Three-loop matching coefficients for hot QCD: Reduction and gauge independence

TL;DR

This paper advances the calculation of three-loop matching coefficients in hot QCD, ensuring gauge independence and setting the stage for improved high-temperature QCD predictions.

Contribution

It performs integral reduction for three-loop effective parameters in hot QCD and demonstrates explicit gauge independence, paving the way for more precise theoretical predictions.

Findings

Expressed parameters in terms of master integrals

Showed explicit gauge parameter independence

Highlighted calculational techniques for master integrals

Abstract

We perform an integral reduction for the 3-loop effective gauge coupling and screening mass of QCD at high temperatures, defined as matching coefficients appearing in the dimensionally reduced effective field theory (EQCD). Expressing both parameters in terms of a set master (sum-) integrals, we show explicit gauge parameter independence. The lack of suitable methods for solving the comparatively large number of master integrals forbids the complete evaluation at the moment. Taking one generic class of masters as an example, we highlight the calculational techniques involved. The full result would allow to improve on one of the classic probes for the convergence of the weak-coupling expansion at high temperatures, namely the comparison of full and effective theory determinations of the spatial string tension. Furthermore, the full result would also allow to determine one new contribution of order O(g**7) to the pressure of hot QCD.