The $\tau\to\nu_\tau\pi e^+e^-$ decay revisited

TL;DR

This paper revisits the decay process $ au o u_ au o ext{pi} e^+ e^-$ using Resonance Chiral Theory, incorporating symmetry-breaking effects to improve understanding of the decay and its radiative corrections.

Contribution

It provides a reanalysis of the decay process with updated theoretical modeling including symmetry-breaking effects, focusing on the $W ext{pi} ext{gamma}^ ext{star}$ vertex.

Findings

Enhanced theoretical description of $ au$ decay process.

Insights into the $W ext{pi} ext{gamma}^ ext{star}$ vertex effects.

Implications for radiative correction calculations.

Abstract

The recent results from Belle of the $\tau^-\to\nu_\tau\pi^-e^+e^-$ analysis has incentivated us to make a reanalysis of a former work where the Structure Dependent parts are obtained using Resonance Chiral Theory. Here we rely on the same theory accounting for effects that explicitly break such symmetry. A motivation is the involved $W\pi\gamma^\star$ vertex, utterly relevant in computing $\tau^- \to \nu_{\tau}\pi^-$ radiative corrections.