The Scalar Contribution to $\tau \to K \pi \nu_\tau$

Abstract

We consider the scalar form factor in $\tau \to K\pi \nu_\tau$ decays. It receives contributions both from the scalar resonance $K_0^*(1430)$ and from the scalar projection of off-shell vector resonances. We construct a model for the hadronic current which includes the vector resonances $K^*(892)$ and $K^*(1410)$ and the scalar resonance $K_0^*(1430)$. The parameters of the model are fixed by matching to the $O(p^4)$ predictions of chiral perturbation theory. Suitable angular correlations of the $K\pi$ system allow for a model independent separation of the vector and scalar form factor. Numerical results for the relevant structure functions are presented.