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 -> pi transition at zero momentum transfer, as well as the decay constant ratio f(K) / f(pi) and its consequences for the CKM matrix elements V-us and V-ud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)(L) x SU(2)(R) and SU(3)(L) x SU(3)(R) Chiral Perturbation Theory. We review the determination of the B-K 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) and m(b) 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 as. 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.

Keywords:

CHIRAL PERTURBATION-THEORY

STRONG-COUPLING-CONSTANT

QUANTUM-FIELD THEORIES

LIGHT-QUARK MASSES

LATTICE GAUGE-THEORIES

RANDOM-MATRIX THEORY

MONTE-CARLO METHODS

QCD DIRAC OPERATOR

PI-PI-SCATTERING

CB-VERTICAL-BAR

FLAG Review 2019

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