Mediation of Supersymmetry Breaking in Gauge Messenger Model(3)

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

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