COSMOLOGICAL CONSTRAINTS ON THE MSSM

Vol.30(1999)ACTAPHYSICAPOLONICABNo11COSMOLOGICALCONSTRAINTSONTHEMSSMTobyFalkDepartmentofPhysis,UniversityofWisonsinMadison,WI53706,USA(ReeivedOtober25,1999)IdisussreentdevelopmentsinthestudyofosmologiallimitsontheMinimalSupersymmetriStandardModel(MSSM).Inpartiular,Ifousontheeetofneutralino-stauoannihilationonthereliabundaneofneutralinos,andIgiveexampleswheretheosmologiallyderivedlimitsonthesupersymmetriparametersarerelaxed,andoneexample(CPviolatingphases)wheretheyarenot.PACSnumbers:11.30.Pb,11.30.Er,95.35.+d1.IntrodutionThetitleofthistalkisratherbroad.SpeiallywhatIwillbetalkingabouttodayisrelidensityonstraintsonsupersymmetrimodels,andIwillfousinpartiularonboundsonminimalSupergravity(mSUGRA).I’llbeginwithabriefreminderofthenotationofsupersymmetry,thengiveanintrodutiontorelidensities,howtheyareomputed,andhowweanusethemtoonstrainmodelsoflow-energysupersymmetry.I’llthendisussoannihilationingeneralandshowhowitdramatiallyrelaxestheosmo-logialupperboundonthemSUGRAmasses.Finally,I’llgiveanexampleofonstraints(onCPviolatingphasesinmSUGRA)whiharenotrelaxedbytheweakenedmasslimits.2.SUSYSinepreviousspeakershaveintroduedtheSupersymmetriStandardModel,Iwillgiveonlyabriefreminder,inordertopresentthepartileontentandparametersandtosetthenotation.ReallthatSUSYessen-tiallydoublesthepartileontentofthestandardmodel(TableI).EahPresentedattheXXIIIInternationalShoolofTheoretialPhysisReentDevelopmentsinTheoryofFundamentalInterations,Ustro«,Poland,September1522,1999.(3401)3402T.FalkTABLEITheSUSYpartnersofStandardModelpartilesSMSUSYfermions!sfermionsu;d;eL;eR:::~u;~d;~eL;~eR:::gaugebosons!gauginosg;Z;;W:::~g;~Z;~;~W:::Higgsbosons!HiggsinosH1;H2:::~H1;~H2:::fermion(infateahfermionhiralstate)hasaspin-0partnersfermion,thegaugebosonshavespin-1/2partnergauginos,andthedegreesoffreedomoftheHiggssetor,whihnowontainstwoHiggsSU(2)doublets,havespin-1/2Higgsinopartners.ThefourneutralgauginosandHiggsinosmixintoneutralinostatesi,sothatanarbitraryneutralinoisalinearombinationi=i~B+i~W3+i~H1+Æi~H2;i=1;:::;4;(1)wherethe~Band~W3arethepartnersoftheU(1)YandneutralSU(2)gaugebosonsandarelinearombinationsofthe~and~Z.Thelightestoftheneutralinos1tendstobethelightestsupersymmetripartile,andinthemodelsofinterestfordarkmatter,1tendstobe~B-like,i.e.j1j1.Similarly,thehargedgauginosandHiggsinosmixintotwoharginos,1;2.AlongwiththenewpartilesoftheMSSMomemanynew(softSUSYbreaking)parameters,inludinginprinipleseparatemassparametersforallthesfermions,Higgsandgauginomassparameters,andtrilinearmassesAioftheHiggs-sfermioninterationterms,alongwiththesupersymmetriHiggsmixingmassanditssoftSUSYbreakingounterpartB,andlastlytheratioofthetwoHiggsvauumexpetationvalues,tanv2=v1:Sfermionmasses:m2~fL;m2~fRHiggsmasses:m2H1;m2H2Gauginomasses:M1;M2;M3Trilinearsalarouplings:Aihi~Qi~UiH2+:::Higgsmixingmasses:^H1^H2;BH1H2Higgsvevratiov2=v1:tanCosmologialConstraintsontheMSSM3403Ifoneinludesavorstrutureintothesfermionandtrilinearmasses,thereareover100newparametersassoiatedwithsoftlybrokensupersymmetry[1℄.ThislargenumberofparametersseverelylimitsthepreditivepowerofthetheMSSM,andinpratie,simpliationstothesetofSUSYparametersarealwaysmade.Oneofthemostpopularandbetter-motivatedhoiesisinspiredbyminimalSupergravity(mSUGRA).InmSUGRA,severalofthemassesaretakendegenerate,sothatm2~fL=m2~fR=m2H1=m2H2m20;(2)M1=M2=M3m1=2;(3)Ae=Ad=Au=:::A0(4)atthesaleMXwherethegaugeouplingsunify.TheparametersarethenevolvedtotheeletroweaksaleusingtheRenormalizationGroupEquationstoomputethelow-energyspetrum.DuetheRGErunning,themassesofthesfermionsdependonbothm0andm1=2.TheparametersjjandBarexedbytheonditionsoforreteletroweaksymmetrybreaking,whihleavesm0;m1=2;A0;tan;sign()asthefreeparametersofmSUGRA.IwillsubsequentlyonentrateonthemSUGRAmodel,butqualitativelysimilarresultsapplyinthegeneralMSSM.3.Theneutralinorelidensity3.1.ReliabundanesThepossibilityofasigniantreliabundaneofneutralinosispartlyduetoR-parity,whihistypiallyimposedonSUSYmodelsinordertopreventrapidprotondeay.Underthisnewsymmetry,standardmodelspartileshaveR-harge+1,whiletheirsuperpartnershaveR-harge1.SineR-parityismultipliativelyonserved,thisimpliesthatallvertiesmustontainanevennumberofSUSYpartiles,andhenethattheLightestSUSYpartile(LSP)isstable.Sineitisstableoverosmologialtimesales,theLSPisadarkmatterandidate,andweanuselimitsonitsreliabundanetoonstrainSUSYmodels,asI’lldesribenext.Now,theveryearlyuniversewashotanddense;partilesinteratedrapidly,andtheLSPs,whihIwilldenote,werekeptinhemialequilib-riumwiththestandardmodelpartilesinthethermalbath,primarilyviaproessesinwhihtwoSUSYpartilesannihilateintostandardmodelparti-les,andtheinverseproessesinwhihstandardmodelpartilesannihilatetoproduetwoSUSYpartiles.3404T.FalkχχχχFig.1.Keepingthe’sinhemialequilibriumAttemperaturesmuhlargerthanthemassofthe,thenumberdensityof’swassimplyaspinfatortimesthenumberdensityofphotons.Astheuniverseexpandedandooled,thetemperatureeventuallyfellbelowthemassofthe,andthenumberdensityof’sbegantodropexponentially.nO(1)nTmn(mT)3=2