The 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 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. a

Lattice Flavour Physics with an eye to Super-B

“…The parameter |V us | relies on the Lattice results for the kaon decay constant f K or for the vector form factor f + (0). The former results allow to determine |V us | from the experimental measurement of the so-called Kl2 leptonic decay K → µν [11], while the latter results are required to extract |V us | from the experimental measurement of the so-called Kl3 semileptonic decay K → πlν [12,13]. For a recent review of the f K and f + (0) lattice results I refer to the FLAG review [8] and to Gilberto Colangelo's plenary talk at the Lattice2012 conference [14].…”

Improved estimates of rareKdecay matrix elements fromKℓ3decays

“…One should also keep in mind that the lattice estimate [27] for f Kπ (0) lattice O(p 6 ) = −0.016, and thus δ lattice CT ≈ −0.031. Further, it is only with this larger O(p 6 ) correction that V us , as extracted from K ℓ3 data, satisfies the CKM unitarity.…”

Status of Kaon physics on the lattice

“…Relevant for lattice computations are also the more recent evaluations of f 2 in partially quenched chiral perturbation theory and the evaluation of finite volume corrections [36,37]. A first estimate of the higher order corrections was given in [33] and more recently estimates for f 4 were given in [38,39,40].…”

“…The technique for the high precision calculation of f Kπ + (0) has been set out in [36] and consists of a 3-step procedure:…”