Kaon semileptonic vector form factor and determination of |V_us| using staggered fermions

Using staggered fermions and partially twisted boundary conditions, we calculate the K meson semileptonic decay vector form factor at zero momentum transfer. The highly improved staggered quark formulation is used for the valence quarks, while the sea quarks are simulated with the asqtad action (MILC Collaboration N_f=2+1 configurations). For the chiral and continuum extrapolation, we use two-loop continuum χPT, supplemented by partially quenched staggered χPT at one loop. Our result is f+Kπ(0)=0. 9667±0.0023±0.0033, where the first error is statistical and the second is the sum in quadrature of the systematic uncertainties. This result is the first N_f=2+1 calculation with two lattice spacings and a controlled continuum extrapolation. It is also the most precise result to date for the vector form factor, and, although the central value is larger than previous unquenched lattice calculations, it is compatible with them within errors. Combining our value for f+Kπ(0) with the latest experimental measurements of K semileptonic decays, we obtain |V_us|=0. 2238±0.0009±0.0005, where the first error is from f+Kπ(0) and the second one is experimental. As a byproduct of our calculation, we obtain the combination of low-energy constants (C12r+C34r-(L5r) 2)(M_ρ)=(3. 62±1.00)×10^-6.