The K→π vector form factor at zero momentum transfer on the lattice

We present a quenched lattice study of the form factors f+(q2) and f0(q2) of the matrix elements 〈π|s¯γμu|K〉. We focus on the second-order SU(3)-breaking quantity [1−f+(0)], which is necessary to extract |Vus| from Kℓ3 decays. For this quantity we show that it is possible to reach the percent precision which is the required one for a significant determination of |Vus|. The leading quenched chiral logarithms are corrected for by using analytic calculations in quenched chiral perturbation theory. Our final result, f+K0π−(0)=0.960±0.005stat±0.007syst, where the systematic error does not include the residual quenched effects, is in good agreement with the estimate made by Leutwyler and Roos. A comparison with other non-lattice computations and the impact of our result on the extraction of |Vus| are also presented.