$\ddot{I}{„}^{-}\to K^{-}\hat{I}{\cdot }^{(\prime )}\hat{I}{½}_{\ddot{I}}„$ decays in Chiral Perturbation Theory with Resonances

Abstract

We have studied the $\ddot{I}{„}^{-}\to K^{-}\hat{I}{\cdot }^{(\prime )}\hat{I}{½}_{\ddot{I}}„$ 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 $K\hat{I}\cdot$ 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 $\hat{I}{“}_{K^{\star \prime }}=(217_{-122}^{+68})$ MeV. These values are competitive with the standard determination from $\ddot{I}{„}^{-}\to (K\ddot{I}€{)}^{-}\hat{I}{½}_{\ddot{I}}„$ decays. The corresponding predictions for the $\ddot{I}{„}^{-}\to K^{-}\hat{I}{\cdot }^{\prime }\hat{I}{½}_{\ddot{I}}„$ channel respect the current upper bound and hint to the discovery of this decay mode in the near future.

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