Renormalons on the Lattice and the OPE for the plaquette: a status report

TL;DR

This paper computes the first ten coefficients of the perturbative expansion of the lattice SU(3) plaquette, confirming the influence of IR renormalons and exploring unexpected scaling behavior after subtraction.

Contribution

It provides the first detailed comparison of perturbative coefficients with renormalon predictions on different lattice sizes, highlighting puzzling residual scaling behaviors.

Findings

Coefficients match IR renormalon growth predictions.

Subtraction leaves a residual that scales as a^2 instead of a^4.

Finite size effects influence the perturbative expansion analysis.

Abstract

The first ten coefficients in the perturbative expansion of the plaquette in Lattice SU(3) are computed both on a 8^4 and on a 24^4 lattice. They are shown to be fully consistent with the growth dictated by the first IR Renormalon and with the expected finite size effects on top of that. As already pointed out a few years ago, this leads to a puzzling result on the smaller lattice: when the contribution associated with the Renormalon is subtracted from Monte Carlo measurements of the plaquette, what is left over does not scale (as expected) as a^4, but as a^2. While the analysis is not yet complete on the larger lattice, the implications of such a finding is discussed.