We present a quenched lattice study of the form factors f + (q 2) and f 0 (q 2) of the matrix elements π|¯ sγ µ 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 K 0 π − + (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.
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