FLAG Review 2019

Abstract

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 $K\to \ddot{I}€$ transition at zero momentum transfer, as well as the decay constant ratio $f_K/f_{\ddot{I}}€$ 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 $D$- 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 $\hat{I}{\pm }_s$. 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.

458 pages, 46 figures, 209 tables, 1146 references. Minor changes, version as published in EPJC. arXiv admin note: substantial text overlap with arXiv:1607.00299, arXiv:1310.8555