Chiral SU(3) Dynamics with Coupled Channels: Inclusion of P-Wave Multipoles

Abstract

We extend our recent non-perturbative chiral SU(3) coupled channel approach to pion- and photon-induced $\eta$- and $K$-meson production off protons by including all strong and electromagnetic p-wave multipoles. We identify the p-wave amplitudes of the next-to-leading order SU(3) chiral meson-baryon Lagrangian with a coupled channel potential which is iterated to infinite orders in a separable Lippmann-Schwinger equation. Our approach to $\eta$- and $K$-photoproduction introduces no additional free parameters. By adjusting a few finite range parameters and the unknown parameters in the Lagrangian, we are able to simultaneously describe a very large amount of low-energy data. These include the total and differential cross sections of the $\pi$-induced reactions $\pi^- p \to \eta n, K^0 \Lambda, K^0 \Sigma^0, K^+ \Sigma^-$ and $\pi^+ p \to K^+ \Sigma^+$ as well as those of photoproduction $\gamma p \to \eta p, K^+\Lambda, K^+ \Sigma^0, K^0 \Sigma^+$. The polarization observables measured in $\eta$- and $K$-photoproduction are particularly sensitive to interference terms between the s- and p-wave multipoles. The total cross section data are remarkably well reproduced in all channels. There remain, however, some open questions concerning details of angular distributions and polarization observables.