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 $K_0^{\ast }(1430)$ and from the scalar projection of off-shell vector resonances. We construct a model for the hadronic current which includes the vector resonances $K^{\ast }(892)$ and $K^{\ast }(1410)$ and the scalar resonance $K_0^{\ast }(1430)$. 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.

Comments: 16 pages, Latex, uses epsfig.sty, 4 figures The complete paper, including figures, is also available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints/