Combined analysis of the decays $τ^-\to K_Sπ^-ν_τ$ and $τ^-\to K^-ην_τ$

Abstract

In a combined study of the decay spectra of $τ^-\to K_Sπ^-ν_τ$ and $τ^-\to K^-ην_τ$ 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 $Γ_{K^{*\prime}} = 171 \pm 62\,$MeV. Further constraints on the width could result from updated analyses of the $Kπ$ and/or $Kη$ spectra using the full Belle-I data sample. Prospects for Belle-II are also discussed. As the $K^-π^0$ vector form factor enters the description of the decay $τ^-\to K^-ην_τ$, we are in a position to investigate isospin violations in its parameters like the form factor slopes. In this respect also making available the spectrum of the transition $τ^-\to K^-π^0ν_τ$ would be extremely useful, as it would allow to study those isospin violations with much higher precision.

20 pages, 1figure