Model Independent Electromagnetic corrections in hadronic $\tau$ decays

TL;DR

This paper calculates electromagnetic long-distance corrections to certain tau decay widths using a model-independent approach that ensures gauge invariance and is free of singularities, applicable to multiple decay channels.

Contribution

It introduces a model-independent method for computing electromagnetic corrections in tau decays, avoiding UV and IR divergences and maintaining gauge invariance.

Findings

Correction is free of UV and IR singularities.

Method applicable to multiple tau decay channels.

Ensures electromagnetic gauge invariance.

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: $\tau^{\pm}\to \pi^{\pm}\pi^{0}\nu, K^{\pm}\pi^{0}\nu$.