Review of lattice results concerning low energy particle physics

TL;DR

This review summarizes recent lattice QCD results on low-energy particle physics, including quark masses, form factors, decay constants, low-energy constants, and kaon mixing parameters, emphasizing their implications for the Standard Model.

Contribution

It provides a comprehensive, accessible overview of lattice QCD results relevant to pion and kaon physics, introducing quality criteria for evaluating computations.

Findings

Determination of light-quark masses with improved precision

Accurate calculation of the form factor f_+(0) for K->pi transitions

Updated values for decay constant ratios and B_K parameter

Abstract

We review lattice results relevant for pion and kaon physics with the aim of making them easily accessible to the particle physics community. Specifically, we review the determination of the light-quark masses, the form factor f_+(0), relevant for the semileptonic K -> pi transition at zero momentum transfer as well as the ratio f_K/f_pi of decay constants and discuss the consequences for the elements V_{us} and V_{ud} of the CKM matrix. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)_LxSU(2)_R and SU(3)_LxSU(3)_R Chiral Perturbation Theory and review the determination of the B_K parameter of neutral kaon mixing. We introduce quality criteria and use these when forming averages. Although subjective and imperfect, these criteria may help the reader to judge different aspects of current lattice computations. Our main results are summarized in section 1.2, but we stress the importance of the detailed discussion that underlies these results and constitutes the bulk of the present review.