A Higher-dimensional Origin of the Inverted Mass H

arXiv:hep-ph/0511336v130Nov2005AHigher-dimensionalOriginoftheInvertedMassHierarchyforNeutrinosM.Tanimoto1andT.Yanagida21DepartmentofPhysics,NiigataUniversity,Niigata950-2181,Japan2DepartmentofPhysics,UniversityofTokyo,Tokyo1130033,JapanAbstractWepresentsuccessfulleptonmassmatriceswithaninvertedmasshierarchyforneu-trinos,whichfollowfromageometricalstructureofa(1+5)dimensionalspace-timewheretwoextradimensionsarecompactifiedontheT2/Z3orbifold.A5∗andaright-handedneutrinoNineachfamilyarelocalizedoneachoftheequivalentthreefixedpointsoftheorbifoldwhilethree10’sandHiggsdoubletsHuandHdliveinthebulk.AnS3familysymmetryisassumedonthree5∗’sandonthreeN’s,sincethethreefixedpointsareequivalenttooneanother.TheHiggsfieldφresponsiblefortheB-Lbreakingislocalizedononeofthethreefixedpoints,whichgeneratestheinvertedhierarchyfortheneutrinomasses.Thebaryonasymmetryiswellexplainedinthenon-thermalleptogenesisviain-flatondecay.Weemphasizethatthepresentmodelpredictstheeffectiveneutrinomass,hmiee,responsibleforneutrinolessdoublebetadecaysashmiee≃50meV.Thiswillbeaccessibletofutureexperiments.11IntroductionItisachallengingandimportanttasktofindanoriginoftheobservedhierarchiesinmassmatricesforquarksandleptons,sinceitmayprovideuswithacluetoamorefundamentaltheorybeyondthestandardmodel.Themostremarkableobservationisthattheweakmixinganglesintheleptonsectorareoftheorder1whilethoseinthequarksectoraresmall.Thisindicatesthatnatureofleft-handedleptondoubletsisverydifferentfromthatofleft-handedquarkdoublets,whichmeansthatthereisabigdisparitybetweenmultiplets5∗’sand10’sintheSU(5)grandunificationmodel.Ithasbeenpointedout[1]thata(1+5)dimensionalspace-timemayexplaintheabovedisparityifextratwodimensionsarecompactifiedontheT2/Z3orbifold.Thisorbifoldhasthreeequivalentfixedpoints.Here,a5∗andaright-handedneutrinoNineachfamilyarelocalizedoneachofthethreefixedpointsoftheorbifold,whilethree10’sliveinthebulk.Onemayobtainnaturallysuccessfuldemocraticmassmatricesforquarksandleptons,providedthatthethree10’s,HiggsdoubletsandaHiggsφresponsiblefortheB-Lsymmetrybreakingaredistributedhomogeneouslyinthebulk.Thus,thistheorymayprovideamodelforthealmostdegenerateneutrinomasses.Ithasbeen,furthermore,shown[2]thatanextensionofthemodeltothetypeIIBstringtheorymayexplainnotonlytheabovegeometricalstructureofthewavefunctionsfor5∗’s,N’sand10’sbutalsothepresenceofHiggsdoubletsHuandHdinthebulk.However,thenatureoftheB-Lbreakingisnotclearlyunderstood.ItisremarkablethatiftheHiggsφfortheB-Lbreakingislocalizedononeofthethreefixedpoints,oneofNacquiresasuperheavyMajoranamassgeneratinganinvertedhierarchyintheneutrinomassspectrum.Thepurposeofthepresentpaperistodiscussthispossibility.Ouranalysisshowsthatthepresentmodelisconsistentwithallobservationsonneu-trinomassesandmixingangles.Furtherweshowthatthematrixelementresponsibleforneutrinolessdoublebetadecaysispredictedashmiee≃50meV.Thepredictionwillbe2testedinfutureexperiments.Insection2,wediscusstheneutrinoandchargedleptonmassmatrices,wheretheinvertedneutrinomassspectrumisnaturallyobtained.Insection3,thenon-thermalleptogenesisviainflatondecayisdiscussedinthepresentmodel.Thesummaryisdevotedtosection4.2NeutrinoMassesandMixingsOurdiscussionisbasedonthemodelproposedin[1,2].Here,a5∗andaright-handedneutrinoNineachfamilyarelocalizedononeoftheequivalentthreefixedpointsoftheT2/Z3orbifoldwhilethree10’sandHiggsdoubletsHuandHdliveinthebulk.WeassumeinthispaperthattheφfortheB-Lbreakingislocalizedonthefixedpointonwhichthe5∗andNinthethirdfamilyreside.Thus,theN3inthethirdfamilyhasaverylargeMajoranamasscomparedwiththoseofotherN’s.Weconsideraninterchangesymmetrybetweenthefieldsontheorbifoldfixedpoints,sincethethreefixedpointsareequivalenttooneanother.Thatis,weassumeanS3familysymmetryactingonthree5∗’sandonthreeN’s.Then,theneutrinoandchargedleptonmassmatricesaregivenintermsofafewparameters.However,wehavetointroducebreakingsoftheS3symmetrytoobtainrealisticmassmatrices.Weassumetwosourcesofthebreaking.Oneisalocalizationofthewavefunctionoftheφandtheotherissmalldistortionsofthewavefunctionsofthethree10’sandthedoubletHiggsesfromhomogeneousformsinthebulk.2.1NeutrinoMassMatrixLetusbeginbydiscussingtheDiracneutrinomassmatrix,whichisgivenbytheYukawacouplingmatrixofN5∗Hu.Therearetwoindependentmatriceswhichareinvariantof3theS3symmetry[3,4].Namely,theS3invariantDiracmassmatrixisgivenby[3]hν=h0100010001+0ǫǫǫ0ǫǫǫ0.(1)Noticethattheparameterǫissuppressedbyseparationofthethreefixedpoints.Weexpectǫ≃exp(−ℓ∗×M∗)whereℓ∗andM∗arethedistancebetweendifferentfixedpointsandamassscaleofthefundamentaltheory,respectively[5].Forinstance,wehaveǫ≃0.001forℓ∗×M∗≃7.Wehaveassumed,sofar,ahomogeneousdistributionoftheHiggsfieldsHuinthebulk.AsmalldistortionoftheHiggswavefunctionmayinduceaviolationoftheS3symmetry.Thebreakingeffectsappearfirstinthediagonalelementsoftheabovemassmatrixandtheeffectsintheǫtermmaybenegligibleforourdiscussion.Therefore,theneutrinoDiracmassmatrixisgivenbyhν=h010001+δ10001+δ2+0ǫǫǫ0ǫǫǫ0=h01ǫǫǫ1+δ1ǫǫǫ1+δ2.(2)Here,wetakeabasiswhereallthediagonalelementsarerealwhiletheoffdia