Leptogenesis and dark matter unified in a non-SUSY

arXiv:0706.2401v1[hep-ph]16Jun2007KANAZAWA-07-06June,2007Leptogenesisanddarkmatterunifiedinanon-SUSYmodelforneutrinomassesDaijiroSuematsu∗InstituteforTheoreticalPhysics,KanazawaUniversity,Kanazawa920-1192,JapanAbstractWeproposeaunifiedexplanationfortheoriginofdarkmatterandbaryonnumberasym-metryonthebasisofanon-supersymmetricmodelforneutrinomasses.Neutrinomassesaregeneratedbytwodistinctways,thatis,tree-levelseesawmechanismwithasingleright-handedneutrinoandone-loopradiativeeffectsbyanewadditionaldoubletscalar.AspontaneouslybrokenU(1)′bringsaZ2symmetrywhichrestrictscouplingsofthisnewscalarandcontrolstheneutrinomasses.ItalsoguaranteesthestabilityofaCDMcandidate.Thedecayofaheavyright-handedneutrinorelatedtotheseesawmechanismgeneratesbaryonnumberasymmetrythroughleptogenesis.∗e-mail:[e-mail]11IntroductionNeutrinomasses[1],colddarkmatter(CDM)[2],andbaryonnumberasymmetryintheuniverse[3]suggestthatthestandardmodel(SM)shouldbeextended.Bothneutrinomassesandbaryonnumberasymmetryarewellknowntobeexplainedinaunifiedwaythroughtheleptogenesisscenariointheframeworkoftheseesawmechanism[4].Extensivestudieshavebeendoneonthissubjectduringrecentseveralyears[5].Ontheotherhand,supersymmetryisknowntobeusefulfortheexplanationofCDMabundanceintheuniverse[6].SupersymmetricmodelshavegoodcandidatesforCDMsuchasthelightestsuperparticle(LSP)aslongasR-parityisconserved.TheneutralinoLSPhasbeenextensivelystudiedasaCDMcandidateinthesupersymmetricSM(MSSM)anditssingletextensions[7,8].IfwetrytoexplainsimultaneouslyboththeleptogenesisandtheCDMabundanceinsupersymmetricmodels,wehaveadifficultyunfortunately.Theout-of-equilibriumdecayofthermalheavyneutrinosgeneratessufficientbaryonnumberasymmetryonlyifthereheatingtemperatureishighenoughsuchasTR108GeV.Forsuchreheatingtemperature,however,weconfronttheseriousgravitinoprobleminsupersymmetricmodels[9].VarioustrialstoovercomethisdifficultyhavebeendonebysearchingscenariostoenhancetheCPasymmetryandlowertherequiredreheatingtemperature[10,11,12].However,inthesestudiestheCDMandthebaryonnumberasymmetryareseparatelyexplainedbasedonunrelatedphysics.WecannothaveanyhintswhytheCDMabundanceissimilarordertothebaryonnumberasymmetryinthepresentuniverse.1Inthiscircumstanceitmaybeusefultoreconsidertheseproblemsinnon-supersymmetricmodelsonthebasisofcloselyrelatedphysics.Recently,ithasbeensuggestedthatneutrinomassesandCDMabundancemayberelatedinsomekindofnon-supersymmetricmodelsforneutrinomasses[14,15].Insuchmodelsneutrinomassesaregeneratedthroughtheone-loopradiativeeffectswhichareinducedbynewscalarfields.AcertainZ2symmetryprohibitinglargeneutrinomassescanalsoguaranteethestabilityofaCDMcandidatelikeR-parityinsupersymmetricmodels.Thebaryonnumberasymmetryhasalsobeendiscussedinthismodel[16].Ifwecanexplainthesethreeexperimentalevidencesbasedonthistypeofmodels,wemightgetimportantcluesforphysicsbeyondtheSM.1ThereareseveralworkstorelatetheCDMabundancetothebaryonnumberasymmetry.Forsuchtrials,see[13]forexample.2InthispaperwestudyapossibilitythatthebaryonnumberasymmetryiscloselyrelatedtotheoriginofbothneutrinomassesandCDMabundance.Weshowthattheordinaryleptogenesisbasedonheavyneutrinodecaycanbeembeddedconsistentlyinanon-supersymmetricmodelforneutrinomassesproposedin[15].AmodelconsideredhereisanextensionoftheSMbyintroducingalocalU(1)′symmetry,anadditionalSU(2)doubletηT≡(η+,η0),andasingletφatTeVregions.TheU(1)′symmetryrestrictscouplingsofthesefieldsandscalarpotential.ItisspontaneouslybrokentoZ2byavacuumexpectationvalue(VEV)ofφ.ThisZ2symmetryisresponsibleforthesmallnessoftheneutrinomassesandthestabilityofaCDMcandidate.Theη0playsanimportantroleintheneutrinomassgeneration.Thedecayofaheavyright-handedneutrinocancausethegenerationoftheleptonnumberasymmetry.Thisframeworkgivesaunifiedpicturefortheexplanationoftheneutrinomasses,theCDMabundance,andthebaryonnumberasymmetry.2AmodelforneutrinomassesThepresentstudyisbasedonthemodelproposedin[15].IngredientsofthemodelandU(1)′chargeassignmentsaregiveninTable1.WesupposethatU(1)′isleptophobic.2TheextensiontogeneralU(1)′sisstraightforwardasdiscussedin[15].FermionslistedinTable1areassumedtobeleft-handed.AlthoughweneedthreesingletfermionsN1,2,3,onlytwoofthemareassumedtoplayessentialrolestogenerateappropriatemassesandmixingintheneutrinosector.Additionaloneisnecessaryfortheleptogenesis.InvariantLagrangianrelevanttotheneutrinomassescanbeexpressedasLm=Xα=e,μ,τhα1LαH¯N1+hα2LαH¯N2+hα3Lαη¯N3+12M1¯N21+12M2¯N22+12λφ¯N23+h.c..(1)WeassumethatYukawacouplingsforchargedleptonsarediagonalizedalready.TheinvariantscalarpotentialuptodimensionfiveisgivenasV=12λ1(H†H)2+12λ2(η†η)2+12λ3(φ†φ)22Weneedtointroducesomefieldstocancelgaugeanomaly.However,sinceitcanbedonewithoutaffectingthefollowingstudy,wedonotdiscussthispointfurtherhere.3Qα¯Uα¯DαLα¯Eα¯N1,2¯N3HηφU(1)′2q−2q−2q000q0−q−2qZ2+1+1+1+1+1+1−1+1−1+1Table1.Fieldcontentsandtheircharges.Z2istheresidualsymmetryofU(1)′.+λ4(H†H)(η†η)+λ5(H†η)(η†H)+12M∗hλ6φ(η†H)2+h.c.i+(m2H+λ7φ†φ)H†H+(m2η+λ8φ†φ)η†η+m2φφ†φ,(2)wherethecouplingsλiarerealexceptforλ6.Thephaseofλ6caninduceaphysicalonewhi