Searching for Supersymmetric Dark Matter

arXiv:hep-ph/0208092v219Aug2002SEARCHINGFORSUPERSYMMETRICDARKMATTER∗KEITHA.OLIVETheoreticalPhysicsInstitute,SchoolofPhysicsandAstronomy,UniversityofMinnesota,Minneapolis,MN55455USAE-mail:[e-mail]-ph/0208092UMN–TH–2108/02TPI–MINN–02/25August2002ThesupersymmetricextensiontotheStandardModeloffersapromisingcolddarkmattercandidate,thelightestneutralino.Iwillreviewtheprospectsforthede-tectionofthiscandidateinbothacceleratoranddirectdetectionsearches.1.IntroductionAlthoughtherearemanyreasonsforconsideringsupersymmetryasacan-didateextensiontothestandardmodelofstrong,weakandelectromagneticinteractions1,oneofthemostcompellingisitsroleinunderstandingthehierarchyproblem2namely,why/howismW≪MP.OnemightthinknaivelythatitwouldbesufficienttosetmW≪MPbyhand.However,radiativecorrectionstendtodestroythishierarchy.Forexample,one-loopdiagramsgenerateδm2W=OαπΛ2≫m2W(1)whereΛisacut-offrepresentingtheappearanceofnewphysics,andtheinequalityin(1)appliesifΛ∼103TeV,andevenmoresoifΛ∼mGUT∼1016GeVor∼MP∼1019GeV.Iftheradiativecorrectionstoaphysicalquantityaremuchlargerthanitsmeasuredvalues,obtainingthelatterrequiresstrongcancellations,whichingeneralrequirefinetuningofthebareinputparameters.However,thenecessarycancellationsarenaturalinsupersymmetry,whereonehasequalnumbersofbosonsBandfermionsFwithequalcouplings,sothat(1)isreplacedbyδm2W=Oαπ|m2B−m2F|.(2)Theresidualradiativecorrectionisnaturallysmallif|m2B−m2F|∼1TeV2.∗summaryofinvitedtalkatcospa2002,2002internationalsymposiumoncosmologyandparticleastrophysics,may31-june2,2002,nationaltaiwanuniversitytaipei,taiwan.12Inordertojustifytheabsenceofinteractionswhichcanberesponsibleforextremelyrapidprotondecay,itiscommonintheminimalsupersym-metricstandardmodel(MSSM)toassumetheconservationofR-parity.IfR-parity,whichdistinguishesbetween“normal”matterandthesupersym-metricpartnersandcanbedefinedintermsofbaryon,leptonandspinasR=(−1)3B+L+2S,isunbroken,thereisatleastonesupersymmetricpar-ticle(thelightestsupersymmetricparticleorLSP)whichmustbestable.Thus,theminimalmodelcontainsthefewestnumberofnewparticlesandinteractionsnecessarytomakeaconsistenttheory.Thereareverystrongconstraints,however,forbiddingtheexistenceofstableorlonglivedparticleswhicharenotcolorandelectricallyneutral3.StrongandelectromagneticallyinteractingLSPswouldbecomeboundwithnormalmatterforminganomalouslyheavyisotopes.Indeed,thereareverystrongupperlimitsontheabundances,relativetohydrogen,ofnuclearisotopes4,n/nH∼10−15to10−29for1GeV∼m∼1TeV.Astronglyinteractingstablerelicisexpectedtohaveanabundancen/nH∼10−10withahigherabundanceforchargedparticles.Therearerelativelyfewsupersymmetriccandidateswhicharenotcol-oredandareelectricallyneutral.Thesneutrino5isonepossibility,butintheMSSM,ithasbeenexcludedasadarkmattercandidatebydirect6andindirect7searches.Infact,onecansetanacceleratorbasedlimitonthesneutrinomassfromneutrinocounting,m˜ν∼44.7GeV8.Inthiscase,thedirectrelicsearchesinundergroundlow-backgroundexperimentsrequirem˜ν∼20TeV6.Anotherpossibilityisthegravitinowhichisprobablythemostdifficulttoexclude.IwillconcentrateontheremainingpossibilityintheMSSM,namelytheneutralinos.2.ParametersThemostgeneralversionoftheMSSM,despiteitsminimalityinparticlesandinteractionscontainswelloverahundrednewparameters.Thestudyofsuchamodelwouldbeuntenablewereitnotforsome(wellmotivated)assumptions.Thesehavetodowiththeparametersassociatedwithsuper-symmetrybreaking.Itisoftenassumedthat,atsomeunificationscale,allofthegauginomassesreceiveacommonmass,m1/2.Thegauginomassesattheweakscalearedeterminedbyrunningasetofrenormalizationgroupequations.Similarly,oneoftenassumesthatallscalarsreceiveacommonmass,m0,attheGUTscale.Thesetooarerundowntotheweakscale.TheremainingparametersofimportanceinvolvetheHiggssector.ThereistheHiggsmixingmassparameter,μ,andsincetherearetwoHiggsdoubletsintheMSSM,therearetwovacuumexpectationvalues.Onecombination3oftheseisrelatedtotheZmass,andthereforeisnotafreeparameter,whiletheothercombination,theratioofthetwovevs,tanβ,isfree.IfthesupersymmetrybreakingHiggssoftmassesarealsounifiedattheGUTscale(andtakethecommonvaluem0),thenμandthephysicalHiggsmassesattheweakscalearedeterminedbyelectroweakvacuumconditions.ThisscenarioisoftenreferredtoastheconstrainedMSSMorCMSSM.Oncetheseparametersareset,theentirespectrumofsparticlemassesattheweakscalecanbecalculated.3.NeutralinosTherearefourneutralinos,eachofwhichisalinearcombinationoftheR=−1neutralfermions,3:thewino˜W3,thepartnerofthe3rdcomponentoftheSU(2)Lgaugeboson;thebino,˜B,thepartneroftheU(1)Ygaugeboson;andthetwoneutralHiggsinos,˜H1and˜H2.AssuminggauginomassuniversalityattheGUTscale,theidentityandmassoftheLSParedeterminedbythegauginomassm1/2,μ,andtanβ.Ingeneral,neutralinoscanbeexpressedasalinearcombinationχ=α˜B+β˜W3+γ˜H1+δ˜H2(3)Thesolutionforthecoefficientsα,β,γandδforneutralinosthatmakeuptheLSPcanbefoundbydiagonalizingthemassmatrix(˜W3,˜B,˜H01,˜H02)M20−g2v1√2g2v2√20M1g1v1√2−g1v2√2−g2v1√2g1v1√20−μg2v2√2−g1v2√2−μ0˜W3˜B˜H01˜H02(4)whereM1(M2)isasoftsupersymmetrybreakingtermgivingmasstotheU(1)(SU(2))gaugino(s).