We derive analytic formulas for the radiatively corrected mass of the scalar Higgs boson in the framework of the minimal supersymmetric standard model (MSSM). Since the scalar-top-quark mass in our analysis include terms proportional to the gauge couplings

2g(m2,m)= tt121m2 t12 2(m2 m). tt 21 (16)

Intheaboveequation,theradiativelycorrectedmass-squaredofthepseudoscalarHiggsbosonisgivenby

m2A=m23

16π2v2sinβcosβ32f(m2,m), tt 12(17)

wherethe rsttermstandsforthemass-squaredofthepseudoscalarHiggsbosonatthetree-level.Eveniftermsproportionaltothegaugecouplingsinthescalar-top-quarkmassareincluded,theradiativelycorrectedmassofthepseudoscalarHiggsbosondoesnotchanged.Themass-squaredsofthescalarHiggsbosonareobtainedas

m2h,H=

mh≤mH.

Nowletussetareasonableregioninparameterspaceinordertoobtainthenu-mericalresultfortheneutralHiggsbosonmass.TheCDFandD0collaborations,respectively,predictthatthetop-quarkmassis176±8±10and199+19 21±22GeV[5].Thereforewetakethetopquarkmassof175GeV.TheHiggsmixingparameterµisthemassparameterintroducedinthesuperpotentialtermµH1H2.Thevaluesofthe

2functionf(m2,m)arealwayspositiveinourparametersetting.Ifwesetµ·Atas tt12apositivevalue,radiativecorrectionswillbepositivelycontributedtothetreelevel

massofthepseudoscalarHiggsboson.Inthispaper,we xµastheelectroweakscale,100GeV.Inournumericalanalysis,therangesofparametersarepresentedinTable

1.TheupperlimitoftanβinTable.1isgivenbyequation,tanβ=mt/mb≈40formt=175GeVTheupperlimitonthetreelevelmassofthepseudoscalarHiggsboson

2is xedas950GeVinournumericalanalysis.Thusm23canbeincreasedupto150

fortanβ=40.ExperimentallysupersymmetricparticlesareconstrainedtobeheavierthantheirSMpartners[6].Thereforeweassumethatthelowerlimitonthelighterscalar-top-quarkmassislargerthanthetop-quarkmass.

TableI.TherangesfortheMSSMparameters

102

2

100

100

100≤≤≤≤≤m23tanβmQmT

At≤1502≤40≤1000GeV≤1000GeV≤3000GeV1(TrMS)2 4det(MS), (18)

NextletusevaluatethenumericalresultfortheupperboundontheneutralHiggsbosonmassincludingradiativecorrectionsintheMSSM.InFig.1,weplotmhinclud-ingthepartialcontributionsofthegaugebosonsatthe1-looplevel.mhismaximized