Testing the OPE Wilson coefficient for $A^2$ from lattice QCD with a dynamical charm

TL;DR

This paper tests the Operator Product Expansion (OPE) Wilson coefficient for the $A^2$ operator in lattice QCD with dynamical charm, comparing numerical data with high-order theoretical predictions to validate the approach.

Contribution

It provides a precise comparison of lattice data with four-loop perturbative and nonperturbative OPE corrections, confirming the validity of the OPE in describing gluon and ghost propagators.

Findings

Wilson coefficients match theoretical ${ m O}(\alpha^4)$ expressions

Consistent extraction of $ m \Lambda_{MSbar}$ for $N_f=2+1+1$

Validation of the OPE approach for lattice QCD observables

Abstract

Gluon and ghost propagators data, obtained in Landau gauge from lattice simulations with two light and two heavy dynamical quark flavours ($N_f$=2+1+1), are described here with a running formula including a four-loop perturbative expression and a nonperturbative OPE correction dominated by the local operator $A^2$. The Wilson coefficients and their variation as a function of the coupling constant are extracted from the numerical data and compared with the theoretical expressions that, after being properly renormalized, are known at ${\cal O}(\alpha^4)$. As also $\Lambda_{\msbar}$ is rather well known for $N_f$=2+1+1, this allows for a precise consistency test of the OPE approach in the joint description of different observables.