title: Review of lattice results concerning low-energy particle physics.
abstract: We review lattice results related to pion, kaon, [Formula: see text]- and [Formula: see text]-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor [Formula: see text], arising in semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay-constant ratio [Formula: see text] of decay constants and its consequences for the CKM matrix elements [Formula: see text] and [Formula: see text]. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of [Formula: see text] and [Formula: see text] Chiral Perturbation Theory and review the determination of the [Formula: see text] parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on [Formula: see text]- and [Formula: see text]-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant [Formula: see text].
authors.affiliation: Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502 Japan.
authors.forename: S
authors.initials: S
authors.lastname: Aoki
authors.affiliation: Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Nagoya, 464-8602 Japan ; RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973 USA.
authors.forename: Y
authors.initials: Y
authors.lastname: Aoki
authors.affiliation: Department of Physics, Washington University, Saint Louis, MO 63130 USA.
authors.forename: C
authors.initials: C
authors.lastname: Bernard
authors.affiliation: RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973 USA ; Physics Department, University of Connecticut, Storrs, CT 06269-3046 USA.
authors.forename: T
authors.initials: T
authors.lastname: Blum
authors.affiliation: Albert Einstein Center for Fundamental Physics, Institut für theoretische Physik, Universität Bern, Sidlerstr. 5, 3012  Bern, Switzerland.
authors.forename: G
authors.initials: G
authors.lastname: Colangelo
authors.affiliation: CP3-Origins & Danish IAS, University of Southern Denmark, Campusvej 55, 5230  Odense M, Denmark ; IFIC (CSIC), c/ Catedrático José Beltrán, 2, 46980  Paterna, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Della Morte
authors.affiliation: Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany ; Jülich Supercomputing Center, Forschungszentrum Jülich, 52425  Jülich, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Dürr
authors.affiliation: Department of Physics, University of Illinois, Urbana, IL 61801 USA.
authors.forename: A X
authors.initials: AX
authors.lastname: El-Khadra
authors.affiliation: Department of Physics, Osaka University, Toyonaka, Osaka, 560-0043 Japan.
authors.forename: H
authors.initials: H
authors.lastname: Fukaya
authors.affiliation: School of Physics, University of Edinburgh, Edinburgh, EH9 3JZ UK.
authors.forename: R
authors.initials: R
authors.lastname: Horsley
authors.affiliation: School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ UK.
authors.forename: A
authors.initials: A
authors.lastname: Jüttner
authors.affiliation: High Energy Accelerator Research Organization (KEK), Ibaraki, 305-0801 Japan.
authors.forename: T
authors.initials: T
authors.lastname: Kaneko
authors.affiliation: SUPA, Department of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ UK ; Department of Physics, Syracuse University, Syracuse, New York USA.
authors.forename: J
authors.initials: J
authors.lastname: Laiho
authors.affiliation: Aix-Marseille Université, CNRS, CPT, UMR 7332, 13288  Marseille, France ; Université de Toulon, CNRS, CPT, UMR 7332, 83957  La Garde, France.
authors.forename: L
authors.initials: L
authors.lastname: Lellouch
authors.affiliation: Albert Einstein Center for Fundamental Physics, Institut für theoretische Physik, Universität Bern, Sidlerstr. 5, 3012  Bern, Switzerland.
authors.forename: H
authors.initials: H
authors.lastname: Leutwyler
authors.affiliation: Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, 00146  Rome, Italy ; INFN, Sezione di Roma Tre, Via della Vasca Navale 84, 00146  Rome, Italy.
authors.forename: V
authors.initials: V
authors.lastname: Lubicz
authors.affiliation: Physics Department, Indiana University, Bloomington, IN 47405 USA.
authors.forename: E
authors.initials: E
authors.lastname: Lunghi
authors.affiliation: Albert Einstein Center for Fundamental Physics, Institut für theoretische Physik, Universität Bern, Sidlerstr. 5, 3012  Bern, Switzerland.
authors.forename: S
authors.initials: S
authors.lastname: Necco
authors.affiliation: Department of Physics, Osaka University, Toyonaka, Osaka, 560-0043 Japan.
authors.forename: T
authors.initials: T
authors.lastname: Onogi
authors.affiliation: Instituto de Física Teórica UAM/CSIC and Departamento de Física Teórica, Universidad Autónoma de Madrid, Cantoblanco, 28049  Madrid, Spain.
authors.forename: C
authors.initials: C
authors.lastname: Pena
authors.affiliation: School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ UK.
authors.forename: C T
authors.initials: CT
authors.lastname: Sachrajda
authors.affiliation: Physics Department, University of Washington, Seattle, WA 98195-1560 USA.
authors.forename: S R
authors.initials: SR
authors.lastname: Sharpe
authors.affiliation: INFN, Sezione di Roma Tre, Via della Vasca Navale 84, 00146  Rome, Italy.
authors.forename: S
authors.initials: S
authors.lastname: Simula
authors.affiliation: NIC @ DESY, Platanenallee 6, 15738  Zeuthen, Germany.
authors.forename: R
authors.initials: R
authors.lastname: Sommer
authors.affiliation: Fermi National Accelerator Laboratory, Batavia, IL 60510 USA.
authors.forename: R S
authors.initials: RS
authors.lastname: Van de Water
authors.affiliation: INFN, Sezione di Tor Vergata, c/o Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133  Rome, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Vladikas
authors.affiliation: Albert Einstein Center for Fundamental Physics, Institut für theoretische Physik, Universität Bern, Sidlerstr. 5, 3012  Bern, Switzerland.
authors.forename: U
authors.initials: U
authors.lastname: Wenger
authors.affiliation: PRISMA Cluster of Excellence, Institut für Kernphysik and Helmholtz Institute Mainz, University of Mainz, 55099  Mainz, Germany.
authors.forename: H
authors.initials: H
authors.lastname: Wittig