Non-perturbative chiral approach to Kp --gamma Y reactions(12)

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

asecondpole.Bycomparingthe rsttworowsinTableV,weseethatthissecondpoletermcanchangetheγΣ0branchingratiobyabout40%,butmuchlessforγΛ.Consequently,thethepredictedratiobecomesclosertotheexperimentalvalue.

Animportant ndingofRef.[19]wasthatthecouplingwiththeηchannelsisessentialinobtainingagoodagreementwithalloftheexistingS= 1meson-baryonreactiondatawhenusingonlythelowestorderlagrangianasinput.Thein uenceofthiscouplingonourpredictionsisalsosigni cant.ThiscanbeseenbycomparingthesecondandthirdrowsinTableV.WeseethatthepredictedbranchingratioforγΛproductionisincreasedbyabout60%iftheηchannelsareomittedinthecalculationofthestrongamplitudesTMB,K pappearinginEq.(19).ItisclearthatincludingtheηchannelsisalsocrucialinusingthisreactiontotestthechiralSU(3)symmetry.WenotethattheηchannelswereomittedinthemodelofRef.[9].AtthesametimethecouplingsinthatworkhadtobesubstantiallychangedwithrespecttotheirSU(3)valuesinordertoobtainagood ttothedata.InretrospectivewecansaythatwhattheexplicitbreakingofSU(3)symmetrydoesinrealityistorestoreitafterithasbeenbrokenbytheomissionoftheηchannels.

Finally,wenotethatthestrongmeson-baryon-baryonvertexineachofthephotopro-ductionamplitudesshouldinprinciplehaveaformfactorbecausehadronsarecompositeparticles.Toseehowourresultswillbechangedwhenthisistakenintoaccount,weperformacalculationincludingamonopoleformfactorwithtypicalcuto ,Λπ,valuesof1.2and1GeV.Theintroductionofthiscuto reducestheratioRtovaluesinbetteragreementwiththedata.ChangesofΛπfrom1to1.2GeVintroduceonlycorrectionsoftheorderof10%.TheresultsobtainedwithΛπ=1GeV,avaluewhichiscommonlyaccepted,roughlyagreewiththedatawithinexperimentalerrors,whichareoforderof20%.Ifonecompareswiththecentralvaluesoftheexperimentalbranchingratios,ourresultsareontheupperedgeoftheBK p→γΛratiowhilethoseforBK p→γΣ0areontheloweredge.LookedatitinthecontextthatthecoupledchannelsandunitarizationhavereducedtheratioRbyafactor14,di erencesoftheorderof10–20%arenotsosigni cative.Yet,thefactthatabetteragreementwiththecentralvaluesofthedataisobtainedin[9],atthepriceof tting