D-term inflation and neutrino mass

arXiv:hep-ph/0207041v227Sep2002KANAZAWA-02-11July,2002D-terminflationandneutrinomassDaijiroSuematsu∗InstituteforTheoreticalPhysics,KanazawaUniversity,Kanazawa920-1192,JapanAbstractWestudyaD-terminflationscenarioinamodelextendedfromtheminimalsupersym-metricstandardmodel(MSSM)bytwoadditionalabelianfactorgroupsfocussingonitsparticlephysicsaspects.Condensatesofthefieldsrelatedtotheinflationcannaturallygiveapossiblesolutiontoboththeμ-problemintheMSSMandtheneutrinomassthroughtheirnonrenormalizablecouplingstotheMSSMfields.Mixingsbetweenneutrinosandneutralinosarealsoinducedbysomeofthesecondensates.Smallneutrinomassesaregeneratedbyaweakscaleseesawmechanismasaresultofthesemixings.Moreover,thedecayofthecondensatesmaybeabletocausetheleptogenesis.Usuallyknowndiscrep-ancybetweenbothvaluesofaFayet-IliopoulosD-termwhicharepredictedbytheCOBEnormalizationandalsobyananomalousU(1)intheweakly-coupledsuperstringmightbereconciled.∗e-mail:[e-mail]11IntroductionRecentobservationsinbothastrophysicsandparticlephysicsprovidecrucialinforma-tionstoastro-particlephysics.Observationofthecosmicmicrowavebackgroundradia-tion(CMB)givesastrongsupportfortheinflation[1].Moreover,preciseestimationsofthespectralindexofthedensityperturbationsbasedontherecentobservationsstrictlyrestricttheformoftheinflatonpotential.Particlephysicsmodelsseemtoberequiredtohaveastructuretoinducetheinflationconsistentwiththeseobservationsinit.Ontheotherhand,observationsoftheatmosphericandsolarneutrinosatSuper-Kamiokandesuggesttheexistenceofnonzeroneutrinomassesandthisfactrequiressomemodificationofthestandardmodel(SM)[2].Fromthetheoreticalpointofviewofparticlephysics,moreover,supersymmetrizationoftheSMisconsideredtobethemostpromisingcandi-datetosolvethegaugehierarchyproblem,althoughwehavenodirectevidenceforitstillnow.Thusatthepresentstageitseemstobenaturaltoconsidertheinflationbasedonasuitablesupersymmetricmodelwhichismotivatedfromaviewpointofparticlephysicssuchastheexplanationof,forexample,theneutrinomass,theμ-problem,thestrongCPproblemandsoon[3]-[11].Variousideasfortheinflation[12]-[15]havebeenextendedtothesupersymmetricmodelsbynow.Theymaybeclassifiedintotwotypesofmodels,thatis,anF-terminflationmodelandaD-terminflationmodel.IfweconsidertheF-terminflation,wearealwayssufferedfromtheη-problemwhichiscausedbythesupergravitycorrectiontoaninflatonmassasaresultofthesupersymmetrybreakingduringtheinflation[16].AsfaraswedonotintroduceaspecialK¨ahlerpotential[16],thereisalargecorrectiontotheinflatonmassoftheorderofaHubbleconstantandthentheinflationcannotoccur.AD-terminflation[17]hasbeenproposedasamodelwhichcanescapethisη-problem.IntheD-terminflationmodelthereappearseveralSMsingletfieldsintimatelyrelatedtotheinflation.Althoughtheyplayacrucialroleintheinflationphenomena,theyusuallyhavenoroleinparticlephysics.Ifwecanrelatetheirexistencetotheimportantproblemsinparticlephysics,forexample,theneutrinomass,theμ-problemandsoon,theD-terminflationscenariomightbemuchmorepromising.InthispaperweinvestigatesomeparticlephysicsaspectsoftheSMsingletfieldsinvolvedintheinflationinacertainD-terminflationmodel.ThemodelisdefinedasanextensionfromtheMSSMbytwoabelianfactorgroupsU(1)X×U(1)A,whichare2extendedbyanadditionalabelianfactorgroupincomparisonwiththeordinaryD-terminflationscenario.Weshowthatthecondensatesofthesesingletfieldscanberelatedtosmallneutrinomassesandtheμ-probleminthismodel.Theirdecayalsomayinducetheleptogenesis.Moreover,theintroductionofthisnewfactorgroupmightbeabletorelaxthediscrepancybetweenthescalesoftheD-termpredictedbythecosmicbackgroundexplorer(COBE)normalizationandbytheweakly-coupledsuperstring.Thepaperisorganizedasfollows.Inthenextsectionwediscussvariousaspectsoftheinflationinthismodel.Insection3westudythefeaturesasaparticlephysicsmodel,especially,theoriginoftheneutrinomassesandtheμ-term.Thepossibilityoftheleptogenesisisalsobrieflydiscussed.Thelastsectionisdevotedtothesummary.2AmodelofD-terminflationInourmodelfieldcontentsandagaugestructurearemotivatedbytheweakly-coupledsuperstringmodelsbasedon,forexample,E6.Suchkindofthefieldcontentsandthegaugestructurehavebeensuggestedtoappearoftenintheireffectivetheories[18].U(1)AisassumedtohaveaFayet-Iliopoulos(F-I)D-term,whichmightbeconsideredtobeananomalousU(1).Asfieldsrelatedtotheinflation,weintroduceagaugesingletchiralsuperfieldφandtwopairsofchiralsuperfields(N,¯N)and(S,¯S),whicharetheSMsingletfieldsbuthavechargesofU(1)X×U(1)A.ArenormalizablesuperpotentialconstitutedbythesefieldsisassumedtobeW1=kφN¯N,(1)wherekisconsideredtoberealandpositivebyasuitableredefinitionoffields.AvalueofkisconstrainedonthebasisofsomeobservationalrequirementssuchastheCMBdataandsoon.Thepotentialforthescalarcomponentsofthesefieldscanbewrittenas1V=g2X2hQNX|˜N|2−|˜¯N|2+QSX|˜S|2−|˜¯S|2i2+g2A2hQNA|˜N|2−|˜¯N|2+QSA|˜S|2−|˜¯S|2+ξAi2+k2h|˜φ|2|˜N|2+|˜¯N|2+|˜N˜¯N|2i.(2)1Inthefollowingdiscussionwedenoteascalarcomponentofthesuperfieldbyaddingatildeonthesamecharacterasthesuperfieldandaspinorcomponentbythesamenotationasthem.3ThefirsttwolinesareD-termcontributionsandthelastlineisanF-termcontribution