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

1.Introduction

Theelectroweakgaugebosonmasses(mW,mZ)inthestandardmodel(SM)aregeneratedthroughtheHiggsmechanism.ThentheSMpredictsanewscalarparticle,theHiggsparticle.ButanevidencefortheexistenceoftheHiggsparticlehasnotbeenexperimentallyobserveduptonow.ThereforeastudyfortheHiggsparticleisoneofthemostimportantissuesinelementaryparticlephysicsatthepresent.IntheSMonlyoneHiggsdoubletisrequiredtogivemassestoquarksandleptons.ThereforethereisjustonescalarHiggsbosonintheSM.Thelowerboundofabout60GeVontheHiggsbosonmassoftheSMisestimatedfromthenegativeexperimentresultsofLEP1.TheupperboundontheHiggsbosonmassoftheSMisknownasalmostfreeparameter.Ontheotherhand,supersymmetricmodelsimposeastrongconstraintontheupperboundontheHiggsbosonmass.Insupersymmetricmodels,atleasttwoHiggsdoubletsarerequiredtogivemassestofermionsviaspontaneoussymmetrybreaking.Hence,severalHiggsbosonsarepresentinsupersymmetricmodels.

Oneofthemostwidelystudiedsupersymmetricmodelsistheminimalsupersym-metricstandardmodel(MSSM).TheMSSMisthesimplestsupersymmetricextensionoftheSM.TheMSSMo ersasolutiontothegaugehiearchyprobleminatechnicalway.ItsHiggssectorconsistsoftwoHiggsdoublets,H1andH2.ThehyperchargesoftwoHiggsdoubletsareY= 1forH1andY=1forH2,respectively.IntheMSSM,down-typequarksandleptonsaregeneratedintermsofthevacuumexpectationvalue(v1)ofH1whileup-typequarksaregeneratedintermsofthevacuumexpectationvalue(v2)ofH2.TheHiggsspectraoftheMSSMconsistsoftwoneutralscalarHiggsboson(h,H),oneneutralpseudoscalarHiggsboson(A),apairofchargedHiggsbosons(H±)ually,oneoftwoparametersischosentobetheratioofthevacuumexpectationvaluesoftwoHiggsdoublets,tanβ,andtheotherbeeitherthelighterscalarHiggsbosonmassorthepseudoscalarHiggsbosonmass.Accordingtothetreelevelpotential,themassofthelighterscalarHiggsbosonhastobesmallerthanboththeZbosonmassandthepseudoscalarHiggsbosonmass.AlsotheMSSMpredictsatthetreelevelthatthemassofthechargedHiggsbosonmustbelargerthantheWbosonmass.Atthetreelevel,anotherdistinctfeatureisthattheHiggsbosonmassposessesasymmetricpropertyunderinterchangecosβ sinβ.

Ithasbeenrecentlypointedoutthatradiativecorrectionsgiveapositivecon-tributiontothetreelevelmassofthescalarHiggsboson.EspeciallythedominantcontributiontothetreelevelHiggsbosonmasscomesfromradiativecorrectiosduetothetop-quarkandscalar-top-quarkloops.TheradiativelycorrectedmassofthelighterscalarHiggsbosoncanbelargerthanboththeZbosonmassandtheradia-tivelycorrectedmassofthepseudoscalarHiggsboson[1].Furthermore,theradiativelycorrectedmassofthechargedHiggsbosoncanbesmallerthanWbosonmass[2].ThismeansthatradiativecorrectionstothetreelevelmassofthechargedHiggsbosoncanbenegativecontributions.Whenradiativecorrectionstothetreelevelmassof