ABSTRACT

We review lattice results related to pion, kaon, $$D$$D- and $$B$$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 $$f_+(0)$$f+(0), arising in semileptonic $$K \rightarrow \pi $$K→π transition at zero momentum transfer, as well as the decay-constant ratio $$f_K/f_\pi $$fK/fπ of decay constants and its consequences for the CKM matrix elements $$V_{us}$$Vus and $$V_{ud}$$Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $$\hbox {SU}(2)_L\times \hbox {SU}(2)_R$$SU(2)L×SU(2)R and $$\hbox {SU}(3)_L\times \hbox {SU}(3)_R$$SU(3)L×SU(3)R Chiral Perturbation Theory and review the determination of the $$B_K$$BK 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 $$D$$D- and $$B$$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 $$\alpha _\mathrm{s}$$αs.

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