Non-perturbative chiral approach to Kp --gamma Y reactions(6)

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

Tij(ki,kj,√

Ml

(2π)32ωl(k)V(k,k)Tlj(k,kj,√ili√

4f2(ki+kj)u kj.(8)

Inthenearthresholdregion,onecanusetheheavy-baryonapproximationtoreducethepotentialintoaspin-independents-waveinteraction

Vij(k′,k)→ Cij

s)=1

skis)|2(10)

and(10)de nepreciselythemodelusedin[19]. where¯standsforthesumandaverageoverthe nalandinitalspinindices.Eqs.(7),(9),

InRef.[19]Eq.(7)issolvedbyevaluatingthepotentialVijon-shellandhenceitfactorsoutoftheintegral.Itwasarguedthattheo -shelle ectsareintherenormalizationofcouplingconstantsandcanbeneglectedinthecalculationusingphysicalmassesandcouplingconstants.Eq.(7)thenbecomesasimplealgebraicequationwhichcanbesolvedeasily.Acuto qmax=630MeVisfoundtobeneededtoregularizetheintegrationinEq.(7)andgiveagooddescriptionofalloftheexistingS= 1meson-nucleonreactionsnearthreshold.Thisfactorizationtechniqueissimilartothat rstintroduced[20]inthestudyofmeson-mesonscatteringusingchirallagrangians,wheretheo -shellcontributionscanbeabsorbedintotherenormalizationofmassesandcouplingconstants.