Review of lattice results concerning low energy particle physics

Abstract

We review lattice results related to pion, kaon, D-and B-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 f + (0), arising in semileptonic K → π transition at zero momentum transfer, as well as the decay constant ratio f K /f π of decay constants 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 × SU (2) R and SU (3) L × SU (3) R Chiral Perturbation Theory and review the determination of the B K 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 D-and B-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 α s .

Lattice QCD for Cosmology

“…Lattice QCD for Cosmology Sz. Borsanyi 1 , Z. Fodor 1,2,3 , K.-H. Kampert 1 , S. D. Katz 3,4 , T. Kawanai 2 , T. G. Kovacs 5 , S. W. Mages 2 , A. Pasztor 1 , F. Pittler 3,4 , J. Redondo 6,7 , A. Ringwald 8 , K. K. Szabo Table S7: Topological susceptibility of QCD taking into account the effect of the up, down, strange, charm and bottom quarks.…”

“…A common set of criteria for assessing the reliability of lattice results was set by FLAG and published in Ref. [2]. They introduced for some quantities a measure indicating how far the continuum extrapolated result is from the lattice data.…”

Determining the QCD coupling from lattice vacuum polarization

“…s (m Z ) = 0.1155 ± 0.0018. For comparison, the FLAG Working Group result is [1] α (5) s (m Z ) = 0.1184 ± 0.0012.…”

“…Several lattice QCD methods have been employed to determine α s , including the short-distance QCD potential, Wilson loops, the Schrödinger functional, the ghostgluon vertex, current two-point functions with heavy valence quarks, and vacuum polarization at short distances. For a review and references, see [1].…”

$\mathbb{Z}_N$ lattice gauge theory in a ladder geometry

“…Their pervasive importance, however, is flanked by the extreme difficulty in obtaining exact solutions for such strongly correlated models: many non-perturbative phenomena of quantum chromodynamics and other gauge theories remain open challenges at the core of intense research efforts [2]. These difficulties prompted a long-standing endeavor in the simulation of gauge theories, generally based on the framework of lattice gauge theories (LGT) [3] and Monte Carlo techniques, which achieved many accurate results, including, for example, the definition of both the hadrons and light mesons spectra [4].…”