τ → πKν decay and πK scattering

Using chiral low energy theorems and elastic unitarity assumption, the τ → πKν 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.