Hunting the static energy renormalon

TL;DR

This paper uses advanced numerical methods to investigate the leading renormalon in static energy perturbation series, aiming to confirm theoretical predictions about its behavior compared to other quantities.

Contribution

It introduces a novel combination of NSPT and TBC to analyze the static energy and provides preliminary results up to 12 loops to support theoretical expectations.

Findings

Preliminary results up to 12 loops show promising signs of the expected renormalon behavior.

The method advances the search for renormalons in static energy perturbation series.

Results suggest the leading renormalon emerges faster than in the gluon condensate case.

Abstract

We employ Numerical Stochastic Perturbation Theory (NSPT) together with twisted boundary conditions (TBC) to search for the leading renormalon in the perturbative expansion of the static energy. This renormalon is expected to emerge four times faster than the one for the gluon conden- sate in the plaquette. We extract the static energy from Polyakov loop calculations up to 12 loops and present preliminary results, indicating a significant step towards confirming the theoretical expectation.