TL;DR
This paper reviews and unifies the evaluation of key three-loop sum-integrals used in thermodynamics, aiming to streamline existing methods and explore potential generalizations for future calculations.
Contribution
It provides a systematic, unified approach to evaluating important massless bosonic three-loop sum-integrals, enhancing clarity and potential for generalization.
Findings
Unified notation for three-loop sum-integrals
Streamlined evaluation methods
Discussion on generalization options
Abstract
In order to prepare the ground for evaluating classes of three-loop sum-integrals that are presently needed for thermodynamic observables, we take a fresh and systematic look on the few known cases, and review their evaluation in a unified way using coherent notation. We do this for three important cases of massless bosonic three-loop vacuum sum-integrals that have been frequently used in the literature, and aim for a streamlined exposition as compared to the original evaluations. In passing, we speculate on options for generalization of the computational techniques that have been employed.
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