10Cosmological Constraints on the MSSM

UniversityofWisconsin-MadisonMADPH-99-1144November1999CosmologicalConstraintsontheMSSMTobyFalkDepartmentofPhysics,UniversityofWisconsin,Madison,WI53706,USAIdiscussrecentdevelopmentsinthestudyofcosmologicallimitsontheMinimalSupersymmetricStandardModel(MSSM).Inparticular,Ifocusontheeectofneutralino-staucoannihilationontherelicabundanceofneutralinos,andIgiveexampleswherethecosmologicallyderivedlimitsonthesupersymmetricparametersarerelaxed,andoneexample(CPviolatingphases)wheretheyarenot.PACSnumbers:11.30.Pb,11.30.Er,95.35.+d1.IntroductionThetitleofthistalkisratherbroad.SpecicallywhatIwillbetalkingabouttodayisrelicdensityconstraintsonsupersymmetricmodels,andIwillfocusinparticularonboundsonminimalSupergravity(mSUGRA).I’llbeginwithabriefreminderofthenotationofsupersymmetry,thengiveanintroductiontorelicdensities,howtheyarecomputed,andhowwecanusethemtoconstrainmodelsoflow-energysupersymmetry.I’llthendiscusscoannihilationingeneralandshowhowitdramaticallyrelaxesthecosmologicalupperboundonthemSUGRAmasses.Finally,I’llgiveanexampleofconstraints(onCPviolatingphasesinmSUGRA)whicharenotrelaxedbytheweakenedmasslimits.2.SUSYSincepreviousspeakershaveintroducedtheSupersymmetricStandardModel,Iwillgiveonlyabriefreminder,inordertopresenttheparticlecontentandparametersandtosetthenotation.RecallthatSUSYessen-tiallydoublestheparticlecontentofthestandardmodel(Table1).EachPresentedattheXXISchoolofTheoreticalPhysics,Ustro~n’99:RecentDevelopmentsinTheoryofFundamentalInteractions.(1)2fermion(infacteachfermionchiralstate)hasaspin-0partnersfermion,thegaugebosonshavespin-1/2partnergauginos,andthedegreesoffree-domoftheHiggssector,whichnowcontainstwoHiggsSU(2)doublets,havespin-1/2Higgsinopartners.ThefourneutralgauginosandHiggsinosmixinto\neutralinostatesi,sothatanarbitraryneutralinoisalinearcombinationi=i~B+i~W3+i~H1+i~H2;i=1;:::;4(1)wherethe~Band~W3arethepartnersoftheU(1)YandneutralSU(2)gaugebosonsandarelinearcombinationsofthe~and~Z.Thelightestofthetheneutralinos1tendstobethelightestsupersymmetricparticle,andinthemodelsofinterestfordarkmatter,1tendstobe~B-like,i.e.j1j1.Similarly,thechargedgauginosandHiggsinosmixintotwo\charginos,1;2.SMSUSYfermions!sfermionsu;d;eL;eR:::~u;~d;~eL;~eR:::gaugebosons!gauginosg;Z;;W:::~g;~Z;~;~W:::Higgsbosons!HiggsinosH1;H2:::~H1;~H2:::Table1.TheSUSYpartnersofStandardModelparticles.AlongwiththenewparticlesoftheMSSMcomemanynew(softSUSYbreaking)parameters,includinginprincipleseparatemassparametersforallthesfermions,Higgsandgauginomassparameters,andtrilinearmassesAioftheHiggs-sfermioninteractionterms,alongwiththesupersymmetricHiggsmixingmassanditssoftSUSYbreakingcounterpartB,andlastlytheratioofthetwoHiggsvacuumexpectationvalues,tanv2=v1:3Sfermionmasses:m2~fL;m2~fRHiggsmasses:m2H1;m2H2Gauginomasses:M1;M2;M3Trilinearscalarcouplings:Aihi~Qi~UciH2+:::Higgsmixingmasses:^H1^H2;BH1H2Higgsvevratiov2=v1:tanIfoneincludesavorstructureintothesfermionandtrilinearmasses,thereareover100newparametersassociatedwithsoftlybrokensupersymmetry[1].ThislargenumberofparametersseverelylimitsthepredictivepowerofthetheMSSM,andinpractice,simplicationstothesetofSUSYparametersarealwaysmade.Oneofthemostpopularandbetter-motivatedchoicesisinspiredbyminimalSupergravity(mSUGRA).InmSUGRA,severalofthemassesaretakendegenerate,sothatm2~fL=m2~fR=m2H1=m2H2m20(2)M1=M2=M3m1=2(3)Ae=Ad=Au=:::A0(4)atthescaleMXwherethegaugecouplingsunify.TheparametersarethenevolvedtotheelectroweakscaleusingtheRenormalizationGroupEquationstocomputethelow-energyspectrum.DuetotheRGErunning,themassesofthesfermionsdependonbothm0andm1=2.TheparametersjjandBarexedbytheconditionsofcorrectelectroweaksymmetrybreaking,whichleavesm0;m1=2;A0;tan;sign()asthefreeparametersofmSUGRA.IwillsubsequentlyconcentrateonthemSUGRAmodel,butqualitativelysimilarresultsapplyinthegeneralMSSM.3.TheNeutralinoRelicDensity3.1.RelicAbundancesThepossibilityofasignicantrelicabundanceofneutralinosispartlyduetoR-parity,whichistypicallyimposedonSUSYmodelsinordertopreventrapidprotondecay.Underthisnewsymmetry,standardmodelsparticleshaveR-charge+1,whiletheirsuperpartnershaveR-charge1.SinceR-parityismultiplicativelyconserved,thisimpliesthatallvertices4mustcontainanevennumberofSUSYparticles,andhencethattheLightestSUSYparticle(LSP)isstable.Sinceitisstableovercosmologicaltimescales,theLSPisadarkmattercandidate,andwecanuselimitsonitsrelicabundancetoconstrainSUSYmodels,asI’lldescribenext.Now,theveryearlyuniversewashotanddense;particlesinteractedrapidly,andtheLSPs,whichIwilldenote,werekeptinchemicalequilib-riumwiththestandardmodelparticlesinthethermalbath,primarilyviaprocessesinwhichtwoSUSYparticlesannihilateintostandardmodelparti-cles,andtheinverseprocessesinwhichstandardmodelparticlesannihilatetoproducetwoSUSYparticles.χχχχFig.1.Keepingthe’sinchemicalequilibrium.Attemperaturesmuchlargerthanthemassofthe,thenumberdensityof’swassimplyaspinfactortimesthenumberdensityofphotons.Astheuniverseexpandedandcooled,thetemperatureeventuallyfellbelowthemassofthe,andthenumberdensityof