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
asapossiblesolutiontothelittlehierarchyproblem,andapossibilityofitbeinggeneratedradiativelywithoutintroducinglargesoft-trilinearcouplingsattheGUTscale.InSec.3wepresentagaugemessengermodelandbrie ydiscusspossiblecontributionfromgravitymediationofSUSYbreaking.TheresultsaregiveninSec.4togetherwithdiscussionofphenomenology.WeconcludeinSec.5.ForconveniencewesummarizeformulaenecessarytoderivesoftSUSYbreakingparametersfromgaugemessengermodelsintheAppendixA,andwediscussdi erentpossibilitiesforgravitymediatedcontributionsinmoredetailintheAppendixB.
2.Maximalmixingscenario–asolutiontothe netuningproblem
AsmentionedintheIntroduction,thephysicalHiggsbosonmassreceivesanadditionalcontributionfromstopmixing[13],
24m3GmA2 Ftt222tlogmh MZcos2β+(1 m22π2 t
6whichcorrespondstothemaximalmixing
3/2m(nomixing),scenario.Inthiscasethestopcanbelighter,mt (maximalmixing)=e t
anditcanbeaslightas250～300GeVwhileful llingthephysicalHiggsmassboundfromtheLEP.
InsteadofusingEq.(1.3)asaroughestimateofthecontributionofstopmasstotherunningofm2Huitisinstructivetobemoreprecise.ForgiventanβwecansolveRG22equationsexactlyandexpressEWvaluesofm2Hu,µ,andconsequentlyMZgivenbyEq.(1.2),asfunctionsofallGUTscaleparameters.Fortanβ=10,wehave:
2222MZ 1.9µ2+5.9M3 1.2m2 0.8AtM3+0.2At+···,Hu+1.5mt(2.2)
whereparametersappearingontheright-handsidearetheGUTscaleparameters,wedonotwritethescaleexplicitly.OtherscalarmassesandM1andM2appearwithnegligiblecoe cientsandweneglecttheminourdiscussion.Thecoe cientsinthisexpressiondependonlyontanβ(theydonotchangedramaticallywhenvaryingtanβbetween5and
50)andlog(MGUT/MZ).
LetusalsoexpresstheEWscalevaluesofstopmasssquared,gluinomassandtoptrilinearcouplingfortanβ=10inasimilarway:
22m2 +0.2AtM3 (MZ) 5.0M3+0.6mtt(2.3)
(2.4)
(2.5)M3(MZ) 3M3At(MZ) 2.3M3+0.2At.
Inthecaseofmt thecoe cientsrepresentaveragesofexactcoe cientsthatwouldappear
2.inseparateexpressionsform2 R LandmttFromEqs.(2.2),(2.3)and(2.4),weseetheusualexpectationfromSUSY,MZ mt 1,2 mg ,whenallthesoftSUSYbreakingparametersarecomparable.Furthermore,