Perturbative expansions from Monte Carlo simulations at weak coupling: Wilson loops and the static-quark self-energy

TL;DR

This paper extracts perturbative coefficients for Wilson loops and static-quark self-energy from Monte Carlo simulations at weak coupling, confirming second-order results and providing new third-order coefficients with high precision.

Contribution

It introduces a method to accurately determine higher-order perturbative coefficients from Monte Carlo simulations using twisted boundary conditions.

Findings

Monte Carlo results agree with second-order perturbation theory.

New third-order coefficients for Wilson loops and static-quark self-energy are reported.

Simulations cover a wide range of lattice volumes and couplings.

Abstract

Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative. Twisted boundary conditions are used to eliminate the effects of lattice zero modes and to suppress nonperturbative finite-volume effects due to Z(3) phases. Simulations of the Wilson gluon action are done with both periodic and twisted boundary conditions, and over a wide range of lattice volumes (from $3^4$ to $16^4$) and couplings (from $\beta \approx 9$ to $\beta \approx 60$). A high precision comparison is made between the simulation data and results from finite-volume lattice perturbation theory. The Monte Carlo results are shown to be in excellent agreement with perturbation theory through second order. New results for third-order coefficients for a number of Wilson loops and the static-quark self-energy are reported.