Improved non-perturbative renormalization without $c_{NGI}$

TL;DR

This paper examines the impact of omitting the gauge non-covariant improvement coefficient $c_{NGI}$ in non-perturbative renormalization, assessing the resulting errors in physical quantities and improvement coefficients.

Contribution

It provides an analysis of the errors introduced when $c_{NGI}$ is neglected in the O(a) improvement method for composite operators.

Findings

Neglecting $c_{NGI}$ introduces quantifiable errors in physical quantities.

The size of errors depends on the specific operators and conditions.

Omission of $c_{NGI}$ may be acceptable within certain error margins.

Abstract

Recently, a method for O(a) improvement of composite operators has been proposed which uses the large momentum behavior of fixed gauge quark and gluon correlation functions (G. Martinelli et al., hep-lat/0106003). A practical problem with this method is that a particular improvement coefficient, $c_{NGI}$, which has a gauge non-covariant form, is difficult to determine. Here I work out the size of the errors made in improvement coefficients and physical quantities if one does not include the $c_{NGI}$ term.