Non-perturbative chiral approach to Kp --gamma Y reactions(3)

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

matrixapproach,whichwouldimplementunitarityintheamplitudes[9,16,17].ThemeritofthechirallagrangiansisthattheycanprovideanexpansionforthisKmatrixconsistentwithchiralsymmetryanditsbreakinginthedi erentstrangenesschannels,S=0,1, 1.Theextensionoftheworkof[15]totheS=0,1channelsisdoneinRef.[18].Particularly,whenworkingintheS=0sector,πNandcoupledchannels,theN (1535)resonanceisalsogenerateddynamically.Simultaneously,theηandKphotoproductionprocessesintheS=0channelswerealsostudiedinasimilarapproach,andwithafewmoreparametersaglobalreproductionofthestrongandelectromagneticcrosssectionswasobtained.

Theworkof[19]wasinspiredbyRef.[15],butfollowedcloselytheapproachdevelopedinthestudyofthes-wavemeson-mesonscatteringofRef.[20].Startingwithacoupled-channelequationbasedonthelowestorderchirallagrangian,itwasfoundthattheo shelle ectsintheverticescanbeabsorbedincouplingconstantsrenormalization.Hence,onlytheon-shellpartoftheverticesneededtobeconsidered.Theloopintegralswereregularizedbymeansofacuto ,ratherthanusingaformfactorasdonein[15],whichallowsonetokeepthechirallogarithms.Theresultingcoupled-channelequationissimilartothatofRef.[15].AnothermajorsteptakeninRef.[19]wastoincludetheηandΞchannelsinordertohaveexactSU(3)symmetrywhenthemassdi erencesamongthemembersofeachOctet,mesonicorbaryonic,areneglected.Bothchannelsarenotopenedatlowenergiesandtheloopintegrationsinvolvingthesetwochannelsonlycontributetotherealpartoftheamplitudes.TheinclusionoftheΞchannelswasfoundtohavenegligiblee ects,buttheηchannelswerefoundnumericallyimportant.Theapproachof[19]turnsouttobemoreeconomicalbecausewiththeuseofonlyonecuto parameterandtheinputofthelowestorderlagrangianonecanreproducefairlywellallthelowenergydataintheS= 1sector.However,thefactthattheηmesonloopsonlyprovidearealparttotheamplitudes,allowsthee ectofthesechannelstobee ectivelytakenintoaccountbymeansoftheparametersofthesecondorderlagrangians,asdonein[15],providedoneisnottooclosetothethresholdsofthesechannels.Conversely,thee ectsofthesecondorderlagrangiancanbee ectivelyincorporatedbymeansofasuitablecuto in[19],muchasithappenedinthestudyof