Combined analysis of the decays τ ⁻ → K <inf> S</inf> π ⁻ ν <inf> τ</inf> and τ ⁻ → K ⁻ ην <inf> τ</inf>

© 2014, The Author(s). Abstract: In a combined study of the decay spectra of τ−− KSπ−ντ and τ−− K−ηντ 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 MK*′ = 1304 ± 17 MeV and ΓK*′ = 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−π0 vector form factor enters the description of the decay τ−− K−ηντ, 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−π0ντ would be extremely useful, as it would allow to study those isospin violations with much higher precision.