Kaon physics from lattice

precise SM tests

“…Lattice calculations for both f + (0) and F K /F π are nowadays possible and have already reached the necessary precision to make a sensitive test of the unitarity of the CKM matrix. The current status of these has been reviewed in the talks of Boyle [5] and Mescia [6]. Moreover, if one uses the independent determination of V ud from superallowed Fermi decay of nuclei together with F K /F π to extract V us from the ratio Γ(K → ℓν)/Γ(π → ℓν) one obtains two independent and compatible determinations of V us [7,8].…”

“…Different collaborations have reported a failure of NLO χPT in describing the quark-mass dependence of the lattice data for m s close to the physical value, but form such that M π ∼ 400 MeV (cf. [5]). This is not that surprising, after all, in view of the fact that in this case the kaon mass is around 600 MeV and that the physical value of the kaon mass is already at the border of where one can hope to apply the chiral expansion successfully.…”

“…The reader interested in learning more about the current status of lattice calculations relevant for kaon decays is referred to the contributions by Boyle [5], Christ [11], Mescia [6] and Noaki [9].…”

“…Dealing with four-quark operators, on the other hand, is not anymore a major obstacle per se, as the successful calculations of B K (see, [60,61,62], reviewed at this conference in [5]) show. The combination of these lattice calculations with the precise perturbative analysis of the weak Hamiltonian [50] leads to an accurate SM prediction for ε K , with a theoretical error (excluding the parametric one coming from the uncertainties in the CKM matrix elements) of about 6%.…”

Precision SM calculations and theoretical interests beyond the SM in Kl2 and Kl3 decays

“…The agreement between the different results is remarkable and the present overall accuracy is very good being of about 1%. For discussions and details on the lattice set-ups and results, we refer to the forthcoming review by the Flavianet Lattice Averaging Group (FLAG) presented at this conference by G. Colangelo [59] and also to the talk by P. Boyle [70]. As presented in [71], taking for illustrative purpose the HPQCD-UKQCD result [65], one gets |V us |/|V ud | = 0.2319(15).…”