ChatConfined quarks inside protons and mesons cannot be weighed on physical scales; the Flavour Lattice Averaging Group (FLAG) review establishes global consensus benchmarks for quark masses, decay constants, and CKM matrix parameters from lattice QCD.
Quarks are the fundamental bricks of hadronic matter, yet because of color confinement, an isolated quark can never be observed in a physical laboratory detector. Measuring their fundamental masses and coupling strengths requires simulating the seething quantum chromodynamic vacuum on supercomputers.
Dozens of independent lattice QCD collaborations produce conflicting calculations using different fermion actions, lattice spacings, and pion mass extrapolations, creating confusion for experimental particle physicists searching for Standard Model deviations.
The Flavour Lattice Averaging Group (FLAG) established rigorous quality criteria—auditing chiral extrapolations, finite-volume errors, and continuum extrapolations—to produce standardized global averages for light-quark masses (), heavy-quark parameters (), and leptonic decay constants.
These gold-standard lattice benchmarks provide the indispensable baseline needed to test CKM unitarity, search for lepton-flavor universality violations at LHCb and Belle II, and interpret high-energy neutrino collisions across global colliders.
FLAG Review 2021
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 the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. 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. We consider nucleon matrix elements, and review the determinations of the axial, scalar and tensor bilinears, both isovector and flavor diagonal. Finally, in this review we have added a new section reviewing determinations of scale-setting quantities.
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