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.

Comments: 20 pages, 5 figures, accepted for publication in Nucl. Phys. A