Supersymmetry with Small mu Connections between Na

arXiv:hep-ph/0606134v111Jun2006SLAC-PUB-11892UCB-PTH-06/11LBNL-60363SupersymmetrywithSmallμ:ConnectionsbetweenNaturalness,DarkMatter,and(Possibly)FlavorRyuichiroKitanoaandYasunoriNomurab,caStanfordLinearAcceleratorCenter,StanfordUniversity,Stanford,CA94309bDepartmentofPhysics,UniversityofCalifornia,Berkeley,CA94720cTheoreticalPhysicsGroup,LawrenceBerkeleyNationalLaboratory,Berkeley,CA94720AbstractWeakscalesupersymmetrictheoriesoftensufferfromseveralnaturalnessproblems:theproblemsofreproducingthecorrectscaleforelectroweaksymmetrybreaking,thecorrectabundancefordarkmatter,andsmallratesforflavorviolatingprocesses.Wearguethatthefirsttwoproblemspointtoparticularregionsofparameterspaceinmodelswithweakscalesupersymmetry:thosewithasmallμterm.Thishasaninterestingimplicationondirectdarkmatterdetectionexperiments.Wefindthat,ifthesignsofthethreegauginomassparametersareallequal,wecanobtainasolidlowerboundonthespin-independentneutralino-nucleoncrosssection,σSI.Inthecasethatthegauginomassessatisfytheunifiedmassrelations,weobtainσSI∼4×10−46cm2(1×10−46cm2)forfine-tuninginelectroweaksymmetrybreakingnoworsethan10%(5%).Wealsodiscussapossibilitythatthethreeproblemslistedaboveareallconnectedtothehierarchyoffermionmasses.Thisoccursifsupersymmetrybreakingandelectroweaksymmetrybreaking(theHiggsfields)arecoupledtomatterfieldswithsimilarhierarchicalstructures.Thediscoveryofμ→etransitionprocessesinnearfutureexperimentsispredictedinsuchaframework.1IntroductionWeakscalesupersymmetryprovidesanelegantframeworktosolvethenaturalnessproblemofthestandardmodelaswellastoexplainthedarkmatteroftheuniverse.Anextremesensitivityoftheweakscaletoultravioletphysicsinthestandardmodelissoftenedduetotheexistenceofsuperparticlesatthisscale,andthestablelightestsupersymmetricparticle(LSP)leftoverfromtheearlyhistoryoftheuniversecomposesdarkmattertoday.Thesequalitativesuccesses,however,shouldnowbereviewedmuchmorecarefully.Ononehand,non-discoveryofbothsuperparticlesandalightHiggsbosonatLEPII[1]raisestheoverallmassscaleforthesuperparticles,leadingtoatensionwithnaturalnessofelectroweaksymmetrybreaking.Ontheotherhand,theaccuratemeasurementofthedarkmatterdensitybyWMAP[2]givesapreciseconstraintonthespectrumofsuperparticles.Itisplausiblethatacarefulstudyoftheseissuesprovidesstronghintsonapossiblerealizationofsupersymmetryattheweakscale.Phenomenologyofsupersymmetrictheoriesdependsstronglyonhowfundamentalsupersym-metrybreakingismediatedtothesupersymmetricstandardmodelsector.Whatistheunder-lyingmechanismofthemediation?Apromisingpossibilityarisesifmediationoccursthroughgravitationallysuppressedinteractions.ThishasavirtuethatthesupersymmetricmasstermfortheHiggsdoublets(μterm)isnaturallygeneratedwiththeweakscalesize,becauseitcanariseasasortofsupersymmetrybreakingterminthiscase[3].Thisprovidesanelegant“solution”totheμproblem,whichplaguesmanyotherscenariosforsupersymmetrybreaking.Anothervirtueofmediationbygravitationalstrengthinteractionsisthatthegravitinoislikelytobeheavierthanthelightestneutralino,givingapossibilityofweaklyinteractingmassiveparticle(WIMP)darkmatter.Suchamediationisalsominimalinthesensethatitdoesnotrequireanyotherphysicsthanthatatthegravitationalscale,whichweknowexists.Wethusmainlyfocusonthisclassofmediation–gravitymediationbroadlydefined–inthispaper,andstudywhatcurrentexperimentaldataimplyonthestructureofsuperparticlespectra.Wearguethatthecurrentdatastronglysuggestthattheμtermissmall,|μ|∼(200∼400)GeV,regardlessofanydetailsofsupersymmetrybreaking.Thisinturnhasastrikingconsequenceinthecontextoftheminimalsupersymmetricstandardmodel(MSSM)—thecrosssectionfordirectdarkmatterdetectionislargeandcannaturallybeintherangewheretheCDMSIIexperimentwillexploreinthenexttwoyears.Infact,wecanobtainasolidlowerboundonthecrosssectionifthesignsofthegauginomassesareuniversal.Inthecasethatthegauginomassessatisfytheunifiedmassrelations,weobtainσ∼4×10−46cm2(1×10−46cm2)forfine-tuninginelectroweaksymmetrybreakingnoworsethan10%(5%).Animportantconsequenceofmediationbygravitationalscaleinteractionsisthatitopensupawindowtoconnectphysicsattheweakscaletothatathighenergies,suchasthePlanckorunificationscale,sincethelowenergyscalar(squark,sleptonandHiggsboson)massescarryall1informationfromthePlancktotheweakscalesthroughtheirrenormalizationgroupevolutions.Thepossibilityofperturbativeextrapolationsofphysicsacrossavastenergyinterval,infact,isauniquefeatureoftheorieswithweakscalesupersymmetryandsupportedbythesuccessfulunificationofgaugecouplingsatascaleof≈1016GeV[4].Wethusexplorepossibleimpli-cationsoflowenergyspectrasuggestedbythecurrentdata(smallμterm)onphysicsatthegravitationalscale.Wefindthatadesiredpattenofsuperparticlespectraisobtainedifphysicsofsupersymmetrybreakingmediationisintimatelyrelatedtothatofflavor.Thishasinterestingimplicationsonlowenergyexperimentsexploringflavorviolation.Wepresentanexplicitschemeincorporatingtheseideas,whichwecallnexttominimalsupergravity,andestimateratesofvar-iousflavorviolatingprocessesinthisframework.Wefindthatsomeoftheseprocesses,suchasμ→eγ,arenaturallyclosetothecurrentexp