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

Abstract

We present a quenched lattice study of the form factors $f_{+}(q^2)$ and $f_0(q^2)$ of the matrix elements $<\pi |\bar{s}{\gamma }_{\mu }u|K>$. We focus on the second-order SU(3)-breaking quantity $[1-f_{+}(0)]$, which is necessary to extract $|V_{us}|$ from $K_{\ell 3}$ 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, $f_{+}^{K^0{\pi }^{-}}(0)=0.960\pm 0.005_{\mathrm{stat}}\pm 0.007_{\mathrm{syst}}$, 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.

Comments: 25 pages, 7 figures, 4 tables. Version to appear in Nuclear Physics B: improved discussion of minor points; no change in the results and in the conclusions