NSPT estimate of the improvement coefficient $c_A$ to two loops

TL;DR

This paper uses Numerical Stochastic Perturbation Theory to compute the two-loop improvement coefficient $c_A$ for the isovector axial current in lattice QCD, ensuring discretization errors are minimized.

Contribution

It provides a two-loop perturbative estimate of $c_A$ using NSPT within the Schrödinger Functional formalism, advancing precision in lattice improvement coefficients.

Findings

Computed $c_A$ at two loops using NSPT

Fixed $c_A$ by controlling discretization errors in the quark mass

Enhanced accuracy of lattice QCD simulations

Abstract

By using Numerical Stochastic Perturbation Theory (NSPT), we carry out a quenched two-loop computation of the improvement coefficient $c_A$ associated to the isovector axial current. Within the Schr\"odinger Functional formalism, we compute the bare quark mass $m$ and fix $c_A$ by requiring discretization corrections on $m$ to be of order $O(a^2)$ in the lattice spacing $a$.