The K ->pi vector form factor at zero momentum transfer on the lattice

We present a quenched lattice study of the form factors f(+)(q(2)) and f(0)(q2) of the matrix elements <pi\(s) over bar gamma(mu)u\K>. We focus on the second-order SU(3)-breaking quantity [1-f(+)(0)], which is necessary to extract \V-us\ from K-l3 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 \V-us\. The leading quenched chiral logarithms are corrected for by using analytic calculations in quenched chiral perturbation theory. Our final result, f(+)(K0pi-) (0) = 0.960 +/- 0.005(stat) +/- 0.007(syst), 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 \V-us\ are also presented.