],andtheidentificationνx=νeisexcludedbyboththeSuperkamiokandedataandtheChoozexperiment[10,11].Inaddition,theLSNDexperimenthasreportedobserving¯νμ→¯νeandνμ→νeoscil-lationswithΔm2LSND∼0.1−1eV2andarangeofpossiblemixingangles,dependingonΔm2LSND[12].Thisresultisnotconfirmed,butalsonotcompletelyruledout,byasimilarexperiment,KARMEN[13].Therearecurrentlyintenseeffortstoconfirmandextendtheevidenceforneutrinoos-cillationsinallofthevarioussectors–solar,atmospheric,andaccelerator.Someoftheseexperimentsarerunning;theseincludetheSudburyNeutrinoObservatory,SNO,andtheK2KlongbaselineexperimentbetweenKEKandKamioka.Othersareindevelopmentandtestingphases,suchasBOONE,MINOS,theCERN-GranSassoprogram,KAMLAND,andBorexino[14].Amongthelongbaselineneutrinooscillationexperiments,theapproxi-matedistancesareL≃250kmforK2K,730kmforbothMINOS,fromFermilabtoSoudanandtheproposedCERN-GranSassoexperiments.ThesensitivityoftheseexperimentsisprojectedtoreachdownroughlytothelevelΔm2∼10−3eV2.Thereisstrongmotivationforanothergenerationofexperimentswithevenhighersensitivitythatcanconfirmtheνμ→ντtransitionwiththevaluesofΔm2atmandsin22θatmreportedsofarandcarryoutfurthermeasurementsofvariousneutrinooscillationchannels.Recently,therehasbeenconsiderableinterestintheideaofamuonstorageringthatwouldserveasa“neutrinofactory”,i.e.,asourceofquitehighintensity,flavor-pureneutrinoandantineutrinobeams:νμ+¯νe(¯νμ+νe)fromstoredμ−’s(μ+’s)respectively[15]-[20].Giventheveryhighintensitiesanticipatedtobeoforder1020andperhapseven1021muondecaysperyearinvariouspreliminarystudies,onecanenvisionneutrinooscillationexperimentswithquitelongbaselinesoforderseveralthousandkm,withcommensuratesensitivitytovariousneutrinooscillationchannels.Oneoftheappealsofthemuonstoragering/neutrinofactoryisthatonecanmeasureseveraldifferentneutrinooscillationtransitions,usingboththeνμ(¯νμ)and¯νe(νe)fromaμ−(μ+)beam.Inthisparagraphweassumeaμ−beamfordefiniteness(figuresbeloware1shownforneutrinosfrombothstoredμ+andμ−beams).Inadditiontoahigh-statisticsmeasurementofνμ→νμ,asadisappearancetestfortheνμ→ντoscillation,onehasalsovariousotherchannels.Amongtheseare¯νe→¯νμ,forwhichthesignalisa“wrong-signmuon”,μ+,and¯νe→¯ντ,which,inabout18%ofitsdecays,wouldalsoyieldawrong-signmuon.ThemeasurementofthemuonchargewouldbepossiblewitheitheramagnetizedirondetectororacombinationofamassivewaterˇCerenkovdetectorfollowedbyamuonspectrometer.Withsufficientdetectorcapabilities,onecouldalsosearchforτappearance,asisenvisionedbytheICANOEandOPERAexperimentsatGranSasso[21,22],althoughthisrequiresneutrinoenergiesEν∼20GeVtoavoidkinematicsuppressionofτproduction.Animportanteffectthatmustbetakenintoaccountinsuchexperimentsconcernsthematter-inducedoscillationswhichneutrinosundergoalongtheirflightpaththroughtheEarthfromthesourcetothedetector.Giventhetypicaldensityoftheearth,mattereffectsareimportantfortheneutrinoenergyrangeE∼O(10)GeVandΔm2atm∼3×10−3eV2valuesreleva