K pi vector form factor, dispersive constraints and tau -> nu_tau K pi decays

Abstract

Recent experimental data for the differential decay distribution of the decay $τ^-\toν_τK_Sπ^-$ by the Belle collaboration are described by a theoretical model which is composed of the contributing vector and scalar form factors $F_+^{Kπ}(s)$ and $F_0^{Kπ}(s)$. 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 $F_+^{Kπ}(s)$ in the complex $s$-plane, can be extracted, with the result $M_{K^*}=892.0 \pm 0.9 $MeV and $Γ_{K^*}=46.2 \pm 0.4 $MeV. Finally, employing the three-subtracted dispersion relation allows to determine the slope and curvature parameters $λ_+^{'}=(24.7\pm 0.8)\cdot 10^{-3}$ and $λ_+^{''}=(12.0\pm 0.2)\cdot 10^{-4}$ of the vector form factor $F_+^{Kπ}(s)$ directly from the data.