Kaons on the lattice

TL;DR

This paper reviews recent lattice QCD results in kaon physics, focusing on V_{us} and B_K, and discusses the development of SU(2)_L imes SU(2)_R chiral perturbation theory for better theoretical understanding.

Contribution

It introduces the need for and progress in developing SU(2)_L imes SU(2)_R chiral perturbation theory tailored for kaon physics, especially for K_{l3} decays at q^2=0.

Findings

Lattice data supports the calculation of chiral logarithms in K_{l3} decays.

Progress in defining renormalization schemes compatible with lattice and perturbative methods.

Future applications to K→ππ decays are promising.

Abstract

I review recent lattice results in kaon physics, particularly in the determination of V_{us} and the B_K parameter of K^0-\bar{K}^0 mixing. I use lattice data to argue for the need of developing SU(2)_L \times SU(2)_R chiral perturbation theory for kaon physics and discuss some recent progress in achieving this. In particular it is shown that for K_{\ell 3} decays at q^2=0 (where q is the momentum transfer between the kaon and the pion), the chiral logarithms can be calculated in spite of the fact that the external pion carries half the energy of the kaon (in the kaon's rest frame), because these logarithms arise from soft internal loops. Future prospects, including applications to K\to\pi\pi decays are discussed. The need to define and exploit renormalization schemes which can simultaneously be implemented numerically in lattice simulations and used in higher-order perturbative calculations is explained.