https://doi.org/10.1140/epjc/s10052-014-2890-7
Review
Review of lattice results concerning low-energy particle physics
1
Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502, Japan
2
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Nagoya, 464-8602, Japan
3
RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY, 11973, USA
4
Department of Physics, Washington University, Saint Louis, MO, 63130, USA
5
Physics Department, University of Connecticut, Storrs, CT, 06269-3046, USA
6
Albert Einstein Center for Fundamental Physics, Institut für theoretische Physik, Universität Bern, Sidlerstr. 5, 3012 , Bern, Switzerland
7
CP3-Origins & Danish IAS, University of Southern Denmark, Campusvej 55, 5230 , Odense M, Denmark
8
IFIC (CSIC), c/ Catedrático José Beltrán, 2, 46980 , Paterna, Spain
9
Bergische Universität Wuppertal, Gaußstraße 20, 42119, Wuppertal, Germany
10
Jülich Supercomputing Center, Forschungszentrum Jülich, 52425 , Jülich, Germany
11
Department of Physics, University of Illinois, Urbana, IL, 61801, USA
12
Department of Physics, Osaka University, Toyonaka, Osaka, 560-0043, Japan
13
School of Physics, University of Edinburgh, Edinburgh, EH9 3JZ, UK
14
School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK
15
High Energy Accelerator Research Organization (KEK), Ibaraki, 305-0801, Japan
16
SUPA, Department of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK
17
Aix-Marseille Université, CNRS, CPT, UMR 7332, 13288 , Marseille, France
18
Université de Toulon, CNRS, CPT, UMR 7332, 83957 , La Garde, France
19
Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, 00146 , Rome, Italy
20
INFN, Sezione di Roma Tre, Via della Vasca Navale 84, 00146 , Rome, Italy
21
Physics Department, Indiana University, Bloomington, IN, 47405, USA
22
Instituto de Física Teórica UAM/CSIC and Departamento de Física Teórica, Universidad Autónoma de Madrid, Cantoblanco, 28049 , Madrid, Spain
23
Physics Department, University of Washington, Seattle, WA, 98195-1560, USA
24
NIC @ DESY, Platanenallee 6, 15738 , Zeuthen, Germany
25
Fermi National Accelerator Laboratory, Batavia, IL, 60510, USA
26
INFN, Sezione di Tor Vergata, c/o Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 , Rome, Italy
27
PRISMA Cluster of Excellence, Institut für Kernphysik and Helmholtz Institute Mainz, University of Mainz, 55099 , Mainz, Germany
28
Department of Physics, Syracuse University, Syracuse, New York, USA
* e-mail: gilberto@itp.unibe.ch
Received:
3
November
2013
Accepted:
5
May
2014
Published online:
17
September
2014
We review lattice results related to pion, kaon, 
- and 
-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 
, arising in semileptonic 
transition at zero momentum transfer, as well as the decay-constant ratio 
of decay constants 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 and review the determination of the 
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 - and -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 
.
© SIF and Springer-Verlag Berlin Heidelberg, 2014
