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

Abstract

A dynamical model for S-- and P--wave correlated $2 π$ (and $K \bar K$) exchange between a kaon and a nucleon is presented, starting from corresponding $N \bar N \rightarrow K \bar K$ amplitudes in the pseudophysical region, which have been constructed from nucleon, $Δ$--isobar and hyperon ($Λ$, $Σ$) exchange Born terms and a realistic meson exchange model of the $ππ\rightarrow K \bar K$ and $K \bar K \rightarrow K \bar K$ amplitude. The contribution in the s--channel is then obtained by performing a dispersion relation over the unitarity cut. In the $ρ$--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.