Lattice hadron matrix elements with the Schroedinger functional: the case of the first moment of non-singlet quark density

We present the results of a non-perturbative determination of the pion matrix element of the twist-2 operator corresponding to the average momentum of non-singlet quark densities. The calculation is made within the Schroedinger functional scheme. We report the results of simulations done with the standard Wilson action and with the non-perturbatively improved clover action and we show that their ratio correctly extrapolates, in the continuum limit, to a value compatible with the residual correction factor expected from perturbation theory.Comment: LaTeX, 10 pages, 5 figure

Pion parton distribution functions from lattice QCD

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.Comment: Lattice2003(matrix), 3 pages, 4 figure

Heavy quark masses in the continuum limit of quenched Lattice QCD

We compute charm and bottom quark masses in the quenched approximation and in the continuum limit of lattice QCD. We make use of a step scaling method, previously introduced to deal with two scale problems, that allows to take the continuum limit of the lattice data. We determine the RGI quark masses and make the connection to the MSbar scheme. The continuum extrapolation gives us a value m_b^{RGI} = 6.73(16) GeV for the b-quark and m_c^{RGI} = 1.681(36) GeV for the c-quark, corresponding respectively to m_b^{MSbar}(m_b^{MSbar}) = 4.33(10) GeV and m_c^{MSbar}(m_c^{MSbar}) = 1.319(28) GeV. The latter result, in agreement with current estimates, is for us a check of the method. Using our results on the heavy quark masses we compute the mass of the Bc meson, M_{Bc} = 6.46(15) GeV.Comment: 29 pages, 9 figures, version accepted for publication in Nucl. Phys.

Continuous external momenta in non-perturbative lattice simulations: a computation of renormalization factors

We discuss the usage of continuous external momenta for computing renormalization factors as needed to renormalize operator matrix elements. These kind of external momenta are encoded in special boundary conditions for the fermion fields. The method allows to compute certain renormalization factors on the lattice that would have been very difficult, if not impossible, to compute with standard methods. As a result we give the renormalization group invariant step scaling function for a twist-2 operator corresponding to the average momentum of non-singlet quark densities.Comment: 28 pages, 10 figure

Non-perturbative scale evolution of four-fermion operators

We apply the Schroedinger Functional (SF) formalism to determine the renormalisation group running of four-fermion operators which appear in the effective weak Hamiltonian of the Standard Model. Our calculations are done using Wilson fermions and the parity-odd components of the operators. Preliminary results are presented for the operator $O_{VA}=(\bar s \gamma_\mu d)(\bar s \gamma_\mu \gamma_5 d)$.Comment: Lattice2002(improve

Non-perturbative running of the average momentum of non-singlet parton densities

We determine non-perturbatively the anomalous dimensions of the second moment of non-singlet parton densities from a continuum extrapolation of results computed in quenched lattice simulations at different lattice spacings. We use a Schr\"odinger functional scheme for the definition of the renormalization constant of the relevant twist-2 operator. In the region of renormalized couplings explored, we obtain a good description of our data in terms of a three-loop expression for the anomalous dimensions. The calculation can be used for exploring values of the coupling where a perturbative expansion of the anomalous dimensions is not valid a priori. Moreover, our results provide the non-perturbative renormalization constant that connects hadron matrix elements on the lattice, renormalized at a low scale, with the experimental results, renormalized at much higher energy scales.Comment: Latex2e file, 6 figures, 25 pages, Corrected errors on linear fit in table 2 and discussion on anomalous dimension of f_

Non-perturbative renormalization of moments of parton distribution functions

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 Schr\"odinger 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.Comment: Lattice2003(Matrix); 3 pages, 3 figures. Talk by A.

Exact Nonperturbative Renormalization

We propose an exact renormalization group equation for Lattice Gauge Theories, that has no dependence on the lattice spacing. We instead relate the lattice spacing properties directly to the continuum convergence of the support of each local plaquette. Equivalently, this is formulated as a convergence prescription for a characteristic polynomial in the gauge coupling that allows the exact meromorphic continuation of a nonperturbative system arbitrarily close to the continuum limit.Comment: 12 page

Quenched Spectroscopy for the N=1 Super-Yang-Mills Theory

We present results for the Quenched SU(2) N=1 Super-Yang-Mills spectrum at $\beta=2.6$, on a $V=16^3 \times 32$ lattice, in the OZI approximation. This is a first step towards the understanding of the chiral limit of lattice N=1 SUSY.Comment: 3 pages, Latex, 2 ps figures, contribution to Lattice 97, Edinburgh 22-26 July 1997; to appear on Nucl. Phys. B. (Proc. Suppl.