Dark Matter Neutrinos Must Come with Degenerate Ma

arXiv:hep-ph/9712291v227Apr1998TMUP-HEL-9713hep-ph/9712291DarkMatterNeutrinosMustComewithDegenerateMassesHisakazuMinakata∗andOsamuYasuda†DepartmentofPhysics,TokyoMetropolitanUniversityMinami-Osawa,Hachioji,Tokyo192-0397,Japan(February,1997)AbstractIthasbeenknownthattherearetwoschemesintheframeworkofthreeflavorneutrinostoaccommodatetheglobalfeaturesofthehotdarkmatterneutrinos,thesolarneutrinodeficitandtheatmosphericneutrinoanomalyinamannerconsistentwithterrestrialneutrinoexperiments,i.e.,hierarchicalmassneutrinosandalmostdegenerateneutrinos.WedemonstratethattherecentresultbytheCHOOZexperimentexcludestheschemeofhierarchicalneutrinos.WealsopointoutintheschemeofalmostdegenerateneutrinosthatifneutrinosareMajoranaparticlesthenthedoubleβdecayexperimentsmustseepositivesignalsontheirwaytoreachalimitmorestringentthanthepresentonebyafactorof5.∗Email:[e-mail]†Email:[e-mail]inosaretheonlyknownparticlecandidatesforthedarkmatterintheuniverse[1].Whileitisunlikelythattheyareresponsibleforthedarkmatterasawholeinthecosmos,theyserveasthebestcandidatesforthehotcomponentinthemixed(cold+hot)darkmattermodel[2].Themodelisoneoftherivalmodelsthatcanaccountfortheobservedpowerspectrumofdensityfluctuationsoverwidelengthscales,fromgalaxy-galaxytomuchlongerscalesprobedbytheCOBEobservation[3].Theremainingunresolvedissueinthemodelishowmanyflavorsofneutrinosareactingasdarkmatter,e.g.,onlythetauneutrinoorallthreeofthem.TheparameterΩν[1],thefractionofthedensityofneutrinosintheuniverse,issensitivetothesumofneutrinomassesbutnottotheneutrinosmassspectrum.Theproblemofwhichmasspatternofneutrinoisfavoredhasbeendiscussedbasedonthegoodnessoffittovariouscosmologicalobservables[2].However,thedefinitiveconclusiondoesnotappeartobereachedyet.Herewemakeadifferentapproachtothesameproblembasedonaparticlephysicspointofview.Wedemandthatourschemeofthehotdarkmatterneutrinossatisfythefollowingrequirementsintheframeworkofthree-flavorneutrinos:(1)Neutrinosexistinthestandardthree-flavormixingframeworkwithoutsterilespecies.(2)Thethree-flavormixingframeworkmustaccommodatethedeficitofthesolarneutrinos[4]andtheanomalyintheratioR=(νμ/νe)observed(νμ/νe)expectedobservedintheatmosphericneutrinoexperiments[5].(3)Thethree-flavormixingframeworkmustbeconsistentwiththeconstraintsimposedbyallthereactorandtheacceleratorexperiments.11Inthispaper,wetakeaconservativeattitudetotheexperimentalresultsobtainedbytheLSNDgroup[6]whoclaimstoobservetheappearancesignalsconsistentwithneutrinooscillations.Wefeelthatweshouldwaitforconfirmationbyotherexperiments,KARMENandFermilab,beforeconcludingitasanevidenceforneutrinooscillations.Thesimilarattitudeissharedbytheauthor2Severalremarksareinorderontherequirements(1)-(3).(i)Thedarkmatterneutrinohypothesisrequiresneutrinomassesbutnotflavormixings.However,itisalegitimateassumptioninparticlephysicsthatneutrino’sgaugeandmasseigenstatesdifferiftheyaremassive.Itisanaturalassumptionbecauseweknowthattheflavormixingoccursinthequarksector[8].(ii)Itappearsthattheexistenceofthesolarneutrinodeficitandtheatmosphericneu-trinoanomalyarerobust,asconfirmedbytherecenthigh-statisticsmeasurementsbySu-perkamiokande[9].Themostlikelyexplanationoftheseanomaliesisduetotheneutrinomassesandtheflavormixing.(iii)Amongotherterrestrialexperimentstherecent¯νedisappearanceexperimentdonebytheCHOOZgroup[10]putsstringentconstraintsonthethree-flavorframeworkwetakeinthispaper.Intheframeworkofthethreeflavorneutrinostwoschemesofthehotdarkmatterneutrinoshavebeenknownwhichsatisfytherequirements(1)–(3).Oneistheschemeofalmostdegenerateneutrinos(ADN)[11],inwhichthemasssquareddifferencesΔm2ofneutrinosaremuchsmallerthanseveraleV2.Theotheroneisthatofhierarchicalmassneutrinos(HMN)[12–14],inwhichatleastoneofΔm2reflectsthedarkmattermassscale,∼afeweV.InthispaperweshowthattherecentresultbytheCHOOZexperimentexcludestheHMNscheme.WealsoshowthattheCHOOZresultputsastrongconstraintontheADNschemeandthattheADNscenariopredictsapositivesignalinneutrinolessdoubleβdecayexperimentsinthenearfuture.Insection2wesummarizetheconstraintsfromtheacceleratorandreactorexperiments.Insection3weperformaqualitativeanalysisinwhichweonlyrelyontheglobalfeaturesoftheanomalies.Insection4weanalyzeindetailthegoodnessoffitoftheHMNschemetothesolarandtheatmosphericneutrinodata,takingintoaccountmoresophisticatedissues,suchofRef.[7]3asthezenith-angledistributionoftheatmosphericneutrinodata.Insection5wediscusstheconstraintsonthehotdarkmatterscenariowiththeADNschemebytheCHOOZresultandtheneutrinolessdoubleβdecayexperiments.Insection6wesummarizeourconclusionsandgiveremarksonpossiblesignalsinthenearfutureexperiments.II.CONSTRAINTSFROMACCELERATORANDTHEREACTOREXPERIMENTSThemass-squareddifferencesΔm2greaterthan1eV2aresubjecttotheconstraintsbytheshort-baselineacceleratorandthereactorexperiments.Therefore,themixingparametersoftheHMNscenarioaretightlyconstrainedbythem.ThispointhasrecentlybeenrevealedexplicitlybytheauthorsofRefs.[12,15–17]inagenericthree-flavormixingframework,whereasitmayhavebeenimplicitlynoticedbefor