WMAP Constraints, SUSY Dark Matter and Implication

arXiv:hep-ph/0303201v228Jul2003WMAPConstraints,SUSYDarkMatterandImplicationsfortheDirectDetectionofSUSYUtpalChattopadhyay1(a),AchilleCorsetti2(b)andPranNath3(b)(a)DepartmentofTheoreticalPhysics,IndianAssociationfortheCultivationofScience,Jadavpur,Kolkata700032,India(b)DepartmentofPhysics,NortheasternUniversity,Boston,MA02115-5005,USAAbstractRecentlyWMAPhasmeasuredthecosmologicalparameterstoamuchgreateraccuracy.Weanalyzetheimplicationsofthismoreprecisemea-surementforsupersymmetricdarkmatterandforthedirectdetectionofsupersymmetryataccelerators.WeconsidermSUGRAincludingalsothehyperbolicbranch(HB)intheradiativebreakingoftheelectroweaksym-metry.Onthepartofthehyperbolicbranchwherethelightestneutralinoisdominantlyahiggsinoratherthanbeingmostlyabino,therelicdensityconstraintsaresatisfiedbycoannihilationwiththenextlightestneutralinoandthelightchargino.Includingthisbranchthelightestneutralinomasssatisfiesmχ01≤1200GeVfortanβ≤50.Constraintsofb→s+γ,ofgμ−2,andofB0s→μ+μ−arealsoanalyzed.Itisshownthattheneutralino-protoncrosssectionineachcasewillfallwithinthereachofdarkmatterexper-iments.PossibilityforthedirectdetectionofsupersymmetryisdiscussedintheallowedregionsoftheparameterspaceconsistentwithWMAPcon-straints.Abriefdiscussionofthehyperbolicbranchandfocuspointregion(HB/FP)isalsogiven..1IntroductionRecentlytheWilkinsonMicrowaveAnisotropyProbe(WMAP)hasmeasuredsomeofthecosmologicalparameterswithsignificantlygreaterprecision[1,2].Specifi-cally,WMAPgivesthematterdensityoftheuniversesothatΩmh2=0.1350.008−0.009andgivesthebaryondensitysothatΩbh2=0.0224±0.0009,whereΩm,b=ρm,b/ρcwhereρm,bisthematter(baryon)densityandρcisthemassdensityneededtoclosetheuniverseandhistheHubbleparameterinunitsof100km/s/Mpc.Assumingthedifferenceofthetwoiscolddarkmatter(CDM)onefindstheCDMdensityintheuniverseaccordingtoWMAPisnowgivenbyΩCDMh2=0.1126+0.008−0.009.In1E-mail:[e-mail]2E-mail:[e-mail]3E-mail:[e-mail]1thispaperweanalyzetheconstraintoftheWMAPresultsforsupersymmetricdarkmatter.FortheanalysiswewillfocusonthemSUGRAmodel[3]andanalyzetheallowedrangeoftheparameterspaceconsistentwiththeWMAPrelicdensityconstraint.Theaboverequirestakingaccountofthefullrangeofthehyperbolicbranchofradiativebreakingoftheelectroweaksymmetry[4].ThemSUGRAmodelischaracterizedbytheparametersm0,m1/2,A0,tanβwherem0istheuniversalscalarmass,m1/2istheuniversalgauginomass,A0istheuniversaltrilinearcou-plingandtanβisthedefinedbytanβ=H2/H1whereH2givesmasstotheupquarkandtheH1givesmasstothedownquarkandthelepton.Intheanalysiswewillalsoconsidertheb→sγconstraintandthegμ−2constraint.tanβintheanalysiswillrangeuptovaluesof50anditisknown[4]thatforval-uesoftanβwhicharelargeorevenmoderatelylargethatradiativebreakingoftheelectroweaksymmetryliesonthehyperbolicbranch.Tomakethediscussionclearerwereviewbrieflyradiativebreakingoftheelectroweaksymmetryanddis-cusshowthehyperbolicbrancharisesinsuchabreaking.Onecanillustratethisphenomenonanalyticallyforthecasewhenthebquarkcouplingscanbeneglected.InthiscaseoneoftheconstraintsofradiativesymmetrybreakingdeterminestheHiggsmixingparameterμsothat[4]C1m20+C3m′21/2+C′2A20+Δμ2loop=μ2+12M2Z(1)Here,m′1/2=m1/2+12A0C4C3,C′2=C2−14C24C3(2)and,C1=1t2−1(1−3D0−12t2),C2=t2t2−1kC3=1t2−1(g−t2e),C4=−t2t2−1f,Δμ2loop=Σ1−t2Σ2t2−1(3)Δμ2istheloopcorrection.Σ1,2isasdefinedinRef.[4],t=tanβandthefunctionse,f,g,kareasdefinedinRef.[5].Further,D0=1−(mt/mf)2andmf≃200sinβGeV.ForsmalltomoderatevaluesoftanβtheloopcorrectionsaretypicallysmallandfurthertherenormalizationgroupanalysisshowsthatC′20andC30.ForsuchvaluesoftanβwheretheloopcorrectionshavereducedscaledependenceonefindsC10independentofanyscalechoiceQforhavingtheradiativeelectroweaksymmetrybreaking(EWSB).Inthiscircumstanceonefindsthattheradiative2symmetrybreakingconstraintdemandsthattheallowedsetofsoftparametersm0andm′12foragivenvalueofμlieonthesurfaceofanellipsoid.ThisconditionthenplacesanupperboundonsparticlemassesforagivenvalueofΦwhichisthefinetuningparameterdefinedbyΦ=μ2M2Z+14[4].Thisistheellipsoidalbranchofradiativebreakingoftheelectroweaksymmetry[4].However,itwasfoundinRef.[4]thatfortypicallylargertanβ(∼7)whentheloopcorrectionstoμaresignificantalongwithasignificantdegreeofitsvariationwiththescaleQ,theabovescenariodoesnotnecessarilyhold.OnewaytoseethisphenomenonistochooseavalueoftherunningscaleQ0atwhichtheloopcorrectionstoμareminimized.Onefindsthenthatinsomepartsoftheparameterspacewherem0andm1/2arerelativelylargertheminimizationscaleQ0occursinsucharegionthatitleadstoaswitchinthesignofC1,i.e.sign(C1(Q0))=−1.Inthiscircumstanceonefindsthattheradiativesymmetrybreakingconditiontakestheformm′21/2α2(Q0)−m20β2(Q0)≃±1(4)wherethesign±isdeterminedbytheconditionsign((Φ+14)M2Z−C′2A20)=±andwhereα2=|(Φ0+14)M2Z−C′2A20||C3|,β2=|(Φ0+14)M2Z−C′2A20||C1|(5)Fromtheaboveweseethatthepresenceoftherelativeminussignleadstoadrasticallydifferentconstraintonthesoftparametersduetoconstraintoftheradiativebreakingoftheelectroweaksymmetry.HereforfixedvaluesofA0onefindsthatm0andm′12lieonahyperbolaandthustheseparameterscangetlargeforfixedvaluesofμorforfixedvaluesofthefi