K π vector form factor, dispersive constraints and τ→ν <inf>τ</inf> K π decays

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 +K π (s) and F 0K π (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 π (s) in the complex s-plane, can be extracted, with the result MK*=892. 0±0.9 MeV and ΓK*=46.2±0.4 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 +K π (s) directly from the data. © 2008 Springer-Verlag / Società Italiana di Fisica.