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
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Figure3:RenormalizationgrouprunningofsoftSUSYbreakingparametersforgaugemediation,Nmess=0andbG=3,withacontributionfromgravitymediationintheHiggssectorforMSUSY=40GeV,tanβ=29,cHu=38andcHd=37.ThemeaningofthelinesisthesameasinFig.1.
breakingparameters.Themajoradvantageofaddingapositivecontributiontom2Huisthatitallowssmallerµterm.Thisfurtherreduces netuningofEWSB,seetheTable1,becausetheoriginal(somewhatlarge)contributionfromgaugemediationcanbecanceledinanequalwaybytheadditionalcontributionfromgravityandbytheµterm.
Exploringthewholeparameterspaceinthiscaseismorecomplicated.InFig.4we
presentatypicalcutthroughtheparameterspaceinMSUSY cHuplanewith xedtanβ
andcHd.Weseethat,dependingonthesizeofcHu, netuningfromanyoftheparameters
canbereducedtothelevelof10%.Besidesexcludedregionsthatalreadyappearedinthecaseofpuregaugemediation,Fig.2,thereisalsoaregionexcludedbylimitsonthestopmass.Thisisduetoasubtlee ectoflargermHuintheevolutionofstopmasses
squared.Stopmassessquaredruntoslightlysmallervalueswhichincreasesstopmixingandconsequentlyleadstomuchsmallervalueofthelighteststopmasseigenstate.Forthesamereason,besidesneutralino(N)LSPandstauNLSP,thereisaregionwithstopNLSP.TheNLSPsituationcanbeeasilychangedwhenconsideringcontributionfromgravitymediationalsotosquarksandsleptons.
4.3Othercases
Addingauniversalcontributiontoallscalarmassesfromgravitymediationhasanegligiblee ectontheEWscalevalueofm2Hu.ThiscanbeeasilyseenfromEq.(2.2)inwhichthe2approximatelycanceleachotherform2=m2=m2atthetermscontainingm20 HuHuandmttGUTscale.Therefore,addingm0(unlessitisverylarge)doesnotchange netuningofEWSB.Thecontributionfromm0alsomakesstopsheavierandreducesthemixing.ThisreducestheHiggsmassandsoonlysmallvaluesofm0areallowedforsmallMSUSY–theregionweareinterestedin.Smallm0ishoweversu cienttochangetheNLSPofamodel.Forsmallertanβitcanhighlyenlargetheregionwhereneutralinois(N)LSPinsteadofsneutrinoorstop,andforlargertanβitcanbasicallyeliminatetheregionwherestopisNLSP.