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.