TY  - JOUR
AU  - Aoki, Y.
AU  - Blum, T.
AU  - Colangelo, G.
AU  - Collins, S.
AU  - Morte, M. Della
AU  - Dimopoulos, P.
AU  - Dürr, S.
AU  - Feng, X.
AU  - Fukaya, H.
AU  - Golterman, M.
AU  - Gottlieb, Steven
AU  - Gupta, R.
AU  - Hashimoto, S.
AU  - Heller, U. M.
AU  - Herdoiza, G.
AU  - Hernandez, P.
AU  - Horsley, R.
AU  - Jüttner, A.
AU  - Kaneko, T.
AU  - Lunghi, E.
AU  - Meinel, S.
AU  - Monahan, C.
AU  - Nicholson, A.
AU  - Onogi, T.
AU  - Pena, C.
AU  - Petreczky, P.
AU  - Portelli, A.
AU  - Ramos, A.
AU  - Sharpe, S. R.
AU  - Simone, J. N.
AU  - Simula, S.
AU  - Sint, S.
AU  - Sommer, R.
AU  - Tantalo, N.
AU  - Van de Water, R.
AU  - Wenger, U.
AU  - Wittig, H.
TI  - FLAG Review 2021
JO  - The European physical journal / C
VL  - 82
IS  - 10
SN  - 1434-6044
CY  - Heidelberg
PB  - Springer
M1  - FZJ-2023-00111
SP  - 869
PY  - 2022
N1  - 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
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000864362300001
DO  - DOI:10.1140/epjc/s10052-022-10536-1
UR  - https://juser.fz-juelich.de/record/916808
ER  -