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 ${\tau }^{-}\to {\nu }_{\tau }{K}_S{\pi }^{-}$ by 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 $K^{\ast }(892)$ meson, defined as the pole of $F_{+}^{K\pi }(s)$ in the complex $s$-plane, can be extracted, with the result $M_{K^{\ast }}=892.0\pm 0.9$MeV and ${\Gamma }_{K^{\ast }}=46.2\pm 0.4$MeV. Finally, employing the three-subtracted dispersion relation allows to determine the slope and curvature parameters ${\lambda }_{+}^{{}^{\prime }}=(24.7\pm 0.8)\cdot 10^{-3}$ and ${\lambda }_{+}^{{}^{\prime \prime }}=(12.0\pm 0.2)\cdot 10^{-4}$ of the vector form factor $F_{+}^{K\pi }(s)$ directly from the data.

Comments: 16 pages, 1 figure, version to appear in Eur. Phys. J. C