Kπ vector form factor constrained by τ → Kπντ and Kl3 decays

Dispersive representations of the K π vector and scalar form factors are used to fit the spectrum of τ → K πν τ obtained by the Belle collaboration incorporating constraints from results for K l 3 decays. The slope and curvature of the vector form factor are obtained directly from the data through the use of a three-times-subtracted dispersion relation. We find λ′ + = (25.49 ± 0.31) × 10 −3 and λ″ + = (12.22 ± 0.14) × 10 −4 . From the pole position on the second Riemann sheet the mass and width of the K *(892) ± are found to be m K * (892) ± = 892.0 ± 0.5MeV and Γ K * (892) ± = 46.5 ± 1.1MeV. The phase-space integrals needed for K l 3 decays are calculated as well. Furthermore, the K π isospin-1/2 P -wave threshold parameters are derived from the phase of the vector form factor. For the scattering length and the effective range we find respectively a 1 1/2 = (0.166 ± 0.004) m π −3 and b 1 1/2 = (0.258 ± 0.009) m π −5 .