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arXiv · 2603.15252

The elliptic three-loop integrals of hadronic vacuum polarization in chiral perturbation theory

Laurent Lellouch·Alessandro Lupo·Mattias Sjö·Pierre Vanhove
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Abstract

This work presents a detailed account of the Feynman integrals required for the three-loop hadronic vacuum polarization calculation performed in arXiv:2510.12885. 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.

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Laurent Lellouch, Alessandro Lupo, Mattias Sjö, Pierre Vanhove. 2026-03-16. The elliptic three-loop integrals of hadronic vacuum polarization in chiral perturbation theory. https://arxiv.org/abs/2603.15252

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