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

Abstract

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 $M_{K^{\star \prime }}=(1330_{-41}^{+27})$ MeV and ${\Gamma }_{K^{\star \prime }}=(217_{-122}^{+68})$ MeV. These values are competitive with the standard determination from ${\tau }^{-}\to (K\pi {)}^{-}{\nu }_{\tau }$ decays. The corresponding predictions for the ${\tau }^{-}\to K^{-}{\eta }^{\prime }{\nu }_{\tau }$ channel respect the current upper bound and hint to the discovery of this decay mode in the near future.

arXiv comment26 pages, 6 tables, 4 figures. Minor changes to match published version. Journal reference and DOI added

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