On the CP Violation Associated with Majorana Neutr

arXiv:hep-ph/0209059v15Sep2002Ref.SISSA60/2002/EPDO-TH02/12August2002hep-ph/0208XXXOntheCPViolationAssociatedwithMajoranaNeutrinosandNeutrinolessDouble-BetaDecayS.Pascolia,b),S.T.Petcova,b)1andW.Rodejohannc)a)ScuolaInternazionaleSuperiorediStudiAvanzati,I-34014Trieste,Italyb)IstitutoNazionalediFisicaNucleare,SezionediTrieste,I-34014Trieste,Italyc)DepartmentofPhysics,UniversityofDortmund,GermanyAbstractAssuming3-νmixingandmassiveMajorananeutrinos,weanalyzethepossibilityofestab-lishingtheexistenceofCP-violationassociatedwithMajorananeutrinosintheleptonsectorbyi)measuringoftheeffectiveMajoranamass|m|inneutrinolessdoublebetadecaywithasufficientprecisionandii)bymeasuringof,orobtainingastringentupperlimiton,thelightestneutrinomassm1.Informationonm1canbeobtainedinthe3Hβ-decayexperimentKATRINandfromastrophysicalandcosmologicalobservations.ProvingthattheindicatedCP-violationtakesplacerequires,inparticular,arelativeexperimentalerroronthemeasuredvalueof|m|notbiggerthan20%,a“theoreticaluncertainty”inthevalueof|m|duetoanimpreciseknowledgeofthecorrespondingnuclearmatrixelementssmallerthanafactorof2,avalueoftan2θ⊙∼0.55,andvaluesoftherelevantMajoranaCP-violatingphasestypicallywithintheintervalsof∼(π/2−3π/4)and∼(5π/4−3π/2).1Alsoat:InstituteofNuclearResearchandNuclearEnergy,BulgarianAcademyofSciences,1784Sofia,Bulgaria11IntroductionTherecentresultsoftheSNOsolarneutrinoexperiment[1,2](seealso[3])providedfurtherstrongevidencesforoscillationsortransitionsofthesolarνeintoactiveneutrinosνμ(τ)(and/orantineutrinos¯νμ(τ)).TheseevidencesbecomeevenstrongerwhentheSNOdataarecombinedwiththedataobtainedintheothersolarneutrinoexperiments,Homestake,Kamiokande,SAGE,GALLEX/GNOandSuper-Kamiokande[4,5].Asthetwo-neutrinooscillationanalyzesofthesolarneutrinodatashow(see,e.g.,[1]),thelatterfavorthelargemixingangle(LMA)MSWνe→νμ(τ)transitionsolutionwithΔm2⊙∼5×10−5eV2andtan2θ⊙∼0.33,tan2θ⊙1,whereΔm2⊙andθ⊙aretheneutrinomasssquareddifferenceandmixinganglewhichcontrolthesolarneutrinotransitions.StrongevidencesforoscillationsofatmosphericneutrinoshavebeenobtainedintheSuper-Kamiokandeexperiment[6].Theatmosphericneutrinodata,asiswellknown,isbestdescribedintermsofdominantνμ→ντ(¯νμ→¯ντ)oscillationswith|Δm2atm|∼(2.5−3.0)×10−3eV2.Theexplanationofthesolarandatmosphericneutrinodataintermsofneutrinooscillationsrequirestheexistenceof3-neutrinomixingintheweakchargedleptoncurrent(see,e.g.,[7,8]):νlL=3Xj=1UljνjL.(1)HereνlL,l=e,μ,τ,arethethreeleft-handedflavorneutrinofields,νjListheleft-handedfieldoftheneutrinoνjhavingamassmjandUisthePontecorvo-Maki-Nakagawa-Sakata(PMNS)neutrinomixingmatrix[9,10].IftheneutrinoswithdefinitemassνjareMajoranaparticles,theprocessofneutrinolessdouble-beta((ββ)0ν-)decay,(A,Z)→(A,Z+2)+e−+e−,(A,Z)and(A,Z+2)beinginitialandfinalstatenuclei,willbeallowed(forreviewssee,e.g.,[11,12]).ForMajorananeutrinosνjwithmassesnotexceedingfewMeV,thedependenceofthe(ββ)0ν-decayamplitudeontheneutrinomassandmixingparametersisconfinedtoonefactor—theeffectiveMajoranamass|m|,whichcanbewrittenintheform(see,e.g.,[11]):|m|=m1|Ue1|2+m2|Ue2|2eiα21+m3|Ue3|2eiα31(2)whereα21andα31arethetwoMajoranaCP-violatingphases2[13,14].IfCP-invarianceholds,onehas[15,16]α21=kπ,α31=k′π,wherek,k′=0,1,2,....Inthiscaseη21≡eiα21=±1,η31≡eiα31=±1,(3)representtherelativeCP-paritiesoftheneutrinosν1andν2,andν1andν3,respectively.Onecanexpress[17,18,19,20,21]themassesm2andm3enteringintoeq.(2)for|m|intermsofΔm2⊙andΔm2atm,measuredinthesolarandatmosphericneutrinoexperiments,andm1,while|Uej|2,j=1,2,3,arerelatedtothemixinganglewhichcontrolsthesolarνetransitionsθ⊙,andtotheleptonmixingparametersin2θlimitedbythedatafromtheCHOOZandPaloVerdeexperiments[22,23].Withintheconventionm1m2m3wearegoingtouseinwhatfollows,onehasΔm2atm≡Δm231,whereΔm2jk≡m2j−m2k,andm3=qm21+Δm2atm.ForΔm2⊙therearetwopossibilities,Δm2⊙≡Δm221andΔm2⊙≡Δm232,correspondingrespectivelytotwodifferenttypesofneutrinomassspectrum—withnormalandwithinvertedhierarchy.Inthefirstcaseonehasm2=qm21+Δm2⊙,|Ue1|2=cos2θ⊙(1−|Ue3|2),|Ue2|2=sin2θ⊙(1−|Ue3|2),and|Ue3|2≡sin2θ,whileinthesecondm2=qm21+Δm2atm−Δm2⊙,|Ue2|2=cos2θ⊙(1−|Ue1|2),|Ue3|2=sin2θ⊙(1−|Ue1|2),and|Ue1|2≡sin2θ.Thus,givenΔm2⊙,Δm2atm,θ⊙andsin2θ,|m|depends,ingeneral,on2Weassumethatmj0andthatthefieldsoftheMajorananeutrinosνjsatisfytheMajoranacondition:C(¯νj)T=νj,j=1,2,3,whereCisthechargeconjugationmatrix.2thelightestneutrinomassm1,onthetwoMajoranaCP-violatingphasesα21andα31andonthe“discreteambiguity”relatedtothetwopossibletypesofneutrinomassspectrum.Inthecaseofquasi-degenerate(QD)neutrinomassspectrum,m1∼=m2∼=m3,m21≫Δm2atm,Δm2⊙,|m|essentiallydoesnotdependonΔm2atmandΔm2⊙,andthetwopossibilities,Δm2⊙≡Δm221andΔm2⊙≡Δm232,leadtothesamepredictionsfor3|m|.Theobservationof(ββ)0ν-decaywillhavefundamentalimplicationsforourunderstandingoftheelementaryparticleinteractions.Itwouldimply,inparticular,thattheelectronleptonchargeLeandthetotalleptonchargeLarenotconservedandcanchangebytwounitsinthelatter,andwouldsuggestthatthemassiveneutrinosareMajoranaparticles.Underthegeneralandplausibleassumptionsof3-νmixingandmass