Combined analysis of the decays $\tau^-\to K_S\pi^-\nu_\tau$ and $\tau^-\to K^-\eta\nu_\tau$

Understand

In a combined study of the decay spectra of $\tau^-\to K_S\pi^-\nu_\tau$ and $\tau^-\to K^-\eta\nu_\tau$ decays within a dispersive representation of the required form factors, we illustrate how the $K^*(1410)$ resonance parameters, defined through the pole position in the complex plane, can be extracted with improved precision as compared to previous studies.

• While we obtain a substantial improvement in the mass, the uncertainty in the width is only slightly reduced, with the findings $M_{K^{*\prime}}=1304 \pm 17\,$MeV and $\Gamma_{K^{*\prime}} = 171 \pm 62\,$MeV.
• Further constraints on the width could result from updated analyses of the $K\pi$ and/or $K\eta$ spectra using the full Belle-I data sample.
• Prospects for Belle-II are also discussed.