Non-perturbative chiral approach to Kp --gamma Y reactions(4)

A recently developed nonperturbative chiral approach to describe the S=-1 meson-baryon reactions has been extended to investigate the near threshold $K^- p \to \gamma \Lambda, \gamma \Sigma^0$ reactions. With the parameters governed by chiral SU(3) symmetr

thescalarsectorinthemeson-mesoninteractionin[20,21].Thephysicscontainedintheapproachesof[15,19]isbasicallythesame,inspiteofthedi erentinputsandtreatmentofthescatteringequations,andtheresultsareremarkablysimilar.However,itisnotclearthatthissimpleapproachcanbeextendedtotheS=0andS=1sectorsbecausehigherordercounterterms,whichcannotbeaccountedforbymeansofjustonecuto ,couldappear.Preliminaryresultsforthemeson-baryoninteraction[22]alsopointinthesamedirection.Inthispaper,weextendtheunitarycoupledchannelchiralapproachof[19]inordertoinvestigatetheK p→γΛ,γΣ0reactions.Ourmainobjectiveistoinvestigatewhetherthedataforthesereactionscanalsobewelldescribedwiththeparameters xedbytheSU(3)chiralsymmetryandhencecanprovideuswithanadditionalsupporttotheinterpretationoftheΛ(1405)asaquasi-boundmeson-baryonstatewithS= 1.

InsectionII,wepresentaderivationoftheapproach[19]withinawell-de nedformula-tionofrelativisticquantum eldtheory.Thiswillallowustoclearlyestablishtherulesbywhichtheapproximationswereintroducedinsolvingtheproblem.TheserulesthenallowustoeasilyderiveinsectionIIItheK p→γYamplitudethatisconsistentwiththemodelofRef.[19].TheresultsanddiscussionsarepresentedinsectionIV.

II.DERIVATIONOFTHEUNITARYCOUPLEDCHANNELMETHOD

TheapproachesfollowedinRefs.[15,19]weredevelopedbyimplementingsomephysicalconsiderationsofchiralsymmetryintoapostulatedcoupled-channelscatteringequation.ToextendthemodelofRef.[19]toinvestigateK p→γYreactions,itisusefultoestablishitsderivationfromawell-de nedformulationofrelativisticquantum eldtheory.

Withintherelativisticquantum eldtheory[23],theS-matrixforthereactionsweareconsideringcanbede nedas

ij,Sij=δij (2π)4iδ(4)(Pi Pf)T(1)

wherei,jdenoteeitherameson-baryon(MB)channeloraphoton-hyperon(γY)channel,andPiisthetotalfour-momentumofthesystem.Thescatteringamplitudeisde nedby