https://doi.org/10.1140/epjc/s10052-019-7354-7
Review
FLAG Review 2019
Flavour Lattice Averaging Group (FLAG)
1
Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, 606-8502, Sakyo-ku, Kyoto, Japan
2
High Energy Accelerator Research Organization (KEK), 305-0801, Tsukuba, Japan
3
RIKEN BNL Research Center, Brookhaven National Laboratory, 11973, Upton, NY, USA
4
Laboratoire de Physique Théorique (UMR8627), CNRS, Université Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
5
Physics Department, University of Connecticut, 06269-3046, Storrs, CT, USA
6
Albert Einstein Center for Fundamental Physics, Institut für Theoretische Physik, Universität Bern, Sidlerstr. 5, 3012, Bern, Switzerland
7
Institut für Theoretische Physik, Universität Regensburg, 93040, Regensburg, Germany
8
CP3-Origins and IMADA, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark
9
Centro Fermi – Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Compendio del Viminale, Piazza del Viminiale 1, 00184, Rome, Italy
10
c/o Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Rome, Italy
11
University of Wuppertal, Gaußstraße 20, 42119, Wuppertal, Germany
12
Jülich Supercomputing Center, Forschungszentrum Jülich, 52425, Jülich, Germany
13
Department of Physics, Osaka University, 560-0043, Toyonaka, Osaka, Japan
14
Dept. of Physics and Astronomy, San Francisco State University, 94132, San Francisco, CA, USA
15
Department of Physics, Indiana University, 47405, Bloomington, IN, USA
16
Los Alamos National Laboratory, Theoretical Division T-2, 87545, Los Alamos, NM, USA
17
School of High Energy Accelerator Science, The Graduate University for Advanced Studies (Sokendai), 305-0801, Tsukuba, Japan
18
American Physical Society (APS), One Research Road, 11961, Ridge, NY, USA
19
Instituto de Física Teórica UAM/CSIC and Departamento de Física Teórica, Universidad Autónoma de Madrid, 28049, Cantoblanco, Madrid, Spain
20
Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, EH9 3FD, Edinburgh, UK
21
School of Physics & Astronomy, University of Southampton, SO17 1BJ, Southampton, UK
22
Institute of Physics, National Chiao-Tung University, 30010, Hsinchu, Taiwan
23
Centre for High Energy Physics, Chung-Yuan Christian University, 32023, Chung-Li, Taiwan
24
Physics Department, Columbia University, 10027, New York, NY, USA
25
Dept. of Physics and Astronomy, University of North Carolina, 27516-3255, Chapel Hill, NC, USA
26
School of Mathematics & Hamilton Mathematics Institute, Trinity College Dublin, Dublin 2, Ireland
27
Physics Department, University of Washington, 98195-1560, Seattle, WA, USA
28
Fermi National Accelerator Laboratory, 60510, Batavia, IL, USA
29
Sezione di Roma Tre, INFN, Via della Vasca Navale 84, 00146, Rome, Italy
30
John von Neumann Institute for Computing (NIC), DESY, Platanenallee 6, 15738, Zeuthen, Germany
31
Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489, Berlin, Germany
32
Sezione di Tor Vergata, INFN, c/o Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Rome, Italy
33
PRISMA Cluster of Excellence, Institut für Kernphysik and Helmholtz Institute Mainz, University of Mainz, 55099, Mainz, Germany
34
RIKEN Center for Computational Science, 650-0047, Kobe, Japan
Received:
26
March
2019
Accepted:
5
September
2019
Published online:
11
February
2020
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 
arising in the semileptonic 
transition at zero momentum transfer, as well as the decay constant ratio 
and its consequences for the CKM matrix elements 
and 
. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of 
and 
Chiral Perturbation Theory. We review the determination of the 
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 
and 
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 
. 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.
© The Author(s) 2020
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Funded by SCOAP3
