IMPROVED RENORMALIZATION OF LATTICE OPERATORS - A CRITICAL REAPPRAISAL

We systematically examine various proposals which aim at increasing th e accuracy in the determination of the renormalization of two-fermion lattice operators. We concentrate on three finite quantities which are particularly suitable for our study: the renormalization constants of the vector and axial currents and the ratio of the renormalization co nstants of the scalar and pseudoscalar densities. We calculate these q uantities in boosted perturbation theory, with several running boosted couplings, at the ''optimal'' scale q. We find that the results of b oosted perturbation theory are usually (but not always) in better agre ement with non-perturbative determinations of the renormalization cons tants than those obtained with standard perturbation theory. The finit e renormalization constants of two-fermion lattice operators are also obtained non-perturbatively, using Ward Identities, both with the Wils on and the tree-level Clover improved actions, at fixed cutoff (beta = 6.4 and 6.0 respectively). In order to amplify finite cutoff effects, the quark masses (in lattice units) are varied in a large interval 0 less than or similar to am less than or similar to 1. We find that dis cretization effects are always large with the Wilson action, despite o ur relatively small value of the lattice spacing (a(-1) similar or equ al to 3.7 GeV). With the Clover action discretization errors are signi ficantly reduced at small quark mass, even though our lattice spacing is larger (a(-1) similar or equal to 2 GeV). However, these errors rem ain substantial in the heavy quark region. We have implemented a propo sal for reducing O(am) effects, which consists in matching the lattice quantities to their continuum counterparts in the free theory. We fin d that this approach still leaves appreciable, mass dependent, discret ization effects.