Tackling the infamous $g^6$ term of the QCD pressure

TL;DR

This paper discusses progress in calculating the QCD pressure at order g^6, involving complex four-loop Feynman integrals, by decomposing tensor integrals into scalar master sum-integrals already known.

Contribution

The work introduces a formalism for tensor decomposition of Feynman integrals and maps complex integrals onto known scalar master sum-integrals, advancing the calculation of QCD thermodynamics.

Findings

Identified a class of contributing Feynman sum-integrals with lower-loop factors.

Developed a tensor decomposition formalism for these integrals.

Mapped integrals onto scalar master sum-integrals previously evaluated.

Abstract

We report on ongoing efforts to tackle an important open problem in QCD thermodynamics, namely an evaluation of the pressure to order $g^6$ in a weak-coupling expansion, corresponding to four loops. In particular, we identify a class of contributing Feynman sum-integrals with lower-loop factors, describe the formalism to tensor decompose those, and manage to map them onto scalar master sum-integrals that have already been evaluated in the literature.