A bstract 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.
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