Constraining the Kpi vector form factor by tau---> K pi nu_tau and K_l3 decay data

A subtracted dispersive representation of the $K\pi$ vector form factor, $F_{+}^{K\pi }$, is used to fit the Belle spectrum of $\text{tauKpi}$ decays incorporating constraints from results on $K_{l3}$ decays. Through the use of three subtractions, the slope and curvature of $F_{+}^{K\pi }$ are obtained directly from the data yielding ${\lambda }_{+}^{\mathrm{\prime }}=(25.49\pm 0.31)\times {10}^{-3}$ and ${\lambda }_{+}\mathrm{"}=(12.22\pm 0.14)\times {10}^{-4}$. The phase-space integrals relevant for $K_{l3}$ analyses are calculated. Additionally, from the pole position on the second Riemann sheet the mass and width of the $K^{\ast }(892{)}^{\pm }$ are found to be $m_{K^{\ast }(892{)}^{\pm }}=892.0\pm 0.5$ MeV and ${\mathrm{\Gamma }}_{K^{\ast }(892{)}^{\pm }}=46.5\pm 1.1$ MeV. Finally, we study the $P$-wave isospin-1/2 $K\pi$ phase-shift and its threshold parameters.