Marco Guagnelli

Precision computation of a low-energy reference scale in quenched lattice QCD

We present results for the reference scale r0 in SU(3) Lattice Gauge Theory for β = 6g02 in the range 5.7 ⩽ β ⩽ 6.57. The high relative accuracy of 0.3–0.6% in r0/a was achieved through good statistics, the application of a multi-hit procedure and a variational approach in the computation of Wilson loops. A precise definition of the force used to extract r0 has been used throughout the calculation which guarantees that r0/a is a smooth function of the bare coupling and that subsequent continuum extrapolations are possible. The results are applied to the continuum extrapolations of the energy gap Δ in the static quark potential and the scale Lmax/r0 used in the calculation of the running coupling constant.

Universality and the approach to the continuum limit in lattice gauge theory

Abstract The universality of the continuum limit and the applicability of renormalized perturbation theory are tested in the SU(2) lattice gauge theory by computing two different non-perturbatively defined running couplings over a large range of energies. The lattice data (which were generated on the powerful APE computers at Rome II and DESY) are extrapolated to the continuum limit by simulating sequences of lattices with decreasing spacings. Our results confirm the expected universality at all energies to a precision of a few percent. We find, however, that perturbation theory must be used with care when matching different renormalized couplings at high energies.

Non-perturbative results for the coefficients bm and bA−bP in O(a) improved lattice QCD

We determine the improvement coefficients b_m and b_a-bp in quenched lattice QCD for a range of beta-values, which is relevant for current large scale simulations. At fixed beta, the results are rather sensitive to the precise choices of parameters. We therefore impose improvement conditions at constant renormalized parameters, and the coefficients are then obtained as smooth functions of g_0^2. Other improvement conditions yield a different functional dependence, but the difference between the coefficients vanishes with a rate proportional to the lattice spacing. We verify this theoretical expectation in a few examples and are therefore confident that O(a) improvement is achieved for physical quantities. As a byproduct of our analysis we also obtain the finite renormalization constant which relates the subtracted bare quark mass to the bare PCAC mass.

Hadron masses and matrix elements from the QCD Schrödinger functional

We explain how masses and matrix elements can be computed in lattice QCD using Schrodinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical sample of the same size, our hadron masses have a precision similar to what is achieved with standard methods, but for the computation of matrix elements such as the pseudoscalar decay constant the Schrodinger functional technique turns out to be much more efficient than the known alternatives.

Nonperturbative results for the coefficients b(m) and b(a) - b(P) in O(a) improved lattice QCD

We determine the improvement coefficients b_m and b_a-bp in quenched lattice QCD for a range of beta-values, which is relevant for current large scale simulations. At fixed beta, the results are rather sensitive to the precise choices of parameters. We therefore impose improvement conditions at constant renormalized parameters, and the coefficients are then obtained as smooth functions of g_0^2. Other improvement conditions yield a different functional dependence, but the difference between the coefficients vanishes with a rate proportional to the lattice spacing. We verify this theoretical expectation in a few examples and are therefore confident that O(a) improvement is achieved for physical quantities. As a byproduct of our analysis we also obtain the finite renormalization constant which relates the subtracted bare quark mass to the bare PCAC mass.

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

Abstract 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.

fB and two-scales problems in lattice QCD

Abstract A novel method to calculate f B on the lattice is introduced, based on the study of the dependence of finite size effects upon the heavy quark mass of flavoured mesons and on a non-perturbative recursive finite size technique. We avoid the systematic errors related to extrapolations from the static limit or to the tuning of the coefficients of effective Lagrangian and the results admit an extrapolation to the continuum limit. We perform a first estimate at finite lattice spacing, but close to the continuum limit, giving f B =170(11)(5)(22) MeV. We also obtain f B s =192(9)(5)(24) MeV. The first error is statistical, the second is our estimate of the systematic error from the method and the third the systematic error from the specific approximations adopted in this first exploratory calculation. The method can be generalized to two-scale problems in lattice QCD.

Scattering Lengths From Fluctuations

Abstract We measure mesonic and meson-nucleon scattering lengths in quenched lattice QCD by monitoring the statistical fluctuations of the mesonic and baryonic propagators. The scattering lengths are related to finite volume effects. We use different lattice sizes (that we find in excellent agreement) and we measure at different β values. We discuss the chiral limit, the isospin content of the observables, and our physical results.

Universal continuum limit of non-perturbative lattice non-singlet moment evolution

Abstract We present evidence for the universality of the continuum limit of the scale dependence of the renormalization constant associated with the operator corresponding to the average momentum of non-singlet parton densities. The evidence is provided by a non-perturbative computation in quenched lattice QCD using the Schrodinger Functional scheme. In particular, we show that the continuum limit is independent of the form of the fermion action used, i.e. the Wilson action and the non-perturbatively improved clover action.

Non-perturbative determination of the running coupling constant in quenched SU (2)

Abstract Through a finite-size renormalization group technique we calculate the running coupling constant for quenched SU(2) with a few percent error over a range of energy varying by a factor thirty. The definition is based on ratio of correlations of Polyakov loops with twisted boundary conditions. The extrapolation to the continuum limit is governed by corrections due to lattice artifacts which appear to be rather smooth and proportional to the square of the lattice spacing.