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 $\bar K$ induced reactions on $Λ$ and $Σ$ in a coupled-channel approach. Including the four channels of $\bar KΛ$, $\bar KΣ$, $πΞ$, 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 with empirical input, we find that the cross sections for the reactions $\bar KΛ\toπΞ$, $\bar KΣ\toπΞ$, $\bar KΛ\toηΞ$, and $\bar KΣ\toηΞ$ 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 $\bar KΛ\to\bar KΛ$, $\bar KΣ\to\bar KΣ$, $πΞ\toπΞ$, and $ηΞ\toηΞ$ as well as for the inelastic processes $\bar KΛ\to\bar KΣ$ and $πΞ\toηΞ$. Implications of the reactions studied here in $Ξ$ production from relativistic heavy ion collisions are discussed.