$τ\to πK ν$ Decay and $πK$ Scattering

Abstract

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