The three-loop hadronic vacuum polarization in chiral perturbation theory

TL;DR

This paper computes the hadronic vacuum polarization to three loops in chiral perturbation theory, significantly improving the precision of low-energy QCD predictions relevant for the muon magnetic moment.

Contribution

It presents the first three-loop (next-to-next-to-next-to-leading order) calculation of hadronic vacuum polarization in chiral perturbation theory, enhancing the accuracy of low-energy QCD analyses.

Findings

Achieved unprecedented precision in hadronic vacuum polarization calculations.

Reduced uncertainties related to low-energy constants in the model.

Extended computational methods for multiloop integrals with massive propagators.

Abstract

Hadronic vacuum polarization is a key observable in low-energy QCD, and is famously the greatest contributor to the theoretical uncertainty in the muon magnetic moment. Its long-distance part in particular is a weak point of the current best lattice QCD computations. In this summary of our recent work, we present its computation to next-to-next-to-next-to-leading order in chiral perturbation theory, capturing the lowest-energy hadronic contributions to unprecedented precision and opening the door for improved control over lattice finite volume effects. The result depends on a small number of low-energy constants, whose values are mostly under good control. This calculation pushes the envelope of high-order chiral perturbation theory and of the evaluation of multiloop integrals with massive propagators, thereby extending the toolbox for precision calculations in very low-energy QCD.