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We consider the possibility of using reweighting techniques in order to correct the breaking of unitarity when twisted boundary conditions are imposed on valence fermions in simulations of lattice gauge theories. We start by studying the properties of reweighting factors and their variances at tree-level. This leads us to the introduction of a factorization for the fermionic reweighting determinant. In the numerical, stochastic implementation of the method, we find that the effect of reweighting is negligible in the case of large volumes but it is sizeable when the volumes are small and the twisting angles are large. More importantly, we find that for un-improved Wilson fermions, and in small volumes, the dependence of the critical quark mass on the twisting angle is quite pronounced and results in large violations of the continuum dispersion relation. [ABSTRACT FROM AUTHOR]

The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the corresponding transfer matrix elements can be exploited to devise a multi-level Monte Carlo integration scheme for computing correlation functions whose numerical cost, at a fixed precision and at asymptotically large times, increases power-like with the time extent of the lattice. As a result the numerical effort is exponentially reduced with respect to the standard Monte Carlo procedure. We test this strategy in the SU(3) Yang–Mills theory by evaluating the relative contribution to the partition function of the parity odd states. [Copyright &y& Elsevier]

The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them, normalized to the one with vacuum quantum numbers, by a Monte Carlo procedure whose cost increases power-like with the time extent of the lattice. This is achieved thanks to a multi-level integration scheme, inspired by the transfer matrix formalism, which exploits the symmetry and the locality in time of the underlying statistical system. As a result the cost of computing the lowest energy level in a given channel, its multiplicity and its matrix elements is exponentially reduced with respect to the standard path-integral Monte Carlo. We test the strategy with a one-dimensional harmonic oscillator, by computing the ratio of the parity odd over the parity even functional integrals and the two-point correlation function. The cost of the simulations scales as expected. In particular the effort for computing the lowest energy eigenvalue in the parity odd sector grows linearly with the time extent. At a fixed CPU time, the statistical error on the two-point correlation function is exponentially reduced with respect to the standard Monte Carlo procedure, and at large time distances it is lowered by many orders of magnitude. [Copyright &y& Elsevier]

Abstract: As a feasibility study for a scaling test we investigate the behavior of algorithms for dynamical fermions in the Schrödinger functional at an intermediate volume of . Simulations were performed using HMC with two pseudo-fermions and PHMC at lattice spacings of approximately 0.1 and . We show that some algorithmic problems are due to large cutoff-effects in the spectrum of the improved Wilson–Dirac operator and disappear at the smaller lattice spacing. The problems discussed here are not expected to be specific to the Schrödinger functional. [Copyright &y& Elsevier]

I consider the recent proposal by R. Frezzotti and G. Rossi to chirally improve Wilson fermions in such a way that mixings among operators of different chirality can be excluded. The method, which is based on the use of twisted mass QCD with several replica of valence quarks, is extended here to static-light systems. The operators relevant for the computation of the parameter (in the static approximation) are discussed. In this case the same renormalization pattern as for Gingsparg–Wilson fermions is obtained by a simple modification of the discretization of the action for valence quarks. [Copyright &y& Elsevier]

Abstract: We report on the ALPHA Collaborationʼs lattice B-physics programme based on improved Wilson fermions and HQET, including all NLO effects in the inverse heavy quark mass, as well as non-perturbative renormalization and matching, to fix the parameters of the effective theory. Our simulations in large physical volume cover 3 lattice spacings and pion masses down to 190 MeV to control continuum and chiral extrapolations. We present the status of results for the b-quark mass and the -meson decay constants, and . [Copyright &y& Elsevier]

Abstract: We study autocorrelation times of physical observables in lattice QCD as a function of the molecular dynamics trajectory length in the hybrid Monte-Carlo algorithm. In an interval of trajectory lengths where energy and reversibility violations can be kept under control, we find a variation of the integrated autocorrelation times by a factor of about two in the quantities of interest. Trajectories longer than conventionally used are found to be superior both in the and examples considered here. We also provide evidence that they lead to faster thermalization of systems with light quarks. [Copyright &y& Elsevier]