Factorizing two-loop vacuum sum-integrals
High Energy Physics - Phenomenology
2026-03-24 v2 High Energy Physics - Theory
Abstract
We derive analytic results for scalar massless bosonic vacuum sum-integrals at two loops. Building upon a recent factorization proof of massive two-loop vacuum integrals, we are able to solve the corresponding Matsubara sums and map the result onto one-loop structures, thereby proving factorization also in the sum-integral setting. Analytic results are provided for generic integer-valued propagator- and numerator-powers of the class of sum-integrals under consideration, allowing to eliminate them from any perturbative expansion, dramatically simplifying the evaluation of some observables encountered e.g. in hot QCD.
Cite
@article{arxiv.2312.17367,
title = {Factorizing two-loop vacuum sum-integrals},
author = {Andrei I. Davydychev and Pablo Navarrete and York Schröder},
journal= {arXiv preprint arXiv:2312.17367},
year = {2026}
}
Comments
20 pages, 2 figures; v2: fixed a sign in code of appendix B