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

Abstract

In a combined study of the decay spectra of τ − → K S π − ν τ and τ − → 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 * = 1304 ± 17 MeV and Γ K * = 171 ± 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 − → 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 − → K − π 0 ν τ would be extremely useful, as it would allow to study those isospin violations with much higher precision.