First determination of f +(0)|V us | from a combined analysis of τ → Kπν τ decay and πK scattering with constraints from K ℓ3 decays

We perform a combined analysis of τ → Kπν τ decay and πK scattering with constraints from K l3 data using a N/D approach that fulfills requirements from unitarity and analyticity. We obtain a good fit of the I = 1/2 πK amplitude in the P wave using the LASS data above the elastic region while in this region data are generated via Monte Carlo using the FOCUS results based on D l4 decay. The spectrum and branching ratio of τ → Kπν τ constrained by K l3 decays are also well reproduced leading to f +(0)|V us | = 0.2163±0.0014. Furthermore, we obtain the slope of the vector form factor λ + = (25.56 ± 0.40) × 10−3 while the value of the scalar form factor at the Callan-Treiman point is ln C = 0.2062 ± 0.0089. Given the experimental precision our results are compatible with the Standard Model.