The small $K \pi$ component in the $K^*$ wave functions

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 $K^*$ wave function. A fit is made to the $K \pi$ phase shifts in p-wave, from where the coupling of $K^*$ to $K \pi$ and the $K \pi$ loop function are determined. These ingredients allow us to determine that the $K^*$ is a genuine state, different to a $K \pi$ component, in a proportion of about 80%.