Two-loop Neutrino Mass Generation and its Experime

arXiv:hep-ph/0212058v14Dec2002OSU-HEP-02-15Two–loopNeutrinoMassGenerationanditsExperimentalConsequencesK.S.BabuandC.MacesanuDepartmentofPhysicsOklahomaStateUniversityStillwater,OK74078,USAAbstractIfneutrinomasseshavearadiativeorigin,theirsmallnesscanbenaturallyunderstoodevenwhenleptonnumberviolationoccursneartheweakscale.Weanalyzeaspecificmodelofthistypewhereintheneutrinomassesariseastwo–loopradiativecorrections.Weshowthatthemodeladmitsthenearbimaximalmixingpatternsuggestedbythecurrentneutrinooscillationdata.Unliketheconventionalseesawmodels,thesetwo–loopmodelscanbedirectlytestedinleptonflavorviolatingdecaysτ→3μandμ→e+γaswellasatcollidersbythedirectobservationofchargedscalarsneededforthemassgeneration.ItisshownthatconsistencywiththeneutrinooscillationdatarequiresthattheleptonicraredecaysshouldbewithinreachofforthcomingexperimentsandthatthechargedscalarsarelikelytobewithinreachoftheLHC.1I.INTRODUCTIONRecentneutrinooscillationexperiments,notablySuper-KamiokandeandSNO,havepro-videdawealthofinformationonneutrinomassesandmixingpattern.Firstandforemost,thesolar[1]andtheatmosphericneutrinodata[2]areincompatiblewiththehypothesisofzeroneutrinomass.Theinferredvaluesofneutrinomassesareinthesub–eVrange.Themixingangleθ12relevantforsolarneutrinooscillationsappearstobelarge(tan2θ12∼0.4)[3],whiletheoneforatmosphericneutrinooscillationsθ23∼π/4isnearmaximal.Re-actorneutrinoexperiments[4]constrainthethirdmixingangleθ13toberelativelysmall,θ13≤0.16.Itwillbeofgreatinteresttoseekatheoreticalunderstandingoftheseobserva-tions.Theseesawmechanism[5]hasbeenthemostpopularexplanationofthesmallneutrinomasses.Itiselegantandsimple,andreliesonlyondimensionalanalysisfortherequirednewphysics.CurrentneutrinodatapointstoaseesawscaleofMR∼1010−1015GeV,whereleptonnumberviolationoccursthroughtheMajoranamassesoftheright–handedneutrinos.Withsuchahighscale,effectsofleptonflavorviolationinprocessesotherthanneutrinooscillationitselfbecomesextremelysmall.Forexample,thebranchingratioforthedecayμ→e+γisoforder10−50withintheseesawextensionoftheStandardModel.Analternativetotheseesawmechanismwhichalsoexplainsthesmallnessofneutrinomassesnaturallyistheradiativemassgenerationmechanism[6–14].Inthisapproach,neutrinomassesarezeroatthetree–level,andareinducedonlyasfiniteradiativecorrections.Theseradiativecorrectionsaretypicallyproportionaltothesquareofthechargedlepton(orquark)massesdividedbythescaleofnewphysicsΛ.Theneutrinomassescanthenbeinthesub–eVrangeevenforΛ∼TeV.Inthiscase,leptonflavorviolationinprocessesotherthanneutrinooscillationsmaybecomeexperimentallyaccessible.Inthispaperweproposetoanalyzeindetailtheexperimentalconsequencesofaspe-cificmodelwhereintheneutrinomassesariseastwo–loopradiativecorrections[8,9].Themagnitudeoftheseinducedmassesareofordermν∼[(f2h)/(16π2)2](m2τ/Λ),wheref,haredimensionlessYukawacouplingsandΛisthescaleofnewphysics.Forf∼h∼0.1andΛ∼1TeV,theneutrinomasswillbeoforder0.1eV,whichiscompatiblewiththeoscillationdata.Withinthismodel,itisrequiredthatf,h≥0.1andΛ≤1TeV,orelsetheinducedneutrinomasswillbetoosmalltoberelevantexperimentally.Theselimits,alongwiththerequirementoflargesolarandatmosphericneutrinooscillationangles,implythatleptonflavorviolationinprocessessuchasτ→3μandμ→e+γcannotbesuppressedarbitrarily.Weshallseethatthesedecaysarewithinreachofthenextroundofraredecayexperiments.Furthermore,theupperlimitonΛimpliesthatitisverylikelythatthenewscalarspredictedbythemodelforneutrinomassgenerationwillbeaccessiblefordirectobservationattheLHCandperhapsevenatRunIIoftheTevatron.Avarietyofradiativeneutrinomassmodelsexistintheliterature.TheZeemodelofneutrinomass[6]isapopularexample.Inthismodel,neutrinomassesariseasone–loopradiativecorrections.ThismodelappearstobeincompatiblewiththelargemixingangleMSWsolutionforthesolarneutrinoproblemasitpredictstherelevantmixingangletotoveryclosetoπ/4[15].Inanycase,onewouldexpectrareleptonicprocessestobemoresuppressedintheZeemodelcomparedtothetwo–loopneutrinomassmodel[8,9].ThisisbecausetheneutrinomassesintheZeemodel,beingofone–looporigin,areoforder2mν∼[fg/(16π2)](m2τ/Λ),andinorderforittoexplaintheatmosphericdata,onemustchooseeitherf≤10−4ifΛ≤TeV,orΛ≥106GeViff∼1.Thisshouldbecontrastedwiththetwo–loopneutrinomassmodelwheretheYukawacouplingsareneededtobeorder0.1andΛoforderTeV.AnotherclassofneutrinomassmodelsthathasbeenwidelystudiedissupersymmetricmodelswithexplicitR–parityviolation[10].Inthiscase,itturnsoutthatonlyoneneutrinoacquiresatree–levelmass,theothertwoobtainmassesasone–loopradiativecorrections.Thephenomenologyofsuchmodels,especiallywhenR–parityviolationissoft,arisingonlythroughbilinearterms,hasbeenthoroughlyinvestigated[13].InRef.[14]ageneraleffectiveoperatorapproachforsmallMajorananeutrinomasseshasbeenpresented.Itfollowsfromthatanalysisthatifleptonnumberviolationresidesonlyintheleptonicsectoranddoesnotinvolvethequarks,thentheonlyinterestingmodelforthecurrentneutrinooscillationdatathatalsopredictsobservableleptonflavorviolationsignalsisthetwo–loopmodelofRef.[8,9].Thisisthemainreasonforrevisitingthetwo–loopmodelinthepresentpaper.The