Review of lattice results concerning low-energy particle physics

Abstract

We review lattice results related to pion, kaon, (formula presented)-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor (formula presented), arising in semileptonic (formula presented) transition at zero momentum transfer, as well as the decay-constant ratio (formula presented) of decay constants and its consequences for the CKM matrix elements (formula presented) and (formula presented). Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of (formula presented) and (formula presented) Chiral Perturbation Theory and review the determination of the (formula presented) parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on (formula presented)-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant (formula presented).