Kπ vector form factor constrained by τ → Kπν <inf>τ</inf> and K<inf>l3</inf> decays

Dispersive representations of the K pi vector and scalar form factors are used to fit the spectrum of tau -> K pi nu(tau) obtained by the Belle collaboration incorporating constraints from results for K-l3 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 lambda'(+) = (25.49 +/- 0.31) x 10(-3) and lambda ''(+) = (12.22 +/- 0.14) x 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 +/- 0.5 MeV and Gamma(K*(892)+/-) = 46.5 +/- 1.1 MeV. The phase-space integrals needed for K-l3 decays are calculated as well. Furthermore, the K pi 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(pi)(-3) and b(1)(1/2) = (0.258 +/- 0.009) m(pi)(-5).