Role of correlated two-pion exchange in $K^{+}N$ scattering

Abstract

A dynamical model for S-- and P--wave correlated $2\pi$ (and $K\bar{K}$) exchange between a kaon and a nucleon is presented, starting from corresponding $N\bar{N}\to K\bar{K}$ amplitudes in the pseudophysical region, which have been constructed from nucleon, $\Delta$--isobar and hyperon ($\Lambda$, $\Sigma$) exchange Born terms and a realistic meson exchange model of the $\pi \pi \to K\bar{K}$ and $K\bar{K}\to K\bar{K}$ amplitude. The contribution in the s--channel is then obtained by performing a dispersion relation over the unitarity cut. In the $\rho$--channel, considerable ambiguities exist, depending on how the dispersion integral is performed. Our model, supplemented by short range interaction terms, is able to describe empirical $K^{+}N$ data below pion production threshold in a satisfactory way.

Comments: 24 pages, REVTEX, figures available from the authors