Non-perturbative results for the coefficients b_m and b_a-b_p in O(a) improved lattice QCD

TL;DR

This paper provides non-perturbative determinations of key improvement coefficients in quenched lattice QCD across various parameters, ensuring O(a) improvement for physical quantities in large-scale simulations.

Contribution

It introduces a method to determine b_m and b_a-bp coefficients as smooth functions of g_0^2, verifying their behavior and impact on O(a) improvement.

Findings

Coefficients are smooth functions of g_0^2.

Differences in improvement conditions vanish with lattice spacing.

Confirmed O(a) improvement for physical quantities.

Abstract

We determine the improvement coefficients b_m and b_a-bp in quenched lattice QCD for a range of beta-values, which is relevant for current large scale simulations. At fixed beta, the results are rather sensitive to the precise choices of parameters. We therefore impose improvement conditions at constant renormalized parameters, and the coefficients are then obtained as smooth functions of g_0^2. Other improvement conditions yield a different functional dependence, but the difference between the coefficients vanishes with a rate proportional to the lattice spacing. We verify this theoretical expectation in a few examples and are therefore confident that O(a) improvement is achieved for physical quantities. As a byproduct of our analysis we also obtain the finite renormalization constant which relates the subtracted bare quark mass to the bare PCAC mass.