Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2004-03-19
Nucl.Phys. B705 (2005) 339-362
Physics
High Energy Physics
High Energy Physics - Phenomenology
25 pages, 7 figures, 4 tables. Version to appear in Nuclear Physics B: improved discussion of minor points; no change in the r
Scientific paper
10.1016/j.nuclphysb.2004.11.017
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, $f_+^{K^0\pi^-}(0) = 0.960 \pm 0.005_{\rm stat} \pm 0.007_{\rm syst}$, 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.
Becirevic Damir
Isidori Gino
Lubicz Vittorio
Martinelli Gabriele
Mescia Federico
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