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 -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi of decay constants and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation Theory and review the determination of the BK parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, for this review, we focus 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 alpha_s.

https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-014-2890-7.pdf

Review of lattice results concerning low-energy particle physics

The QCD transition temperature: Results with physical masses in the continuum limit

Theoretical and numerical studies of the Wilson flow in lattice QCD suggest that the gauge field obtained at flow time t > 0 is a smooth renormalized field. The expectation values of local gauge-invariant expressions in this field are thus well-defined physical quantities that probe the theory at length scales on the order of \( \sqrt {t} \). Moreover, by transforming the QCD functional integral to an integral over the gauge field at a specified flow time, the emergence of the topological (instanton) sectors in the continuum limit becomes transparent and is seen to be caused by a dynamical effect that rapidly separates the sectors when the lattice spacing is reduced from 0.1fm to smaller values.

/pdf/properties-and-uses-of-the-wilson-flow-in-lattice-qcd-2sa4t4lunj.pdf

Properties and uses of the Wilson flow in lattice QCD

A critical point (E) is expected in QCD on the temperature (T) versus baryonic chemical potential (μ) plane. Using a recently proposed lattice method for μ≠0 we study dynamical QCD with nf=2+1 staggered quarks of physical masses on Lt = 4 lattices. Our result for the critical point is TE = 162±2 MeV and μE = 360±40 MeV. For the critical temperature at μ = 0 we obtained Tc = 164±2 MeV. This work extends our previous study [8] by two means. It decreases the light quark masses (mu,d) by a factor of three down to their physical values. Furthermore, in order to approach the thermodynamical limit we increase our largest volume by a factor of three. As expected, decreasing mu,d decreased μE. Note, that the continuum extrapolation is still missing.

https://iopscience.iop.org/article/10.1088/1126-6708/2004/04/050/pdf

Critical point of QCD at finite T and μ, lattice results for physical quark masses

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 [Formula: see text], arising in the semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay constant ratio [Formula: see text] 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. We review the determination of the [Formula: see text] parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for [Formula: see text] and [Formula: see text] (also new compared to the previous review), 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. Finally, we review the status of lattice determinations of the strong coupling constant [Formula: see text].

/pdf/review-of-lattice-results-concerning-low-energy-particle-4ppyuq45zk.pdf

R. Sommer

Papers

A new way to set the energy scale in lattice gauge theories and its application to the static force and σs in SU (2) Yang-Mills theory