K π vector form factor, dispersive constraints and τ→ν τ K π decays

Abstract

Recent experimental data for the differential decay distribution of the decay τ −→ν τ K S π − by the Belle collaboration are described by a theoretical model which is composed of the contributing vector and scalar form factors F + (s) and F 0 (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 + (s) in the complex s-plane, can be extracted, with the result $M_{K^{*}}=892.0\pm 0.9 \mathrm{MeV}$ and $\varGamma_{K^{*}}=46.2\pm 0.4 \mathrm{MeV}$ . Finally, employing a three-times-subtracted dispersion relation allows one to determine the slope and curvature parameters λ′+=(24.7±0.8)×10−3 and λ″+=(12.0±0.2)×10−4 of the vector form factor F + (s) directly from the data.