Combined analysis of the decays $\tau^{-}\to K_{S}\pi^{-}\nu_{\tau}$ and $\tau^{-}\to K^{-}\eta\nu_{\tau}$

TL;DR

This paper demonstrates that a combined analysis of specific tau decay modes within Chiral Perturbation Theory can significantly improve the determination of the $K^{*}(1410)$ resonance's mass and width.

Contribution

It introduces a novel combined analysis approach using dispersive form factors within Chiral Perturbation Theory to better determine the $K^{*}(1410)$ resonance parameters.

Findings

Improved the $K^{*}(1410)$ mass to $1304 ext{ MeV}$ with uncertainty

Refined the $K^{*}(1410)$ width to $171 ext{ MeV}$ with uncertainty

Showed the effectiveness of combined decay analysis in resonance parameter extraction

Abstract

The potential of performing a combined analysis of the strangeness-changing decays $\tau^{-}\to K_{S}\pi^{-}\nu_{\tau}$ and $\tau^{-}\to K^{-}\eta\nu_{\tau}$ for unveiling the $K^{*}(1410)$ resonance pole parameters is illustrated. Our study is carried out within the framework of Chiral Perturbation Theory, including resonances as explicit degrees of freedom. Resummation of final state interactions are considered through a dispersive parameterization of the required form factors. A considerable improvement in the determination of the pole position with mass $M_{K^{*}(1410)}=1304\pm17$ MeV and width $\Gamma_{K^{*}(1410)}=171\pm62$ MeV is obtained.