$\tau^-\to\pi^-\eta^{(\prime)}\nu_\tau$ decays

TL;DR

This paper evaluates the vector and scalar form factors for the rare tau decay modes involving eta and eta' mesons, using Chiral Perturbation Theory with resonances and dispersive analysis to predict decay rates.

Contribution

It introduces a combined approach of Chiral Perturbation Theory and dispersive analysis to accurately predict second-class current tau decays involving eta and eta' mesons.

Findings

Vector form factor fixed from two-pion data

Scalar form factor obtained via dispersive analysis

Predictions for decay rates of tau to pi eta and pi eta' modes

Abstract

The vector and scalar form factors relevant to the second-class current $\tau^-\to\pi^-\eta^{(\prime)}\nu_\tau$ processes are evaluated supplementing Chiral Perturbation Theory with the inclusion of resonances as explicit degrees of freedom. While the vector contribution is essentially fixed from knowledge of the two-pion vector form factor, the scalar form factor demands a coupled channel dispersive analysis to obtain robust predictions for the detection of these decay modes.