The elliptic three-loop integrals of hadronic vacuum polarization in chiral perturbation theory
High Energy Physics - Phenomenology
2026-03-17 v1 High Energy Physics - Lattice
High Energy Physics - Theory
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.
Keywords
Cite
@article{arxiv.2603.15252,
title = {The elliptic three-loop integrals of hadronic vacuum polarization in chiral perturbation theory},
author = {Laurent Lellouch and Alessandro Lupo and Mattias Sjö and Pierre Vanhove},
journal= {arXiv preprint arXiv:2603.15252},
year = {2026}
}
Comments
40 pages; 16 figures; 1 table; implementation code available from https://github.com/mssjo/HVP-numerics