Model Independent Electromagnetic corrections in hadronic $\tau$ decays

Abstract

The long distance correction to the total decay width of the $\tau^{\pm}\to K^{0}\pi^{\pm}\nu$ decay is calculated in a model independent approach where a discrimination of photons in the Bremmstrahlung process is assumed. This correction is completely free of UV and IR singularities and moreover, it satisfies electromagnetic gauge invariance. The result of this work can be applied on the tau decays: $\tau^{\pm}\to \pi^{\pm}\pi^{0}\nu, K^{\pm}\pi^{0}\nu$.