Kπ vector form factor, dispersive constraints and τ → vτKπ decays

Recent experimental data for the differential decay distribution of the decay tau(-) -> v(tau)K(S)pi(-) the Belle collaboration are described by a theoretical model which is composed of the contributing vector and scalar form factors F-+(K pi)(s) and F-0(K pi) (s). Both form factors are constructed such that they fulfil constraints posed by analyticity and unitarity. A good description of the experimental measurement is achieved by incorporating two vector resonances and working with a three-times-subtracted dispersion relation in order to suppress higher-energy contributions. The resonance parameters of the charged K*(892) meson, defined as the pole of F-+(K pi)(s) in the complex s-plane, can be extracted, with the result M-K* = 892.0 +/- 0.9 MeV and Gamma(K*) = 46.2 +/- 0.4 MeV. Finally, employing a three-times-subtracted dispersion relation allows one to determine the slope and curvature parameters lambda(+)' = (24.7 +/- 0.8) x 10(-3) and lambda(+)'' = (12.0 +/- 0.2) x 10(-4) of the vector form factor F-+(K pi) (s) directly from the data.