Non-perturbative determination of improvement coefficients using coordinate space correlators in $N_f=2+1$ lattice QCD

TL;DR

This paper non-perturbatively determines quark mass-dependent improvement coefficients in lattice QCD using coordinate space correlators, across multiple lattice spacings and ensembles, enhancing precision in lattice calculations.

Contribution

It introduces a method to compute order a improvement coefficients in lattice QCD using coordinate space correlators, providing non-perturbative results for multiple ensembles.

Findings

Values of the b_J improvement coefficients are reported.

Method enables determination of coefficients proportional to non-singlet quark masses.

Discussion on the potential to determine trace-dependent coefficients.

Abstract

We determine quark mass dependent order $a$ improvement terms of the form $b_J am$ for non-singlet scalar, pseudoscalar, vector and axialvector currents, using correlators in coordinate space. We use a set of CLS ensembles comprising non-perturbatively improved Wilson Fermions and the tree-level Luescher-Weisz gauge action at $\beta=3.4,3.46,3.55$ and $\beta=3.7$, corresponding to lattice spacings $a$ ranging from $0.05$ fm to $0.09$ fm. We report the values of the $b_J$ improvement coefficients which are proportional to non-singlet quark mass combinations and also discuss the possibility of determining the $\bar{b}_J$ coefficients which are proportional to the trace of the quark mass matrix.