Failure of Breit-Wigner and success of dispersive descriptions of the τ^-\to K^-ην_τdecays

Abstract: The \tau^-\to K^-\eta\nu_\tau decays have been studied using Chiral Perturbation Theory extended by including resonances as active fields. We have found that the treatment of final state interactions is crucial to provide a good description of the data. The Breit-Wigner approximation does not resum them and neglects the real part of the corresponding chiral loop functions, which violates analyticity and leads to a failure in the confrontation with the data. On the contrary, its resummation by means of an Omn`es-like exponentiation of through a dispersive representation provides a successful explanation of the measurements. These results illustrate the fact that Breit-Wigner parametrizations of hadronic data, although simple and easy to handle, lack a link with the underlying strong interaction theory and should be avoided. As a result of our analysis we determine the properties of the K*(1410) resonance with a precision competitive to its traditional extraction using \tau^-\to (K\pi)^-\nu_\tau decays, albeit the much limited statistics accumulated for the \tau^-\to K^-\eta\nu_\tau channel. We also predict the soon discovery of the \tau^-\to K^-\eta'\nu_\tau decays.