K pi vector form factor constrained by tau ---> K pi nu_tau and K_l3 decays

Dispersive representations of the Kpi 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 \(\lambda_+'=(25.49 \pm 0.31) \times 10^{-3}\) and \(\lambda_+"= (12.22 \pm 0.14) \times 10^{-4}\). From the pole position on the second Riemann sheet the mass and width of the \(K^*(892)^{\pm}\) are found to be \(m_{K^*(892)^\pm}=892.0\pm 0.5\)~MeV and \(\Gamma_{K^*(892)^\pm}=46.5\pm 1.1\)~MeV. The phase-space integrals needed for K_l3 decays are calculated as well. Furthermore, the Kpi 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 \(a_{1}^{1/2}\,= ( 0.166\pm 0.004)\,m_\pi^{-3}\) and \(b_{1}^{1/2}\,=( 0.258\pm 0.009)\,m_\pi^{-5}\).