Inverted Mass Hierarchy from Scaling in the Neutri

arXiv:0706.3801v2[hep-ph]17Aug2007InvertedMassHierarchyfromScalingintheNeutrinoMassMatrix:LowandHighEnergyPhenomenologyA.Bluma∗,R.N.Mohapatrab†,W.Rodejohanna‡aMax–Planck–Institutf¨urKernphysik,Postfach103980,D–69029Heidelberg,GermanybDepartmentofPhysicsandMarylandCenterforFundamentalPhysics,UniversityofMaryland,CollegePark,MD–20742,USAandSektionPhysik,Ludwig–Maximilians–Universit¨atM¨unchen,Theresienstrasse37a,D–80333M¨unchen,GermanyandPhysik–Department,TechnischeUniversit¨atM¨unchen,James–Franck–Strasse,D–85748Garching,GermanyAbstractBest-fitvaluesofrecentglobalanalyzesofneutrinodataimplylargesolarneutrinomixing,vanishingUe3andanon-maximalatmosphericneutrinomixingangleθ23.Weshowthatthesevaluesemergenaturallybythehypothesisof“scaling”intheMajorananeutrinomassmatrix,whichstatesthattheratiosofitselementsareequal.Italsopredictsaninvertedhierarchyfortheneutrinomasses.WepointoutseveraladvantagesanddistinguishingtestsofthescalinghypothesiscomparedtotheLe−Lμ−Lτflavorsymmetry,whichisusuallyassumedtoprovideanunderstandingoftheinvertedhierarchy.ScenarioswhichhaveinitiallyvanishingUe3andmaximalatmosphericneutrinomixingareshowntobeunlikelytoleadtonon-maximalθ23whilekeepingsimultaneouslyUe3zero.Wefindapeculiarratioofthebranchingratiosμ→eγandτ→eγinsupersymmetricseesawframeworks,whichonlydependsonatmosphericneutrinomixingandresultsinτ→eγbeingunobservable.Theconsequencesofthescalinghypothesisforhighenergyastrophysicalneutrinosatneutrinotelescopesarealsoinvestigated.ThenweanalyzeaseesawmodelbasedonthediscretesymmetryD4×Z2leadingtoscalinginthelowenergymassmatrixandbeingcapableofgeneratingthebaryonasymmetryoftheUniversevialeptogenesis.TherelevantCPphaseisidenticaltothelowenergyMajoranaphaseandsuccessfulleptogenesisrequiresaneffectivemassforneutrinolessdoublebetadecaylargerthan0.045eV.∗email:[e-mail]†email:[e-mail]‡email:[e-mail]1IntroductionObservedleptonmixingsareconsequencesofanon-trivialstructureoftheneutrinomassmatrixMν.ThissymmetricmatrixforMajorananeutrinos(havingentriesmαβwithα,β=e,μ,τ)isinthechargedleptonbasisdiagonalizedbythePontecorvo-Maki-Nakagawa-Sakata(PMNS)neutrinomixingmatrixU.TheverydifferentstructureofUcomparedtothequarksectorforallpossibleneutrinomassorderingsisindicativeofanunexpectedtex-tureofthemassmatrix,andcouldholdimportantcluestoourunderstandingofthephysicsoffundamentalconstituentsofmatter.Tounravelthisnewphysics,variousAns¨atzeforMνhavebeenmadeintheliterature[1]andtheirassociatedsymmetrieshavebeensoughtafter.Oneparticularproposal,recentlyproposedbytwoofus(R.N.M.andW.R.),onwhichwewillfocusinthisnote,iscalled“scaling”[2].Thescalinghypothesisdemandsthattheratiomαβmαγisindependentoftheflavorα:meβmeγ=mμβmμγ=mτβmτγ=cforfixedβandγ.(1)Therearethreepossibilitiesandtheonlyonephenomenologicallyallowediswhenβ=μandγ=τ.Weshallcallthiscasescalinghenceforth.TheresultingmassmatrixreadsMν=m0ABB/cBDD/cB/cD/cD/c2.(2)Similarmatriceshavebeenfoundindependentlyinthecontextofspecificmodels(seeRef.[3]).ThemostimportantphenomenologicalpredictionofscalingisthatEq.(2)leadstoaninvertedhierarchywithm3=0andUe3=0.Atmosphericneutrinomixingisgovernedbythe“scalingfactor”cviatan2θ23=1/c2,i.e.,isingeneralnon-maximalbecausecisnaturallyoforder,butnotequalto,one.Itisinterestingtonotethatcurrentdataanalyzes(thoughatthepresentstagestatisticallynotverysignificant)yieldnon-maximaltan2θ23=0.89asthebest-fitpoint[4](seealso[5],wherethebest-fitvalueistan2θ23=0.82).ThereasonisthatintheSuperKamiokandeexperimentthereisanexcessofsub-GeVelectronevents,butnoexcesseitherofsub-GeVmuoneventsorofmulti-GeVelectrons.Inarealistic3-flavoranalysisthispreferscosθ23sinθ23[4,5].Thebest-fitvalueofUe3iszero.Ifthesevalues,θ236=π/4andUe3=0,areindeedconfirmedbyfuturedatathenoneshouldlookforsymmetriesand/ormodelswhicharecapableofpredictingsuchasituation.Ideally,suchacandidateshouldberatherinsensitivetoradiativecorrectionsandshouldnotrequiremuch,ifany,breakingtoachievethevaluessoughtfor.Scalingisonesuchappealingpossibility,severalgeneralaspectsofwhichwillbediscussedinSection2.Typicalmodelsareshowntopredict–whenconstructedinasupersymmetricseesawframework–acharacteristicratioofthebranchingratiosμ→eγandτ→eγ.Thelatterdecayisthentooraretobeobservableinpresentlyforeseenexperiments.Simplephenomenologyof2fluxesofhighenergyastrophysicalneutrinosatneutrinotelescopesispredictedandstudiedinSection3.WearguefurtherinSection4thatitisdifficulttoobtainθ236=π/4andUe3=0inscenariosinwhichinitiallyθ23=π/4andUe3=0holds.StressingthatscalingpredictsaninvertedhierarchyleadsustocomparetheAnsatzwiththeflavorsymmetryLe−Lμ−Lτ[6].Thelatterisusuallyassumedtobetheoriginofaninvertedhierarchy.WeshowinSection5thatscalingpossessesseveraladvantagesoverLe−Lμ−Lτ.Iffutureexperimentsindeedshowthatneutrinosobeyaninvertedhierarchy,thenoneneedsafulllistofpossiblescenariosthatcanpredictit.Necessarily,theseareunusualsymmetriesastypicalGUTmodelsdonotleadtoaninvertedordering.Accordingly,weinvestigateinSection6aseesawmodelleadingtoscalingbasedonthediscretesymmetryD4×Z2.