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
wheretanβ=vu/vdistheratioofthevacuumexpectationvalues(VEVs)ofHuandHd.Thedominantoneloopcorrection[1][2][3],in
case
thestopmixingparameterissmall,dependsonlylogarithmicallyonstopmassesandithastobelargeinordertopushtheHiggsmassabovetheLEPlimit,114.4GeV.Atwoloopcalculation(weuseFeynHiggs
2.4.1[5,6]withmt=172.5GeV)revealsthestopmasseshavetobe>～900GeV.
Thisconstrainthasadirectdrawbackintheelectroweaksymmetrybreaking.ThemassoftheZboson(ortheEWscale),determinedbyminimizingtheHiggspotential,isrelatedtothesupersymmetricHiggsmassparameterµandthesoftSUSYbreakingmasssquaredparameterforHuas(fortanβ≥5)
2MZ
4πm2 log2tΛ
6and
withsuchamixingthelimitontheHiggsmasscanbesatis edwithmuchlowerstopmasses,mt (MZ) 300GeV.Thereforeinthis“maximalmixingscenario”(scenariowheremixinginthestopsectorissuchthattheHiggsmassismaximized)the netuninginEWSBishighlyalleviated.Howeveritisverynon-trivialtorealizethisscenarioinmodels,sinceitusuallyrequiresverylargeAtattheGUTscale,severaltimeslargerthanothersoftSUSYbreakingparameters.ThemaximalmixingscenarioanditspossiblerealizationinmodelswillbediscussedinmoredetailinSec.2.
Asimplewayofachievingclosetomaximalmixingwasrecentlysuggestedin[7].IfweallownegativestopmassessquaredattheGUTscaleseveralinterestingthingshappensimultaneously.Firstofall,unlessmt istoolargecomparedtoM3itwillruntopositivevaluesattheEWscale.Atthesametimethecontributiontom2Hufromtheenergyintervalwherem2 <0partiallyorevenexactlycancelsthecontributionfromtheenergyintervalt