The gauge boson contributions to the radiatively corrected m(2)

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