Cascade production from antikaon induced reactions on lambda and sigma

Abstract

Using a gauged flavor SU(3)-invariant hadronic Lagrangian, we study Ξ production from K induced reactions on Λ and Σ in a coupled-channel approach. Including the four channels of KΛ , KΣ , πΞ, and ηΞ, we solve the Bethe–Salpeter equation in the K-matrix approximation by neglecting the off-shell contribution in the intermediate states. For the transition potential which drives the higher-order contribution, we consider all allowed Born diagrams in the s, t, and u channels. With coupling constants determined from the SU(3) symmetry using empirical input, we find that the cross sections for the reactions KΛ→πΞ , KΣ→πΞ , KΛ→ηΞ , and KΣ→ηΞ all have values of a few mb. In contrast to the results from the lowest-order Born approximation, the magnitude of these cross sections is less sensitive to the values of the cut-off parameters in the form factors. From the transition matrix in the coupled-channel approach, we have further evaluated the cross sections for the elastic process KΛ→ KΛ , KΣ→ KΣ , πΞ→πΞ, and ηΞ→ηΞ as well as for the inelastic processes KΛ→ KΣ and πΞ→ηΞ. Implications of the reactions studied here in Ξ production from relativistic heavy ion collisions are discussed.