%0 Journal Article
%A Aoki, Y.
%A Blum, T.
%A Colangelo, G.
%A Collins, S.
%A Morte, M. Della
%A Dimopoulos, P.
%A Dürr, S.
%A Feng, X.
%A Fukaya, H.
%A Golterman, M.
%A Gottlieb, Steven
%A Gupta, R.
%A Hashimoto, S.
%A Heller, U. M.
%A Herdoiza, G.
%A Hernandez, P.
%A Horsley, R.
%A Jüttner, A.
%A Kaneko, T.
%A Lunghi, E.
%A Meinel, S.
%A Monahan, C.
%A Nicholson, A.
%A Onogi, T.
%A Pena, C.
%A Petreczky, P.
%A Portelli, A.
%A Ramos, A.
%A Sharpe, S. R.
%A Simone, J. N.
%A Simula, S.
%A Sint, S.
%A Sommer, R.
%A Tantalo, N.
%A Van de Water, R.
%A Wenger, U.
%A Wittig, H.
%T FLAG Review 2021
%J The European physical journal / C
%V 82
%N 10
%@ 1434-6044
%C Heidelberg
%I Springer
%M FZJ-2023-00111
%P 869
%D 2022
%Z 418 pages, 53 figures, 200 tables, 1056 references. Minor changes, version as published in EPJC. arXiv admin note: substantial text overlap with arXiv:1902.08191, arXiv:1607.00299, arXiv:1310.8555
%X 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 $K \to \pi$ 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 $SU(2)_L\times SU(2)_R$ and $SU(3)_L\times SU(3)_R$ 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 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 $\alpha_s$. 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:000864362300001
%R 10.1140/epjc/s10052-022-10536-1
%U https://juser.fz-juelich.de/record/916808