It is shown that the algorithm introduced in [1] and conceived to deal with continuous degrees of freedom models is well suited to compute the density of states in models with a discrete energy spectrum too. The q=10 D=2 Potts model is considered as
a test case, and it is shown that using the Maxwell construction the interface free energy can be obtained, in the thermodynamic limit, with a good degree of accuracy.
We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $Delta F = 1$ and $Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with quenched Wils
on quarks, we compute non-perturbatively the renormalization group running of these operators in the continuum limit in a large range of renormalization scales. Continuum limit extrapolations are well controlled thanks to the implementation of two fermionic actions (Wilson and Clover). The ratio of the renormalization group invariant operator to its renormalized counterpart at a low energy scale, as well as the renormalization constant at this scale, is obtained for all schemes.
Developed by the APE group, APENet is a new high speed, low latency, 3-dimensional interconnect architecture optimized for PC clusters running LQCD-like numerical applications. The hardware implementation is based on a single PCI-X 133MHz network int
erface card hosting six indipendent bi-directional channels with a peak bandwidth of 676 MB/s each direction. We discuss preliminary benchmark results showing exciting performances similar or better than those found in high-end commercial network systems.
We give a continuum limit value of the lowest moment of a twist-2 operator in pion states from non-perturbative lattice calculations. We find that the non-perturbatively obtained renormalization group invariant matrix element is <x>_{RGI} = 0.179(11)
, which corresponds to <x>^{MSbar}(2 GeV) = 0.246(15). In obtaining the renormalization group invariant matrix element, we have controlled important systematic errors that appear in typical lattice simulations, such as non-perturbative renormalization, finite size effects and effects of a non-vanishing lattice spacing. The crucial limitation of our calculation is the use of the quenched approximation. Another question that remains not fully clarified is the chiral extrapolation of the numerical data.
We investigate finite size effects of the pion matrix element of the non-singlet, twist-2 operator corresponding to the average momentum of non-singlet quark densities. Using the quenched approximation, they come out to be surprisingly large when com
pared to the finite size effects of the pion mass. As a consequence, simulations of corresponding nucleon matrix elements could be affected by finite size effects even stronger which could lead to serious systematic uncertainties in their evaluation.
The renormalisation group running of the quark mass is determined non-perturbatively for a large range of scales, by computing the step scaling function in the Schroedinger Functional formalism of quenched lattice QCD both with and without O(a) impro
vement. A one-loop perturbative calculation of the discretisation effects has been carried out for both the Wilson and the Clover-improved actions and for a large number of lattice resolutions. The non-perturbative computation yields continuum results which are regularisation independent, thus providing convincing evidence for the uniqueness of the continuum limit. As a byproduct, the ratio of the renormalisation group invariant quark mass to the quark mass, renormalised at a hadronic scale, is obtained with very high accuracy.
We compute non-perturbatively the evolution of the twist-2 operators corresponding to the average momentum of non-singlet quark densities. The calculation is based on a finite-size technique, using the Schrodinger Functional, in quenched QCD. We find
that a careful choice of the boundary conditions, is essential, for such operators, to render possible the computation. As a by-product we apply the non-perturbatively computed renormalization constants to available data of bare matrix elements between nucleon states.
Some new results on nonperturbative renormalisation of quark bilinears in quenched QCD with Schroedinger Functional techniques are presented. Special emphasis is put on a study of the universality of the continuum limit for step scaling functions computed with different levels of O(a) improvement.
We report on recent results for the pion matrix element of the twist-2 operator corresponding to the average momentum of non-singlet quark densities. For the first time finite volume effects of this matrix element are investigated and come out to be
surprisingly large. We use standard Wilson and non-perturbatively improved clover actions in order to control better the extrapolation to the continuum limit. Moreover, we compute, fully non-perturbatively, the renormalization group invariant matrix element, which allows a comparison with experimental results in a broad range of energy scales. Finally, we discuss the remaining uncertainties, the extrapolation to the chiral limit and the quenched approximation.
We compute the decay constants for the heavy--light pseudoscalar mesons in the quenched approximation and continuum limit of lattice QCD. Within the Schrodinger Functional framework, we make use of the step scaling method, which has been previously i
ntroduced in order to deal with the two scale problem represented by the coexistence of a light and a heavy quark. The continuum extrapolation gives us a value $f_{B_s} = 192(6)(4)$ MeV for the $B_s$ meson decay constant and $f_{D_s} = 240(5)(5)$ MeV for the $D_s$ meson.
