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

TL;DR

This paper applies a generalized formalism to analyze the $K^*$ meson, concluding it is predominantly a genuine state with about 80% not composed of $K \, \pi$ components, based on phase shift data.

Contribution

It extends Weinberg's compositeness condition to higher partial waves, providing a method to quantify the $K \pi$ component in the $K^*$ wave function.

Findings

The $K^*$ is approximately 80% a genuine state.

The formalism successfully fits $K \pi$ p-wave phase shifts.

Determines the coupling and loop functions for $K^*$.

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 $K^*$ 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%.