Analytical study of Yang-Mills theory in the infrared from first principles

TL;DR

This paper develops a first-principles analytical approach to study the infrared behavior of pure Yang-Mills SU(N) theory, successfully matching lattice data and predicting universal scaling properties.

Contribution

It introduces a novel double perturbative expansion with a massive propagator that remains consistent with the original Lagrangian and matches lattice results.

Findings

Analytical expressions for propagators and coupling agree with lattice data.

Universal scaling property for inverse propagators is confirmed.

Higher-loop corrections are negligible below 300 MeV.

Abstract

Pure Yang-Mills SU(N) theory is studied in the Landau gauge and four dimensional space. While leaving the original Lagrangian unmodified, a double perturbative expansion is devised, based on a massive free-particle propagator. In dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the Lagrangian. No free parameters are included that were not in the original theory, yielding a fully analytical approach from first principles. The expansion is safe in the infrared and is equivalent to the standard perturbation theory in the UV. At one-loop, explicit analytical expressions are given for the propagators and the running coupling and are found in excellent agreement with the data of lattice simulations. A universal scaling property is predicted for the inverse propagators and shown to be satisfied by the lattice data. Higher loops are found to be negligible in the infrared below 300 MeV where the coupling becomes small and the one-loop approximation is under full control.