Improved renormalization of lattice operators: A critical reappraisal

Abstract. We systematically examine various proposals which aim at increasing the 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 constants of the scalar and pseudoscalar densities. We calculate these quantities in boosted perturbation theory, with several running boosted couplings, at the “optimal” scale $q^\ast$. We find that the results of boosted perturbation theory are usually (but not always) in better agreement with non-perturbative determinations of the renormalization constants than those obtained with standard perturbation theory. The finite renormalization constants of two-fermion lattice operators are also obtained non-perturbatively, using Ward Identities, both with the Wilson 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 $0 \lesssim am \lesssim 1$. We find that discretization effects are always large with the Wilson action, despite our relatively small value of the lattice spacing ( $a^{-1} \simeq 3.7$ GeV). With the Clover action discretization errors are significantly reduced at small quark mass, even though our lattice spacing is larger ( $a^{-1} \simeq 2$ GeV). However, these errors remain substantial in the heavy quark region. We have implemented a proposal for reducing ${\cal O} (am)$ effects, which consists in matching the lattice quantities to their continuum counterparts in the free theory. We find that this approach still leaves appreciable, mass dependent, discretization effects.