an introduction to supersymmetry

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1、APCTP{5KEK{TH{501November1996AnIntroductiontoSupersymmetryManuelDreesAsia{PacicCenterforTheoreticalPhysics,Seoul,KoreaAbstractAfairlyelementaryintroductiontosupersymmetriceldtheoriesingeneralandthemin-imalsupersymmetricStandardModel(MSSM)inparticularisgive

2、n.Topicscoveredincludethecancellationofquadraticdivergencies,theconstructionofthesupersymmetricLagrangianusingsuperelds,theeldcontentoftheMSSM,electroweaksymmetrybreakingintheMSSM,mixingbetweendierentsuperparticles(currenteigenstates)toproducemasseigensta

3、tes,andtheembeddingoftheMSSMinso{calledminimalsupergravity.arXiv:hep-ph/9611409v125Nov19961.IntroductionInthelast20yearstheSLACSpiresdatabasehasregisteredalmost10,000papersdealingwithvariousaspectsofsupersymmetriceldtheories.Thisisquiteremarkable,giventhatt

4、hereisnodirectexperimentalevidencefortheexistenceofanyofthenumerousnewparticlespredictedbysuchtheories.Thisapparentdiscrepancybetweentheoreticalspeculationandexperimentalfacthasevencaughtthepubliceye,andledtochargesthatmodernparticlephysicsresemblesmedievala

5、lchemy.Iwillthereforestarttheselecturenotesbyreviewinginsomedetailthemainargumentfortheexistenceofsupersymmetricparticlesattheweakscale"(i.e.,withmassveryroughlycomparabletothoseoftheheaviestknownelementaryparticles,theWandZbosonsandthetopquark).Thisargumen

6、trestsontheobservationthatsupersymmetriceldtheoriesaturally"allowtochosetheweakscaletobemanyordersofmagnitudebelowthehypotheticalscaleMXofGrandUnicationorthePlanckscaleMPl.Thisiscloselyrelatedtothecancellationofquadraticdivergencies[1]insupsersymmetrice

7、ldtheories;suchdivergenciesarenotoriousinnon{supersymmetrictheorieswithelementaryscalarparticles,suchastheStandardModel(SM).InSec.2thisquestionwillbedis-cussedinmoredetail,andthecancellationofquadraticdivergenciesinvolvingYukawainteractionswillbedemonstrated

8、explicitly(in1{looporder).Thisexplicitcalculationwillindicatethebasicfeaturesthattheproposednewsymmetryhastohaveifitistosolvetheaturalnessproblem"[2]oftheSM.Inparticular,wewillneedequalnumbers