Mediation of Supersymmetry Breaking in Gauge Messenger Model(4)

We study gauge mediation of supersymmetry breaking in SU(5) supersymmetric grand unified theory with gauge fields as messengers. The generated soft supersymmetry breaking parameters lead to close to maximal mixing scenario for the Higgs mass and highly red

2wherem2 >0,seeEq.(1.3),andsotheEWscalevalueofmHucanbearbitrarilyclosetotthestartingvalueatMGUT.Nocancelationbetweeninitialvalueofm2Hu(orµ)andthecontributionfromtherunningisrequired.And nally,thestopmixingistypicallymuch

largerthaninthecasewithpositivestopmassessquared.Itturnsoutthatintheregionwherem2Hugetsnegligiblecontributionfromrunning,theradiativelygeneratedstopmixingisclosetomaximalevenwhenstartingwithnegligiblemixingattheGUTscale.Sinceinprinciplethisscenariocaneliminate netuningofEWSBcompletely,itisdesirabletoseehowclosetotheradiativelygeneratedmaximalmixingscenarioonecangetinspeci cmodels.

InthispaperwestudygaugemediationofSUSYbreakinginSU(5)supersymmetricgranduni edtheory(SUSYGUT)withanadjointchiralmultipletandmassivecompo-nentsofvector(gauge)multipletplayingtheroleofmessengers.Thesoftsusybreakingparametersinthis“gaugemessengermodel”aresimilartothosediscussedin[7]whichwereshowntoleadtomaximalmixingscenariofortheHiggsmass.Thecharacteristicfeaturesare:negativeandnon-universalsquarkandsleptonmassessquaredattheGUTscale,non-universalgauginomasses,|M1|>|M2|>|M3|,andsizablesoft-trilinearcouplings.Besidesgaugemessengers,wealsoconsiderapossiblecontributionsfromadditionalmes-sengersinvector-likerepresentations,e.g.5and¯5ofSU(5).Finally,sincethemessengerscaleistheGUTscale,andthegaugemediationisaoneloope ect,thenaivelyestimatedsizeofgravitymediationinducedbynon-renormalizableoperators(suppressedbyMPl)iscomparabletothecontributionfromgaugemediation.Acombinationofgaugemediation(withgaugeandvector-likemessengers)withgravitymediationopenscompletelynewpos-sibilitiesformodelbuilding.WeshowthatalreadysomeofthesimplestmodelsleadtoclosetomaximalmixingscenariofortheHiggsmassandhighlyreducethe netuningofelectroweaksymmetrybreaking.TheSUSYspectrumisverydi erentfromotherscenariostypicallyusedforcolliderstudies.Allsuperpartnerscanbewithin400GeVwithrelativelylightstop,mt 1>～150,whilesatisfyingallexperimentallimits,includingthelimitontheHiggsmass.Thelightestsupersymmetricparticle(LSP)isgravitinoandthenexttothelightestsupersymmetricparticle(NLSP)isneutralino,sneutrino,stauorstopinmostoftheparameterspace.

WenotethatgaugemessengermodelhasbeenconsideredinveryearlystagesofMSSMhistory.Aftertheworkoninvertedmasshierarchy[8],“geometrichierarchymodel”hasbeenconstructedin[9]andsoftscalarmasseshavebeencalculatedin[10].1InthismodeltheSUSYbreakingscaleisanintermediatescaleandthemessengerscaleistheGUTscale.TheexplicitSUSYbreakingmodeltheyconsideredhaslight(TeVscale)adjointchiralsuper eldsunderthestandardmodelgaugegroupandthegaugecouplingsunifyatascalebeyondthePlanckscale,1020GeV.Wedonotconsideraspeci cmodelofSUSYbreaking(althoughweassumeithappensattheGUTscale).WeonlyaddressthemediationofSUSYbreaking.Therefore,wetreatthenumberof eldsinamodelasdiscreteparametersandfocusonminimalmodelswithsmallernumberof elds.

Thispaperisorganizedasfollows.InSec.2wediscussthemaximalmixingscenario

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