$τ^-\to K^-η^{(\prime)}ν_τ$: a primer analysis

The decays $\tau^-\to K^-\eta\nu_\tau$ and $K^-\eta^\prime\nu_\tau$ are studied in the context of Chiral Perturbation Theory supplemented with the explicit inclusion of resonances. For the required vector-form factors we have explored three different possibilities according to the treatment of final-state interactions: Breit-Wigner parametrisation, exponential resummation and dispersive representation. In the first part of the analysis, we predict the invariant mass spectrum and the integrated branching ratio for both decays from a fit to data on $\tau^-\to K_S\pi^-\nu_\tau$ decays. In the second part, we take advantage of existing data on $\tau^-\to K^-\eta\nu_\tau$ from BABAR and Belle collaborations and perform a fit to extract the pole position of the $K^\ast(1410)$ resonance which is seen to be in agreement and competitive with the values obtained before. From the comparison to data we conclude that the Breit-Wigner parametrisation of form factors is too na\"{\i}ve and consequently the use of more advanced treatments such as exponential resummation or dispersive representation is essential.