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

Understand

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.