A fit of the form cV = cV (0) + cV (1) (1 — 3) to extract the improvement constant for the vector current. The pole term is an artifact of lattice discretization, and resolved in our calculation.

Rajan Gupta, Tanmoy Bhattacharya, and Weonjong Lee, Los Alamos National Laboratory
Stephen Sharpe, University of Washington

Research Objectives
Lattice QCD provides the most promising non-perturbative approach to solving the highly non-linear behavior of quarks and gluons, the building blocks of strongly interacting particles. A price paid for discretizing QCD onto a space-time grid to make it amenable to numerical simulations is the introduction of errors associated with the granularity of the lattice. These errors can be reduced by improving the discretization scheme and by calculating the quantum corrections on the operators. Our goal is to carry out a study of phenomenologically interesting quantities using a theory for which all corrections needed to remove the leading discretization errors, i.e., linear in the lattice spacing, have been determined non-perturbatively.

Computational Approach
The basic tools for studying field theories like QCD on a computer are: (1) Monte Carlo methods for generating importance sampled background gauge configurations. We have used a combination of Metropolis and over-relaxed algorithms. (2) The calculation of quark propagators by inverting the Dirac matrix. We have done this using a stabilized bi-conjugate gradient iterative solver. Using these gauge and quark degrees of freedom, physical quantities are extracted by constructing gauge-invariant correlation functions.

Accomplishments
We have extended the method based on using axial and vector Ward identities to calculate the renormalization and improvement constants for lattice QCD. These include all the scale independent renormalization constants, the mass dependence of the renormalization constants for all quark bilinear operators, the improvement constants for currents, and the coefficients of the equation of motion operators that arise at O(a). Precise results have been obtained for two values of the lattice scale at which calculations by many lattice collaborations have been done. One of the highlights of our approach — the result for the improvement constant for the vector current — is shown in the figure. The uncertainty in this quantity was reduced by a factor of 4 compared to an earlier method used by the ALPHA collaboration.

Significance
In order to obtain the full improvement in scaling behavior of quantities calculated using better discretization schemes for the lattice action, it is also necessary to determine all the renormalization and improvement constants. Our results will be used by all lattice collaborations using the Symanzik O(a) improved lattice theory and will also form the basis for our future calculations.

Publications
T. Bhattacharya, S. Chandrasekharan, R. Gupta, W. Lee, and S. Sharpe, "Non-perturbative renormalization constants using Ward identities," Phys. Lett. B 461, 79 (1999).

T. Bhattacharya, S. Chandrasekharan, R. Gupta, W. Lee, and S. Sharpe, "Order a improved renormalization constants," Phys. Rev. D (submitted); hep-lat/0009038 (2000).