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arXiv:hep-ph/9502315v116Feb1995NewSupersymmetricContributionstoNeutrinolessDoubleBetaDecayM.Hirsch1,H.V.Klapdor-Kleingrothaus2Max-Plank-Institutf¨urKernphysik,P.O.103980,D-69029,Heidelberg,GermanyS.G.Kovalenko3JointInstituteforNuclearResearch,Dubna,RussiaAbstractTheneutrinolessdoublebeta(0νββ)decayisanalyzedwithintheMinimalSupersymmetricStandardModelwithexplicitR-parityviola-tion(Rp/MSSM).WehavefoundnewsupersymmetriccontributionstothisprocessandgivethecompletesetofrelevantFeynmandiagrams.Operatorsdescribing0+−→0+nucleartransitionsinducedbythesu-persymmetricinteractionsoftheRp/MSSMarederived.Theseoperatorscanbeusedforcalculatingthe0νββdecayrateapplyinganyspecificnuclearmodelwavefunctions.Theobservationofneutrinolessdoublebeta(0νββ)decaywouldbeaclearsignalforphysicsbeyondthestandardmodel,sinceitviolatesleptonnumberbytwounits(forreviewssee[1],[2]).Nodefiniteobservationof0νββdecayhasbeenreportedtodate,butrecentexperimentalprogresshaspushedtheexistinghalf-lifelimitsof0νββdecaybeyond1024yearsandfurtherprogresscanbeexpectedinthenearfuture[3].Half-lifelimitson0νββdecayareusuallyinterpretedaslimitsontheeffec-tiveMajorananeutrinomass(seefig.1).However,itisknownforsometimethatthereexistalsoothermechanismswhichmightinduce0νββdecays,likeforexampleinleft-rightsymmetricextensionsofthestandardmodelgaugegroup[2].Inthispaperwestudycontributionsto0νββdecaywithinsuper-symmetric(SUSY)theorieswithexplicitR-paritybreaking.R-parity(Rp)isadiscrete,multiplicativesymmetrydefinedasRp=(−1)3B+L+2S,whereS,B1MAHIRSCH@ENULL.MPI-HD.MPG.DE2KLAPDOR@ENULL.MPI-HD.MPG.DE3KOVALEN@NUSUN.JINR.DUBNA.SU1andLarethespin,thebaryonandtheleptonquantumnumber.ConservationofR-parityinturnimpliesbaryonnumber(B)andleptonnumber(L)con-servation.Thissymmetryhasbeenimposedontheminimalsupersymmetricstandardmodel(MSSM)(forareviewsee[4]).However,neithergaugeinvari-ancenorsupersymmetryrequireRpconservation.ThequestionwhetherornotRpisagoodsymmetryofthesupersymmetrictheoryisadynamicalproblemwhichmightberelatedtomorefundamentalphysicsatthePlanckscale.Ingeneral,Rpcanbeeitherbrokenexplicitly[5],[6]orspontaneously[7],[8]bythevacuumexpectationvalueofthescalarsuperpartneroftheRp-oddisos-ingletleptonfield[8].SupersymmetricmodelswithRpnon-conservation(Rp/)havebeenextensivelydiscussedintheliteraturenotonlybecauseoftheirgreattheoreticalinterest,butalsobecausetheyhaveinterestingphenomenological[9],[10],[11],andcosmological[12]-[15]implications.OnecanexpectthatRp/SUSYmodelsgiveaverynaturalframeworkforleptonnumberviolatingprocessesandparticularly0νββdecay[20].Letusstartwithabriefreviewofthemodelweuseinthepresentpaper.WefollowtheMSSMextendedbyinclusionofexplicitR-parityviolating(Rp/)termsintothesuperpotential.Thismodel(Rp/MSSM)hastheMSSMfieldcontentandiscompletelyspecifiedbythestandardSU(3)×SU(2)×U(1)gaugecouplingsaswellasbythelow-energysuperpotentialand”soft”SUSYbreakingterms[4].Themostgeneralgaugeinvariantformofthesuperpoten-tialis[11],[16]W=WRp+WRp/.(1)TheRpconservingparthasthestandardMSSMformWRp=hLH1L¯E+hDH1Q¯D−hUH2Q¯U−μH1H2.(2)WeusenotationsL,Qforleptonandquarkdoubletsuperfieldsand¯E,¯U,¯Dforleptonandup,downquarksingletsuperfields;H1andH2aretheHiggsdoubletsuperfieldswithaweakhyperchargeY=−1,+1,respectively.Sum-mationovergenerationsisimplied.ForsimplicitygenerationindicesoffieldsandYukawacouplingconstantshL,hU,hDaresuppressed.Themass-mixingparameterμisafreeparameterdescribingmixingbetweentheHiggsbosonsH1-H2aswellasbetweenhiggsinos˜H1-˜H2.TheRpviolatingpartofthesuperpotential(1)canbewrittenas[5],[6],WRp/=λijkLiLj¯Ek+λ′ijkLiQj¯Dk+λ′′ijk¯Ui¯Dj¯Dk(3)whereindicesi,j,kdenotegenerations,andthefieldshavebeendefinedsothatthebilinearleptonnumberviolatingoperatorsLiH2[6]havebeenrotated2away.Thecouplingconstantsλ(λ′′)areantisymmetricinthefirst(last)twoindices.Thefirsttwotermsleadtoleptonnumberviolation,whilethelastoneviolatesbaryonnumberconservation.Protonstabilityforbidssimultaneouspresenceofleptonandbaryonnumberviolatingtermsinthesuperpotential[10](unlessthecouplingsareverysmall).Therefore,onlyλ,λ′orλ′′typeinteractionscanbepresent.Theremayexistanunderlyingdiscretesymmetryinthetheorywhichallowseitherthefirstorthesecondsetofcouplings.Thisdiscretesymmetry,calledmatterparity[11],[16]canbeimposed’adhoc’ontheMSSM.ItcanbejustifiedonamorefundamentallevelofPlanckscalephysics.SuchadiscretesymmetryisshowntobecompatiblewiththeordinarySU(5)[6]and”flipped”SU(5)×U(1)[17]grandunification(GUT)scenarios,aswellaswithphenomenologicallyviablesuperstringtheories[18].Neutrinolessdoublebetadecay,whichisthemainsubjectofthepresentpaper,requiresleptonnumberviolatinginteractions.Thereforewebindour-selvestotheRp/MSSMwithleptonnumberviolation(λ6=0,λ′6=0)andbaryonnumberconservation(λ′′=0).Apparently,0νββcanprobeonlythefirstgenerationleptonnumberviolatingYukawacouplingλ′111becauseonlythefirstgenerationfermionsu,d,eareinvolvedinthisprocess.InadditiontoprotondecayconstraintsonRp/couplingstherearealsocon-straintswhichfollowfromcosmologicalargumentsrequiringthatthebaryonasymmetrygeneratedattheGUTscaleisnotwashedoutbyB−Lviolat-inginteractionsprese
本文标题:New Supersymmetric Contributions to Neutrinoless D
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