The small $K\pi$ component in the $K^{\ast }$ wave functions

Abstract

We use a recently developed formalism which generalizes the Weinberg's compositeness condition to partial waves higher than s-wave in order to determine the probability of having a $K\pi$ component in the $K^{\ast }$ wave function. A fit is made to the $K\pi$ phase shifts in p-wave, from where the coupling of $K^{\ast }$ to $K\pi$ and the $K\pi$ loop function are determined. These ingredients allow us to determine that the $K^{\ast }$ is a genuine state, different to a $K\pi$ component, in a proportion of about 80%.