$\tau \to \pi K\nu$ Decay and $\pi K$ Scattering

Abstract

Using chiral low energy theorems and elastic unitarity assumption, the $\tau \to \pi K\nu$ decay is investigated. The vector and scalar $\pi K$ form factors are calculated. It is found that the $\pi K$ spectrum is dominated by the $K^{\ast }$ resonance. By measuring the forward-backward asymmetry, it is shown that the S wave $\pi K$ phase shift can be determined near the $K^{\ast }$ resonance region. The calculated branching ratio and resonance parameters are in good agreement with experiments.

Comments: 15 pages, Tex, 6 included figures