Review of lattice results concerning low-energy particle physics

Abstract

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 .

Baryons as relativistic three-quark bound states

“…In the course of this review we summarise aspects of lattice QCD that are useful for the later discussion of the baryon spectra and form factors. Naturally, in a non-expert review we skip over most technical details and refer the interested reader to specialised lattice reviews such as [156][157][158][159].…”

“…with m π = 138 MeV, have been performed in the past years for some selected observables, see e.g. [157][158][159]257] for reviews and results. Many other quantities, however, are just too cost-intensive and will be discussed later also for a range of heavier pion masses, some even as large as m π = 600 MeV.…”

Perturbative corrections to B → D form factors in QCD

“…With the matching relation (2.6) the static B-meson decay constantf B (µ) can be traded into the QCD decay constant f B , whose values will be taken from lattice QCD simulations f B = (192.0 ± 4.3) MeV [58] with N f = 2 + 1. Likewise, we will adopt the intervals for the D-meson decay constant in QCD from lattice simulations f D = (209.2 ± 3.3) MeV [58] with N f = 2 + 1.…”

“…Likewise, we will adopt the intervals for the D-meson decay constant in QCD from lattice simulations f D = (209.2 ± 3.3) MeV [58] with N f = 2 + 1. In addition, we will employ the MS bottom quark mass m b (m b ) = (4.193 +0.022 −0.035 ) GeV [59] from non-relativistic sum rules and the MS charm quark mass m c (m c ) = (1.288 ± 0.020) GeV [60] from relativistic sum rules, employing the quark vector correlation function computed at O(α 3 s ).…”

S-waveKK*interactions in a finite volume and thefGeng1, Ren2, Zhou3 et al. 2015Phys. Rev. D292330View full textAdd to dashboardCite

“…Although studies of ground-state hadrons, which do not decay via strong interactions, have been well established and have turned out to be quite successful (see, e.g., Refs. [15,16]), studies of resonances are more challenging, since they do not correspond to discrete energy levels on the lattice, and considerable additional efforts are needed to extract physical information from LQCD simulations. The Lüscher method is the de facto standard one in the case of single channel two-body elastic scattering [17,18].…”