SIRENA -- Sum-Integral REductioN Algorithm
Abstract
We present SIRENA, a Python and C++ implementation of the Laporta algorithm for the automatic reduction of multi-loop sum-integrals via integration-by-parts identities. The method builds on established techniques for zero-temperature Feynman integrals and extends them to finite-temperature quantum field theory by consistently accounting for the Matsubara sum structure. We validate the framework by reproducing several known results from the literature up to 3-loop order, and we further provide, for the first time, reductions for selected 3-loop fermionic sum-integrals. In addition to the package, we derive an analytic factorization formula for arbitrary 2-loop fermionic sum-integrals, extending on a previous result for the bosonic case.
Cite
@article{arxiv.2605.06775,
title = {SIRENA -- Sum-Integral REductioN Algorithm},
author = {Luis Gil and Javier López Miras and Adrián Moreno-Sánchez},
journal= {arXiv preprint arXiv:2605.06775},
year = {2026}
}
Comments
39 pages, 1 figure, 1 table