On the absorption and production cross sections of $K$ and $K^{\ast }$

We have computed the isospin and spin averaged cross sections of the processes $\pi K^{\ast }\to \rho K$ and $\rho K^{\ast }\to \pi K$, which are crucial in the determination of the abundances of $K^{\ast }$ and $K$ in heavy ion collisions. Improving previous calculations, we have considered several mechanisms which were missing, such as the exchange of axial and vector resonances ($K_1(1270)$, $K_2^{\ast }(1430)$, $h_1(1170)$, etc…) and also other processes such as $\pi K^\to \omega K, \phi K$and$\omega K^,,\phi K^*\to \pi K$. We find that some of these mechanisms give important contributions to the cross section. Our results also suggest that, in a hadron gas, $K^{\ast }$ production might be more important than its absorption.