FLAG Review 2019

Abstract We review lattice results related to pion, kaon,D-meson,B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $$f_+(0)$$ f+(0) arising in the semileptonic $$K rightarrow pi $$ K→π transition at zero momentum transfer, as well as the decay constant ratio $$f_K/f_pi $$ fK/fπ 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 $$SU(2)_Ltimes SU(2)_R$$ SU(2)L×SU(2)R and $$SU(3)_Ltimes SU(3)_R$$ SU(3)L×SU(3)R Chiral Perturbation Theory. We review the determination of the $$B_K$$ BK parameter of neutral kaon mixing as well as the additional fourBparameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $$m_c$$ mc and $$m_b$$ mb as well as those forD- andB-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $$alpha _s$$ αs . Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.