Review of lattice results concerning low-energy particle physics

We review lattice results related to pion, kaon, D - and B -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 f + ( 0 ) , arising in semileptonic K → π transition at zero momentum transfer, as well as the decay-constant ratio f K / f π of decay constants and its consequences for the CKM matrix elements V u s and V u d . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU ( 2 ) L × SU ( 2 ) R and SU ( 3 ) L × SU ( 3 ) R Chiral Perturbation Theory and review the determination of the B K 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 D - and B -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 α s .