$τ^-\to K^-η^{(\prime)}ν_τ$ decays in Chiral Perturbation Theory with Resonances

Abstract

We have studied the $τ^-\to K^-η^{(\prime)}ν_τ$ 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 $Kη$ 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 $Γ_{K^{\star\prime}}\,=\,(217^{+68}_{-122})$ MeV. These values are competitive with the standard determination from $τ^-\to(Kπ)^-ν_τ$ decays. The corresponding predictions for the $τ^-\to K^-η^{\prime}ν_τ$ channel respect the current upper bound and hint to the discovery of this decay mode in the near future.