We review lattice results related to pion, kaon, D-meson, B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $$f_+(0)$$f+(0) arising in the semileptonic $$K \rightarrow \pi $$K→π transition at zero momentum transfer, as well as the decay constant ratio $$f_K/f_\pi $$fK/fπ and its consequences for the CKM matrix elements $$V_{us}$$Vus and $$V_{ud}$$Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $$SU(2)_L\times SU(2)_R$$SU(2)L×SU(2)R and $$SU(3)_L\times SU(3)_R$$SU(3)L×SU(3)R Chiral Perturbation Theory. We review the determination of the $$B_K$$BK parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $$m_c$$mc and $$m_b$$mb 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. We review the status of lattice determinations of the strong coupling constant $$\alpha _s$$αs. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.

Abstract:We study the perturbative behavior of the Yang-Mills gradient flow in the Schrödinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the size of the finite volume box. From our perturbative computation we estimate the size of cutoff effects of this coupling to leading order in perturbation theory. On a set of N f = 2 gauge field ensembles in a physical volume of L ∼ 0.4 fm we finally demonstrate the suitability of the coupling for a precise continuum limit due to modest cutoff effects and high statistical precision.

In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C boundary conditions. In particular we learn that a certain class of electricallycharged states can be constructed in a fully consistent fashion without relying on gauge fixing and without peculiar complications. This class includes single particle states of most stable hadrons. We also calculate finite-volume corrections to the mass of stable charged particles and show that these are much smaller than in non-local formulations of QED.

We present a lattice determination of the Λ parameter in three-flavor QCD and the strong coupling at the Z pole mass. Computing the nonperturbative running of the coupling in the range from 0.2 to 70 GeV, and using experimental input values for the masses and decay constants of the pion and the kaon, we obtain Λ

We determine from first principles the quark mass anomalous dimension in N f = 3 QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and nonperturbative regimes of the Standard Model in the hadronic sector. The computation is carried out to high accuracy, employing massless O(a)-improved Wilson quarks and finite-size scaling techniques. We also provide the matching factors required in the renormalisation of light quark masses from lattice computations with O(a)-improved Wilson fermions and a tree-level Symanzik improved gauge action. The total uncertainty due to renormalisation and running in the determination of light quark masses in the SM is thus reduced to about 1%.

Every local minimizer of a smooth constrained optimization problem satisfies the sequential approximate Karush-Kuhn-Tucker (AKKT) condition. This optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms. It is natural to ask for conditions on the constraints under which AKKT implies KKT. These conditions will be called strict constraint qualifications (SCQs). In this paper we define a cone-continuity property (CCP) that will be shown to be the weakest possible SCQ. Its relation to other constraint qualifications will also be clarified. In particular, it will be proved that CCP is strictly weaker than the constant positive generator constraint qualification.

We determine the ratio F K =F in QCD with N f ¼ 2 þ 1 flavors of sea quarks, based on a series of lattice calculations with three different lattice spacings, large volumes, and a simulated pion mass reaching down to about 190 MeV. We obtain F K =F ¼ 1:192ð7Þ stat ð6Þ syst . This result is then used to give an updated value of the Cabibbo-Kobayashi-Maskawa) matrix element jV us j. The unitarity relation for the first row of this matrix is found to be well observed. * Centre de Physique Théorique is ''UMR 6207 du CNRS et des universités d'Aix-Marseille I, d'Aix-Marseille II et du Sud Toulon-Var, affiliée à la FRUMAM''.PHYSICAL REVIEW D 81, 054507 (2010) 1550-7998= 2010=81(5)=054507 (8) 054507-1

While electromagnetic and up-down quark mass difference effects on octet baryon masses are very small, they have important consequences. The stability of the hydrogen atom against beta decay is a prominent example. Here, we include these effects by adding them to valence quarks in a lattice QCD calculation based on Nf=2+1 simulations with five lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. This allows us to gain control over all systematic errors, except for the one associated with neglecting electromagnetism in the sea. We compute the octet baryon isomultiplet mass splittings, as well as the individual contributions from electromagnetism and the up-down quark mass difference. Our results for the total splittings are in good agreement with experiment.