τ-→ K-η⁽′⁾ντ: a primer analysis

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The decays τ-→ K-ηντ and K-η′ντ 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 τ-→ Kₛπ-ντ decays. In the second part, we take advantage of existing data on τ-→ K-ηντ from BABAR and Belle collaborations and perform a fit to extract the pole position of the K(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 naıve and consequently the use of more advanced treatments such as exponential resummation or dispersive representation is essential.