We present precise lattice computations for the b-quark mass, the quark mass ratios m b =m c and m b =m s as well as the leptonic B-decay constants. We employ gauge configurations with four dynamical quark flavors, up-down, strange and charm, at three values of the lattice spacing (a ∼ 0.06-0.09 fm) and for pion masses as low as 210 MeV. Interpolation in the heavy quark mass to the bottom quark point is performed using ratios of physical quantities computed at nearby quark masses exploiting the fact that these ratios are exactly known in the static quark mass limit. Our results are also extrapolated to the physical pion mass and to the continuum limit and read m b ðMS; m b Þ ¼ 4.26ð10Þ GeV, m b =m c ¼ 4.42ð8Þ, m b =m s ¼ 51.4ð1.4Þ, f Bs ¼ 229ð5Þ MeV, f B ¼ 193ð6Þ MeV, f Bs =f B ¼ 1.184ð25Þ and ðf Bs =f B Þ=ðf K =f π Þ ¼ 0.997ð17Þ.

We compute the leading QED corrections to the hadronic vacuum polarization (HVP) of the photon, relevant for the determination of leptonic anomalous magnetic moments, al. We work in the electroquenched approximation and use dynamical QCD configurations generated by the CLS initiative with two degenerate flavors of nonperturbatively O(a)-improved Wilson fermions. We consider QEDL and QEDM to deal with the finite-volume zero modes. We compare results for the Wilson loops with exact analytical determinations. In addition we make sure that the volumes and photon masses used in QEDM are such that the correct dispersion relation is reproduced by the energy levels extracted from the charged pions two-point functions. Finally we compare results for pion masses and the HVP between QEDL and QEDM. For the vacuum polarization, corrections with respect to the pure QCD case, at fixed pion masses, turn out to be at the percent level.

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A mixed action composed of valence quark flavours regularized with a fully-twisted tmQCD action and of N f = 2 + 1 flavours of non-perturbatively O(a)-improved Wilson sea quarks is described. Two procedures for the matching of sea and valence quark masses are discussed. We report about a comparison of the continuum-limit scaling of pseudoscalar meson observables and of quark masses using the sea and valence actions.

Within the HMC algorithm, we discuss how, by using the shadow Hamiltonian and the Poisson brackets, one can achieve a simple factorization in the dependence of the Hamiltonian violations upon either the algorithmic parameters or the parameters specifying the integrator. We consider the simplest case of a second order (nested) Omelyan integrator and one level of Hasenbusch splitting of the determinant for the simulations of a QCD-like theory (with gauge group SU(2)). Given the specific choice of the integrator, the Poisson brackets reduce to the variances of the molecular dynamics forces. We show how the factorization can be used to optimize in a very economical and simple way both the algorithmic and the integrator parameters with good accuracy.Gauge theories formulated on Euclidean lattices can be treated as statistical systems and are amenable to numerical simulations. When matter fields (scalars or fermions) are also present, the gauge-field configurations are typically generated using molecular dynamics algorithms, which come with different variations of the Hybrid Monte Carlo (HMC) algorithm [1]. Such algorithms are characterized by a large number of parameters, whose optimal choices depend on the model and the regime (e.g., concerning masses and volumes) considered.The case of QCD has been extensively studied because of its obvious phenomenological relevance. Roughly speaking HMC algorithms can be classified according to the factorization of the quark determinant adopted (typically either masspreconditioning [2], or domain-decomposition [3], or rational factorization [4]) and the symplectic integrator(s) used, the simplest being the leapfrog integrator, and one of the most popular being the second order minimum norm integrator or Omelyanintegrator [5,6]. The two choices are actually connected. The factorization of the determinant translates into a splitting of the fermionic forces in the molecular dynamics, and depending on the hierarchy of such forces various nested integrators can be used where each force is integrated along a trajectory with a different timestep [3,7]. It is well known that for symplectic integrators a shadow Hamiltonian exists, which is conserved along the trajectory. This observation can be exploited to construct efficient integrators, as done in [8,9]. In short, the idea is to minimize the fluctuations in the difference between the Hamiltonian of the HMC and the shadow Hamiltonian along the trajectory. Since the latter is constant, the procedure clearly minimizes, in particular, the difference between the initial and the final Hamiltonian, hence increasing the acceptance.The relation between the shadow Hamiltonian and the Hamiltonian of the system involves complicated functions (Poisson brackets) of the HMC-momenta and of the field variables, however for a particular choice of the integrator, these expressions simplify and one is left with basically the variance of the fermionic forces. We specialize exactly to that choice, that we detail in the following, since in this way the forces...