Neutrinoless double beta decay in Supersymmetry wi

arXiv:hep-ph/9812463v38Jun1999hep-ph/yymmddFTUV/98-100IFIC/98-101NeutrinolessdoublebetadecayinSupersymmetrywithbilinearR-paritybreakingM.Hirsch1andJ.W.F.Valle2InstitutodeF´ısicaCorpuscular–C.S.I.C.DepartamentodeF´ısicaTe`orica,UniversitatofVal`encia46100Burjassot,Val`encia,Spainhttp://flamenco.uv.es//PACS:12.60Jv,14.60Pq,23.40-sAbstractWereanalyzethecontributionstoneutrinolessdoublebeta(ββ0ν)decayfromsupersymmetrywithexplicitbreakingofR-parity.Althoughwekeepbothbilinearandtrilinearterms,ouremphasisisputonbi-linearR-paritybreakingterms,becausethesemimicmorecloselythemodelswherethebreakingofR-parityisspontaneous.ComparingtherelevantFeynmandiagramsweconcludethattheusualmassmechanismofdoublebetadecayisthedominantone.Fromthenon-observationofββ0νdecaywesetlimitsonthebilinearR-paritybreakingparametersoftypicallya(few)100keV.Despitesuchstringentbounds,westressthatthemagnitudeofR-parityviolatingphenomenathatcanbeex-pectedatacceleratorexperimentscanbeverylarge,sincetheyinvolvemainlythethirdgeneration,whileββ0νdecayconstrainsonlythefi[e-mail][e-mail]11IntroductionThemostwell-studiedrealizationofsupersymmetryhasaconservedR-parity.ThisisamultiplicativequantumnumberwhichcanbedefinedasRP=(−1)3B+L+2S,whereBandLarethebaryonandleptonnumberandSthespinofthecorrespondingparticle.ThisdefiningpropertyoftheMinimalSuper-symmetricStandardModel(MSSM)[1]istheoreticallyadhocsincetheoriginofR-parityconservationisunknown.SincetheearlydaysitwasrecognizedthattheviolationofR-paritycouldariseasresidualeffectsinlargertheories[2]orspontaneouslyduetoasneutrinovacuumexpectationvalue(VEV)[3].Wefindthemodelswithpurespontaneousbreakingmorewell-motivatedthanexplicitbreakingmodels,inthesensethattheyputR-paritybreakingonadynamicalfooting.Theyhaveonlyleptonnumberviolating(L/)termsandarethereforeinagreementwithprotonstability.Thesimplestmodelsofthistype(withtheSU(2)⊗U(1)gaugestructure)arecharacterizedbytheexis-tenceofaphysicalGoldstoneboson,genericallycalledmajoron.Intheearlyversionsthemajoronwasanisodoublet(theimaginarypartofthesneutrino)[3];thesearenowruledoutbyLEPmeasurementsoftheinvisibleZwidth[4].However,inthemodernvariantsofsupersymmetricmodelswithspontaneousR-paritybreakingthemajoronisasinglet(suchasaright-handedsneutrino)andthereforecannotbeproducedinthedecaysoftheZ.Such(Rp/)modelsareboththeoreticallyattractiveandphenomenologicallyviable[5,6].However,quitegenerallystudyofbrokenR-parityphenomenologyhasreceivedalotofattentionrecently[7,8,9,10].Especiallyinterestinginviewofthemountingevidencefornon-zeroneu-trinomasses[11,12,13]isthefactthatRp/modelsallowforfinite-andinprinciplecalculable-neutrinomasses,andmoreovercouldevenexplaintheirobservedsmallnesswithoutinvokingsomehigh-energyscalephysics[14],likeonedoesforexampleinthesee-sawmechanism[15].Neutrinolessdoublebeta(ββ0ν)decayisaΔL=2processandthereforeonenaturallyexpectsittooccurinmodelswithleptonnumberviolationintheLagrangian.Eventhoughthereisavarietyofmechanismsinducingββ0νdecayingaugetheories,onecanshowthatwhatevertheleadingmechanismisatleastoneoftheneutrinoswillbeaMajoranaparticle[16],asillustratedintheblack-boxdiagramofFig.1.Thiswell-knownargumentestablishesadeepconnectionbetweenMajorananeutrinomassesandββ0νdecay:ingaugetheoriesonecannotoccurwithouttheotherbeingpresent.Thesameremainstrueinsupersymmetrictheories[17],wheremoreoveronecanshow2thatalsothesupersymmetricpartneroftheneutrinomusthaveaB−LviolatingMajorana-likemassterm,ifaMajoranamassoftheneutrinoexists[17].Turningtheargumentaround,oneexpectsthattheobservedabsenceofββ0νdecayallowstoderivestringentlimitsonRp/parameters.ThishasbeenshownformodelswithexplicittrilinearR-paritybreakingin[18,19].InthecurrentworkwewillconcentrateonthebilinearRp/terms.ββ0νdecaywithinsupersymmetricmodelswithbilinearR-paritybreakinghasbeenconsideredpreviouslyin[20].Inourderivationthefinalexpressionofthedecayrate(andthecorrespondingnuclearmatrixelements),however,differfromtheonegivenin[20],detailsaregiveninsection3.InanexactlysupersymmetricandSU(2)L-invariantworldR-parityVio-lation(RPV)canbemovedaroundtheLagrangianbyfieldredefinitions[2].Thisobservationleadtotheclaim,thatthebilinearRPVtermsareunphysicalandshouldbediscarded.Howeverithasbeenshownthatinrealisticsoftlybrokensupersymmetricmodelsitisingeneralimpossibletoeliminatethebi-linearterms[21].Moreover,asalreadystated,itispossiblethatR-parityisasymmetry(maybeapproximate)attheLagrangianlevel,brokenonlybythegroundstate[5].SuchscenariosleadonlytoL/beingthereforeconsistentwithbaryonnumberconservation.Modelswithbilineartermscanbeimag-inedasatruncatedversionofthefulldynamicalmodels[21]andassuchofferasystematicwaytoinvestigateRPVatthephenomenologicallevel.Thispaperisorganizedasfollows.Inthenextsectionweintroduceourconventionsandnotations.Section3derivestheeffectiveLagrangianofββ0νdecayinRp/SUSYwithbilinearterms,whilesection4summarizesthenecessarynuclearphysicsinput.Section5thenanalyzestheconstraintsββ0νdecaycanputonbilinearRp/parameters.2SupersymmetrywithexplicitR-paritybreak-ingter