FLAG Review 2019

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) arising in the semileptonic 𝐾→𝜋 transition at zero momentum transfer, as well as the decay constant ratio 𝑓𝐾/𝑓𝜋 and its consequences for the CKM matrix elements 𝑉𝑢𝑠 and 𝑉𝑢𝑑. 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. We review the determination of the 𝐵𝐾 parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for 𝑚𝑐 and 𝑚𝑏 as well as those for D- and B-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 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.