$\tau^-\to K^-\eta^{(\prime)}\nu_\tau$ decays in Chiral Perturbation Theory with Resonances

TL;DR

This paper analyzes tau decays into K eta and K eta' using Chiral Perturbation Theory with resonances, comparing different form factors and extracting resonance parameters with implications for future decay observations.

Contribution

It introduces and compares three form factor approaches within Chiral Perturbation Theory with resonances for tau decays, providing new resonance parameter determinations and predictions for unobserved decay modes.

Findings

Breit-Wigner form fails to fit data for K eta mode.

Dispersive and exponential resummation approaches fit data well.

Resonance parameters are determined with competitive precision.

Abstract

We have studied the $\tau^-\to K^-\eta^{(\prime)}\nu_\tau$ decays within Chiral Perturbation Theory including resonances as explicit degrees of freedom. We have considered three different form factors according to treatment of final-state interactions. In increasing degree of soundness: Breit-Wigner, exponential resummation and dispersive representation. We find that although the first one fails in accounting for the data on the $K\eta$ mode, the other two approaches provide good fits to them which are sensitive to the $K^\star(1410)$ pole parameters, that are determined to be $M_{K^{\star\prime}}\,=\,(1330^{+27}_{-41})$ MeV and $\Gamma_{K^{\star\prime}}\,=\,(217^{+68}_{-122})$ MeV. These values are competitive with the standard determination from $\tau^-\to(K\pi)^-\nu_\tau$ decays. The corresponding predictions for the $\tau^-\to K^-\eta^{\prime}\nu_\tau$ channel respect the current upper bound and hint to the discovery of this decay mode in the near future.