Failure-of-JoAnnes-Global-Fit-to-the-Wilson-Coeffi

arXiv:hep-ph/9802401v123Feb1998SLAC-PUB-7702December1997FailureofJoAnne’sGlobalFittotheWilsonCoefficientsinRareBDecays:ALeft-RightModelExample∗ThomasG.RizzoStanfordLinearAcceleratorCenterStanfordCA94309,USAAbstractIntheStandardModelandmanyofitsextensions,itiswellknownthatalloftheobservablesassociatedwiththeraredecaysb→sγandb→sℓ+ℓ−canbeexpressedintermsofthethreeWilsoncoefficients,C7L,9L,10L(μ∼mb),togetherwithseveraluniversalkinematicfunctions.InparticularithasbeenshownthatthenumericalvaluesofthesecoefficientscanbeuniquelyextractedbyathreeparameterglobalfittodataobtainableatfutureB-factoriesgivensufficientintegratedluminosity.Inthispaperweexamineifsuchglobalfitsarealsosensitivetonewoperatorsbeyondthosewhichcorrespondtotheabovecoefficients,i.e.,whetherisitpossiblethatnewoperatorscanbeofsufficientimportanceforthethreeparameterfittofailandforthistobeexperimentallyobservable.UsingtheLeft-RightSymmetricModelasanexampleofascenariowithanextendedoperatorbasis,wedemonstrateviaMonteCarlotechniquesthatsuchapossibilitycanindeedberealized.Insomesensethispotentialfailureoftheglobalfitapproachcanactuallybeoneofitsgreatestsuccessesinidentifyingtheexistenceofnewphysics.∗WorksupportedbytheDepartmentofEnergy,ContractDE-AC03-76SF005151IntroductionRaredecaysofheavyquarkswhichdonotoccuratthetreelevelintheStandardModel(SM)canprovideauniqueopportunityfornewphysicstorevealitself.WhensuchdecaysoccurthroughloopsthentheparticipatingSMparticlesandthoseassociatedwiththenewinter-actionareplacedonthesamefootingandmayyieldcomparablecontributionstothevariousdecayamplitudes.Inthesecasesitmaybepossibletoisolatesuchadditionalcontributionsandlearnsomethingaboutthedetailednatureofthenewphysicsscenario.Amongsttheraredecaysinvolvingbquarks,twoofthecleanestandmostwellunder-stoodinclusiveprocessesareb→sγandb→sℓ+ℓ−.Atpresent,thebranchingfractionfortheb→sγmodehasbeenmeasuredbyCLEO[1]tobeB(b→sγ)=(2.32±0.57±0.35)×10−4whileapreliminaryresultfromALEPH[2]yieldsthevalue(3.38±0.74±0.85)×10−4.Ontheotherhand,thereexistonlyupperboundsforthedecayb→sℓ+ℓ−;thestrongestconstraintatpresentisthe90%CLlimitB(b→sℓ+ℓ−)4.2×10−5[3]fromCLEO,whichisobtainedbycombiningboththeirdi-electronanddi-muondatasamples.Aswewillseebelow,thisisonlyafactorof∼6abovetheexpectationsoftheSMforthisbranchingfractionsothatwemayexpectthisdecaytobeobservedinthenearfuture.IntheSMandinmanyofitsextensions(including,e.g.,fourthgenerationmod-els,modelswithanextradown-typequark,SUSY,extendedHiggssectors,Z′scenarios,theorieswithlargeanomalousgaugebosoncouplings,etc.)thephenomenologyofbothoftheserareprocessesabovearealmostcompletelydeterminedbythenumericalvaluesoftheWilsoncoefficientsofonlyasmallsetofoperatorsevaluatedatthescaleμ∼mb.InoursomewhatunconventionalnotationthesearedenotedasC7L,9L,10L(μ).AttheweakscaletheoperatorscorrespondingtothesecoefficientsariseintheSMfromtheusualγandZpenguinsaswellasWboxdiagrams.Ithasbeensuccessfullyarguedintheliterature[4]1thatbycombiningobservablesassociatedwithboththeb→sγandb→sℓ+ℓ−processes,amodelindependentthreedimensionalglobalfitcanbeperformedtonumericallydeterminethevaluesofthesethreeWilsoncoefficients.Indeed,givensufficientstatisticsatfutureB-factoriesthisapproachleadstoonlyrathermodestuncertaintiesinthefittedvaluesofthesecoefficientsallowingustotesttheSMandlookfornewphysics.Wenotethatonlythemagnitude|C7L(μ)|canbeextractedfromtheb→sγtransitionsothatitssignwouldremainundeterminedfromthischannelaloneevenifinfiniteprecisionwereavailable.Fortheobservablesassociatedwiththeb→sℓ+ℓ−decayallthreeofthecoefficientscontributeandthereforetheirrelativesignsaswellastheirmagnitudescanbeextractedfromthedatawhencombinedwithourknowledgeofB(b→sγ).InsomewaysthedeterminationofthethesethreeWilsoncoefficientsviaaglobalfittingprocedureinrareBdecaysissimilartothesearchesfornewphysicsinprecisionelectroweakmeasurements[5]throughtheuseoftheobliqueparametersS,T,U[6].Asthereadermayrecall,intheSM(forareferencevalueofthetopquarkandHiggsbosonmasses)theseparametersareallidenticallyzero.Forcertainclassesofnewphysics,suchasafourthgenerationofquarksandleptons,fitstoprecisiondatawouldthenleadtosomeconsistentsetofnon-zerovaluesfortheseparameterswithagoodχ2.Ofcourse,iftheseparametersarefoundtobenon-zeroanditisalsofoundthatdifferentprecisionobservablesyieldedstatisticallydistinctS,T,Uvaluesthenwewouldnecessarilyconcludethatthenewinteractionsarenotdescribablebytheobliquecorrectionsalone.(Asiswellknown,anyclassofnewinteractionsthatinducesignificantflavordependentvertexcorrections,suchasaZ′,cannotbeportrayedsolelyintermsofS,T,U.)Suchasituationwouldprovideauniquewindowonthecomplexnatureofthenewphysicsscenario.ItisthenobviousthatwhensufficientstatisticsbecomeavailableinthenottoodistantfutureforthistypeofanalysisofrareBdecaystobeperformed,thereareonlythree2possibleoutcomes:(i)ThenumericalvaluesforthecoefficientsarefoundtoagreewiththeSMexpectationswithagoodχ2.Inthiscasethenewphysicsisdecoupledandeitherhigherprecisiondataorsearcheselsewherearenecessarytouncoverit.(ii)AqualityfitisobtainedbutthevaluesonefindsforthethreeWilsoncoefficientsarefarfromtheSMexpectatio