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

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