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024 7 _ |a 10.1140/epjc/s10052-022-10536-1
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024 7 _ |a 1434-6052
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024 7 _ |a arXiv:2111.09849
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024 7 _ |a 2128/33393
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037 _ _ |a FZJ-2023-00111
082 _ _ |a 530
100 1 _ |a Aoki, Y.
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245 _ _ |a FLAG Review 2021
260 _ _ |a Heidelberg
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500 _ _ |a 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
520 _ _ |a 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.
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700 1 _ |a Blum, T.
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700 1 _ |a Colangelo, G.
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700 1 _ |a Collins, S.
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700 1 _ |a Morte, M. Della
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700 1 _ |a Dimopoulos, P.
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700 1 _ |a Dürr, S.
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700 1 _ |a Feng, X.
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700 1 _ |a Fukaya, H.
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700 1 _ |a Golterman, M.
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700 1 _ |a Gottlieb, Steven
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700 1 _ |a Gupta, R.
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700 1 _ |a Hashimoto, S.
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700 1 _ |a Heller, U. M.
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700 1 _ |a Herdoiza, G.
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700 1 _ |a Hernandez, P.
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700 1 _ |a Horsley, R.
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700 1 _ |a Jüttner, A.
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700 1 _ |a Kaneko, T.
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700 1 _ |a Lunghi, E.
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700 1 _ |a Meinel, S.
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700 1 _ |a Monahan, C.
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700 1 _ |a Nicholson, A.
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700 1 _ |a Onogi, T.
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700 1 _ |a Pena, C.
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700 1 _ |a Petreczky, P.
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700 1 _ |a Portelli, A.
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700 1 _ |a Ramos, A.
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700 1 _ |a Sharpe, S. R.
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700 1 _ |a Simone, J. N.
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700 1 _ |a Simula, S.
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700 1 _ |a Sint, S.
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700 1 _ |a Sommer, R.
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700 1 _ |a Tantalo, N.
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700 1 _ |a Van de Water, R.
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700 1 _ |a Wenger, U.
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700 1 _ |a Wittig, H.
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773 _ _ |a 10.1140/epjc/s10052-022-10536-1
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