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
GauginomassesattheGUTscale(αi=αGUT)are(Eq.(A.12)):Mi=[ 2(5 NCi)+Nmess]MSUSY,
whereNCiisthenumberofcolorsofthegaugegroupSU(NCi).Moreexplicitly,
M3=( 4+Nmess)MSUSY,
M2=( 6+Nmess)MSUSY,
M1=( 10+Nmess)MSUSY.(3.3)(3.4)(3.5)
Intheminimalmessengermodel(Nmess=0),thegauginomassesatthemessengerscale(theGUTscale)are
M3= 4MSUSY,
M2= 6MSUSY,
M1= 10MSUSY.(3.6)(3.7)(3.8)
Notethat|M1|>|M2|>|M3|attheGUTscale(|M1|:|M2|:|M3|=2.5:1.5:1).AsaresultofRGevolution,attheweakscalewe nd|M1(MZ)|:|M2(MZ)|:|M3(MZ)|～1:1:2.Thisisquitedi erentfromscenarioswiththeuniversalgauginomassesattheGUTscalewhichleadtogluinoabout7timesheavierthanbinoattheEWscale.
SoftmasssquaredparametersforsquarksandsleptonsattheGUTscalewithNmess=0aregivenas(seeEq.(A.14)):
2,(3.9)m2 2cibXi+2 cφbGMSUSYφ=
i
where c=c5 3i=1ciandc5,ciarethequadraticcasimirsofφ eldunderSU(5)and
standardmodelgaugegroups,andbXiarethecontributionsofmessenger eldstothe
betafunctioncoe cient.DetailedexpressionisgivenintheAppendixA.Whenthereareadditionalchiralmessengers,wewouldobtain(wellknown)additionalgaugemediationcontribution[31].ExplicitexpressionsforsquarkandsleptonmassesattheGUTscalearegivenas:
m2Q=( 20+3bG+21
2Nmess)MSUSY,
m2dc=( 12+2bG+57(3.11)
m2ec=( 12+6bG+1032Nmess)MSUSY,(3.13)
102Nmess)MSUSY.(3.15)
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