Numerical evidence for loop convergence in Yang-Mills thermodynamics

TL;DR

This paper provides numerical evidence that the loop expansion in Yang-Mills thermodynamics converges rapidly, by analyzing three-loop contributions and comparing them with two-loop results using a validated statistical method.

Contribution

It offers detailed numerical analysis of three-loop contributions in SU(2) Yang-Mills thermodynamics and demonstrates rapid convergence of the loop expansion.

Findings

Three-loop contributions are numerically computed and compared with two-loop results.

The statistical method for irreducible three-loop integrations is validated against analytical results.

Results show a rapid convergence of the loop expansion in Yang-Mills thermodynamics.

Abstract

The numerical results for the computed moduli of the irreducible three-loop contributions to the thermodynamical pressure of an SU(2) Yang-Mills theory in the effective theory for the deconfinning phase are explained in detail. Irreducible three-loop integrations are compared with two-loop integrations and the different nature of their integrations is scrutinized and illustrated numerically. The numerical results show a rapid convergence in the loop expansion of Yang-Mills thermodynamics. The statistical method used for irreducible three-loop integrations is explained and checked for two-loop integrations. The statistical results for two-loop integrations are compatible with the former computed analytical results showing the reliability of the statistical method.This is a companion paper to [1].