Soft thermal contributions to 3-loop gauge coupling

TL;DR

This paper investigates 3-loop contributions to the gauge coupling in hot Yang-Mills theory, revealing cancellations of IR divergences and showing the non-perturbative nature of the ultrasoft gauge coupling at high order.

Contribution

It provides a detailed analysis of soft and ultrasoft 3-loop contributions, clarifying divergence cancellations and the non-perturbative behavior of the ultrasoft gauge coupling.

Findings

Soft/hard term cancellations remove most IR divergences.

Remaining ultrasoft/hard contributions are IR divergent.

Ultrasoft gauge coupling becomes non-perturbative at order O(αs^{3/2}).

Abstract

We analyze 3-loop contributions to the gauge coupling felt by ultrasoft ("magnetostatic") modes in hot Yang-Mills theory. So-called soft/hard terms, originating from dimension-six operators within the soft effective theory, are shown to cancel 1097/1098 of the IR divergence found in a recent determination of the hard 3-loop contribution to the soft gauge coupling. The remaining 1/1098 originates from ultrasoft/hard contributions, induced by dimension-six operators in the ultrasoft effective theory. Soft 3-loop contributions are likewise computed, and are found to be IR divergent, rendering the ultrasoft gauge coupling non-perturbative at relative order O(alphas^{3/2}). We elaborate on the implications of these findings for effective theory studies of physical observables in thermal QCD.