DOI: 10.1007/jhep08(2026)116 ISSN: 1029-8479
The elliptic three-loop integrals of hadronic vacuum polarization in chiral perturbation theory
Laurent Lellouch, Alessandro Lupo, Mattias Sjö, Pierre Vanhove
A
bstract
This work presents a detailed account of the Feynman integrals required for the three-loop hadronic vacuum polarization calculation performed in [1]. We explain how to compute each of the three-loop integrals, and outline the mathematical framework underlying their evaluation. This culminates in a practical numerical implementation that enables fast and accurate evaluation of these integrals for arbitrary complex values of the photon virtuality.