MSW mediated neutrino decay and the solar neutrino

arXiv:hep-ph/0101273v230Mar2001MSWmediatedneutrinodecayandthesolarneutrinoproblemAbhijitBandyopadhyay1,SandhyaChoubey2,SrubabatiGoswami3SahaInstituteofNuclearPhysics,1/AF,Bidhannagar,Calcutta700064,INDIA.AbstractWeinvestigatethesolarneutrinoproblemassumingsimultaneouspresenceofMSWtransitionsinthesunandneutrinodecayonthewayfromsuntoearth.Wedoaglobalχ2-analysisofthedataontotalratesinCl,GaandSuperkamiokande(SK)experimentsandtheSKday-nightspectrumdataanddeterminethechangesintheallowedregionintheΔm2−tan2θplaneinpresenceofdecay.Wealsodiscuss[e-mail][e-mail][e-mail]11IntroductionTheglobalanalysisofthetotalratesmeasuredintheCl,Ga[1]andSKexperimentsandtheday-nightspectrumdataofSK[2]indicatethatthelargemixingangleMSWsolutiongivesthebestdescriptionofthesolarneutrinodata[3].Howeverbeforeaparticularsolutioncanbeestablishedoneshouldruleoutotherpossibili-ties.Inthisspiritpeoplehaveconsideredvariousnon-standardneutrinopropertiesandtheirimplicationforthesolarneutrinoproblem[4].InthispaperweconsiderascenariowhereneutrinosareallowedtodecayontheirwayfromsuntoearthafterundergoingMSWtransitionsinthesun.Suchapossibilitywasdiscussedearlierin[5].Weconsidertwoflavormixingbetweenνeandνμ/ντwiththemasseigenstatesν1andν2.Weassumethattheheaviermassstateν2isunstable,whilethelighterneutrinomassstateν1haslifetimemuchgreaterthanthesun-earthtransittimeandhencecanbetakenasstable.Therearetwopossiblenon-radiativedecaymodes4•Model1:IfneutrinosareDiracparticlesonehasthedecaychannelν2→¯ν1R+φ,where¯ν1Risarighthandedsingletandφisaniso-singletscaler.Thusallthefinalstateparticlesforthismodelaresterileandthereisnodistinctsignatureofthisdecayapartfromindisappearanceexperiments.Thismodelisdiscussedin[7].Inthismodelalightscalarbosonφwithleptonnumber-2andasingletrighthandedneutrinoisaddedtothestandardmodel.Theneutrinocouplingtothisscalarbosonisgivenbyg21νTR1C−1νR2,Cbeingthechargeconjugationoperator.•Model2:IfneutrinosareMajoranaparticles,thedecaymodeisν2→¯ν1+J,whereJisaMajoron,producedasaresultofspontaneousbreakingofaglobalU(1)Le−Lμsymmetry[8].Inthismodeltheneutrinomassesaregeneratedbyextendingthehiggssectorofthestandardmodel.ThoughtheoriginaltripletmajoronmodelproposedbyGelminiandRoncadeli[9]isruledoutfromtheLEPdataonZdecaytoinvisiblemodes[10],themodeldiscussedin[8],whichneedstwoadditionaltripletandonesingletscalarbosoninthetheory,canavoidtheconflictwiththeLEPdata,andatthesametimepredictfastenoughneutrinodecaynecessarytosolvethesolarneutrinoproblem.Inthismodelthe¯ν1canbeobservedasa¯νewithaprobability|Ue1|2andasa¯νμ/¯ντwithaprobability|Ue2|2.4Radiativedecaysareseverelyconstrained[6].2Inboththedecayscenariostherestframelifetimeofν2isgivenby[11]τ0=16πg2m2(1+m1/m2)−2Δm2(1)wheregisthecouplingconstant,miistheνimassandΔm2=m22−m21.Assumingm2m1theequation(1)canbewrittenasg2Δm2∼16πα(2)whereαisthedecayconstantrelatedtoτ0asα=m2/τ0.Ifwenowincorporatetheboundg24.5×10−5asobtainedfromKdecaymodes[12]wegettheboundΔm2106α5.Sinceforatypicalneutrinoenergyof10MeV,onestartsgettingdecayeffectsoverthesun-earthdistanceforα∼10−13eV2,thecorrespondinglimitonΔm2isΔm2∼10−7eV2.InanearlierpaperwehadconsideredhighvaluesofΔm2(10−3eV2)sothatthemattereffectsinsidethesuncanbeneglectedandonecanhavedecayaswellasΔm2independentaverageoscillations[14].Inthispaperweconsider10−6≤Δm2≤10−3eV2suchthatthemattereffectsinsidethesunareimportant.Weincorporatetheearthmattereffectsaswell.Insection2wediscusstheusualtwoflavorMSWsolutionstothesolarneutrinoproblem.Weperformaχ2-analysistotheglobaldataonratesandSKday-nightspectrumandpresenttheallowedregionsintheΔm2−tan2θplane.Insection3weintroducethepossibilityofhavingoneoftheneutrinostates,ν2tobeunstable.WelookfortheeffectsofdecayontheMSWsolutionsandpresenttheallowedareasatvariousvaluesofthedecayconstant.Weshowthatforthemajorondecaymodel(model2)theSKdataon¯νe−peventsrestrictstheallowedvaluesofthedecayconstanttoextremelylowvalues.Insection4wediscusstheimplicationsofnon-zeroneutrinodecayfortheSNOexperiment.Wefinallypresentourconclusionsinsection5.2MSWeffectforstableneutrinosAswasfirstindicatedin[15],interactionofelectronneutrinospropagatingthroughthesunmodifiesthevacuummixingangleθtomattermixingangleθMwhere,tan2θM=Δm2sin2θΔm2cos2θ−2√2GFneE.(3)5Sincethemeeelementofthemassmatrixiszerointhemajorondecaymodelconsidered,the0ν-majoronββdecaydoesnottakeplaceinthismodel[8]andthemorestringentboundongfrommajoronemissioninββdecay[13]isnotapplicable.3Hereneistheambientelectrondensity,Etheneutrinoenergy,andΔm2(=m22−m21)themasssquareddifferenceinvacuum.Thevanishingofthedenomi-natorineq.(3)definestheresonancecondition,wherethemattermixingangleismaximal.Theprobabilityamplitudeofsurvivalforanelectronneutrinoisgivenby,Aee=A⊙e1Avac11A⊕1e+A⊙e2Avac22A⊕2e(4)whereA⊙ekgivestheprobabilityamplitudeofνe→νktransitionatthesolarsurface,A⊙ek=a⊙eke−iφ⊙k(5)a⊙e12=PJsin2θM+(1−PJ)cos2θM=1−a⊙e22(6)PJisthenon-adiabaticleveljumpingprobabilitybetweenthetwomasseigenstatesforwhichweusethestandardexpressionfrom[