DOI 10.1007/s100529800750
Improved renormalization of lattice operators:
A critical reappraisal
M. Crisafulli1 - V. Lubicz2 - A. Vladikas3,4
1 Dipartimento di Fisica, Università di Roma "La Sapienza'' and
INFN, Sezione di Roma,
P.le A. Moro 2, I-00185 Roma, Italy
2 Dipartimento di Fisica, Università di Roma Tre
and INFN, Sezione di Roma,
Via della Vasca Navale 84, I-00146 Roma, Italy
3 Theory Division, CERN, CH-1211 Geneva 23, Switzerland
4 INFN, Sezione di Roma II, and
Dipartimento di Fisica, Università di Roma "Tor Vergata'',
Via della Ricerca Scientifica 1, I-00133 Roma, Italy
Received: 21 July 1997 / Published online: 20 February 1998
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 . 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 (
and 6.0
respectively). In order to amplify finite cutoff effects, the quark masses
(in lattice units) are varied in a large interval
.We find that discretization effects are always large with the Wilson action,
despite our relatively small value of the lattice spacing (
GeV). With the Clover action discretization errors are significantly
reduced at small quark mass, even though our lattice spacing is larger
(
GeV). However, these errors remain substantial in the heavy
quark region.
We have implemented a proposal for reducing
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.
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