We review lattice results related to pion, kaon, - and -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 , arising in semileptonic transition at zero momentum transfer, as well as the decay-constant ratio of decay constants and its consequences for the CKM matrix elements and . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of and Chiral Perturbation Theory and review the determination of the 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 - and -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 .

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 , arising in the semileptonic transition at zero momentum transfer, as well as the decay constant ratio and its consequences for the CKM matrix elements and . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of and Chiral Perturbation Theory. We review the determination of the parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for and (also new compared to the previous review), 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. Finally, we review the status of lattice determinations of the strong coupling constant .

We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with N f = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210 ÷ 450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI -MOM method. The results for the quark masses converted to the MS scheme are: m ud (2 GeV) = 3.70(17) MeV, m s (2 GeV) = 99.6(4.3) MeV and m c (m c ) = 1.348(46) GeV. We obtain also the quark mass ratios m s /m ud = 26.66(32) and m c /m s = 11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate m u /m d = 0.470(56), leading to m u = 2.36(24) MeV and m d = 5.03(26) MeV.

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 $$SU(2)_L\times SU(2)_R$$SU(2)L×SU(2)R and $$SU(3)_L\times SU(3)_R$$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 four B parameters 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 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 $$\alpha _s$$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.