Cascade production from antikaon induced reactions on lambda and sigma

Abstract

Using a gauged flavor SU(3) invariant hadronic Lagrangian, we study $\Xi$ production from $\bar{K}$ induced reactions on $\Lambda$ and $\Sigma$ in a coupled-channel approach. Including the four channels of $\bar{K}\Lambda$, $\bar{K}\Sigma$, $\pi \Xi$, and $\eta \Xi$, 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 $\bar{K}\Lambda \to \pi \Xi$, $\bar{K}\Sigma \to \pi \Xi$, $\bar{K}\Lambda \to \eta \Xi$, and $\bar{K}\Sigma \to \eta \Xi$ 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 $\bar{K}\Lambda \to \bar{K}\Lambda$, $\bar{K}\Sigma \to \bar{K}\Sigma$, $\pi \Xi \to \pi \Xi$, and $\eta \Xi \to \eta \Xi$ as well as for the inelastic processes $\bar{K}\Lambda \to \bar{K}\Sigma$ and $\pi \Xi \to \eta \Xi$. Implications of the reactions studied here in $\Xi$ production from relativistic heavy ion collisions are discussed.

Comments: 11 pages and 10 figures