Perturbative Wilson loops from unquenched Monte Carlo simulations at weak couplings

TL;DR

This paper introduces a Monte Carlo simulation approach to compute perturbative expansions of Wilson loops in unquenched lattice QCD at weak couplings, providing a simpler alternative to traditional diagrammatic methods and validating results against established perturbation theory.

Contribution

It demonstrates the first application of unquenched Monte Carlo simulations to perturbative calculations of Wilson loops in full QCD, including systematic uncertainty analysis and comparison with diagrammatic perturbation theory.

Findings

Excellent agreement with diagrammatic perturbation theory.

Reliable extraction of third-order perturbative components from simulation data.

Validation of Monte Carlo approach as a cross-check for perturbative calculations.

Abstract

Perturbative expansions of several small Wilson loops are computed through next-to-next-to-leading order in unquenched lattice QCD, from Monte Carlo simulations at weak couplings. This approach provides a much simpler alternative to conventional diagrammatic perturbation theory, and is applied here for the first time to full QCD. Two different sets of lattice actions are considered: one set uses the unimproved plaquette gluon action together with the unimproved staggered-quark action; the other set uses the one-loop-improved Symanzik gauge-field action together with the so-called ``asqtad'' improved-staggered quark action. Simulations are also done with different numbers of dynamical fermions. An extensive study of the systematic uncertainties is presented, which demonstrates that the small third-order perturbative component of the observables can be reliably extracted from simulation data. We also investigate the use of the rational hybrid Monte Carlo algorithm for unquenched simulations with unimproved-staggered fermions. Our results are in excellent agreement with diagrammatic perturbation theory, and provide an important cross-check of the perturbation theory input to a recent determination of the strong coupling $\alpha_{\bar{\rm MS}}(M_Z)$ by the HPQCD collaboration.