Non-perturbative chiral approach to Kp --gamma Y reactions(11)

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

Allquantitesintheaboveequationareevaluatedaton-shellmomenta.Obviouslytheterm

[1+GT]MB,K pmeasuresthestrengthoftheK p→MBtransition.InTableIII,welistthesematrixelementsaswellasthevaluesoftheon-shellphotoproductionamplitudesFγY,MB.Weseethatthetotalamplitude,de nedbyEq.(25)inthisestimate,involvesanontrivalinterplaybetweenthestrongtransitionsandelectromagnetictransitions.Inparticular,thelargeenhancementoftheγΣ0productionbythecoupled-channele ectscanbeunderstoodfromthesecondcolumnofTableIII.WeseethatFγΣ0,π+Σ andFγΣ0,π Σ+areafactorofabout3largerthanFγΣ0,K p,whiletheirstrongtransitionstrengthsincolumn3arecomparableinmagnitude.Consequently,thebranchingratioforγΣ0isgreatlyenhancedwhentheπchannelsareincluded.Thisisveri edinourexactcalculationsbasedonEqs.(19)-

(20),ascanbeseeninthesecondrowofTableIV.WeseethatthebranchingratioforγΣ0productionisincreasedfrom0.14to1.28whentheπ+andπ channelsareincluded.Fromcolumn1ofTableIII,wealsoexpectthatthee ectofπchannelsontheγΛproductionismuchless,mainlybecausethephotoproductionamplitudesforthe rstthreechannelsarecomparableandthecontributionsfromπ+andπ channelshaveoppositesigns.Asshowninthe rstrowofTableIV,thecouplingwiththeπchannelscanlowertheproductionrateonlyfrom2.47to1.56.Neverthelesss,itisinstrumentalinbringingourpredictionclosertotheexperimentalvalue0.86±0.16.Wefurthernoticethatthereductionfrom2.47to1.33whentheπ+Σ channelisincluded( rstrowofTableIV)islargelyduetothecancellationcausedbytheoppositesignsoftheimaginarypartsof[1+GT],asseeninthethirdcolumnofTableIII.Notethattherelativesignsbetweenthecontributionsfromdi erentchannelsaredeterminednotonlybythemesoncharges(eM)butalsobythechiralSU(3)parameterslistedinTableI.Thus,thecoupled-channele ectsarecrucialintestingthechiralSU(3)symmetry.Thee ectduetotheK+Ξ channelisveryweakbecausetheirstrongtransitionisanorderofmagnitudesmallerthanothers,ascanbeseeninthethirdcolumnofTableIII.

Wenowturntoillustratingseveralimportantfeaturesofourapproach.TheexacttreatmentofmesonpropagatorsinFig.2cleadstoacontribution( γY,K pinEq.(19))from