A new method for taming tensor sum-integrals

TL;DR

This paper introduces a novel tensor reduction technique using dimensionality shifts at finite temperature, enabling the computation of complex three-loop sum-integrals crucial for precise Debye mass evaluation in hot QCD.

Contribution

It generalizes existing tensor reduction methods to finite temperature, allowing the calculation of previously inaccessible sum-integrals for NNLO Debye mass determination.

Findings

Developed a tensor reduction method applicable at finite temperature.

Enabled computation of new three-loop sum-integrals.

Facilitated progress towards NNLO Debye mass evaluation.

Abstract

We report on the computation of a class of massless bosonic three-loop vacuum sum-integrals which are key building blocks for an evaluation of the Debye screening mass in hot QCD. Generalizing known techniques and introducing the concept of tensor reduction by dimensionality shifts (known to the zero-temperature community since the work of Tarasov in 1996) to finite temperature, we are able to treat hitherto unaccessible cases, which will allow us to finalize the long-term project of NNLO Debye mass evaluation.