Order a improved renormalization constants

TL;DR

This paper non-perturbatively determines renormalization constants for on-shell and off-shell $O(a)$ improvement of Wilson fermion bilinear operators, using Ward identities and non-degenerate quarks at specific lattice couplings.

Contribution

It introduces a method for calculating $c_V$ with reduced errors and compares various Ward identity approaches for determining improvement constants.

Findings

Smaller errors in $c_V$ calculation compared to previous methods.

Consistent results with ALPHA collaboration and perturbation theory.

Effective use of non-degenerate quarks and Ward identities for improvement constants.

Abstract

We present non-perturbative results for the constants needed for on-shell $O(a)$ improvement of bilinear operators composed of Wilson fermions. We work at $\beta=6.0$ and 6.2 in the quenched approximation. The calculation is done by imposing axial and vector Ward identities on correlators similar to those used in standard hadron mass calculations. A crucial feature of the calculation is the use of non-degenerate quarks. We also obtain results for the constants needed for off-shell $O(a)$ improvement of bilinears, and for the scale and scheme independent renormalization constants, (Z_A), (Z_V) and (Z_S/Z_P). Several of the constants are determined using a variety of different Ward identities, and we compare their relative efficacies. In this way, we find a method for calculating $c_V$ that gives smaller errors than that used previously. Wherever possible, we compare our results with those of the ALPHA collaboration (who use the Schr\"odinger functional) and with 1-loop tadpole-improved perturbation theory.