Higher-order hadronic and heavy-lepton contributions to the anomalous magnetic moment

TL;DR

This paper presents advanced calculations of the muon anomalous magnetic moment, including three-loop hadronic vacuum polarization and four-loop heavy-lepton corrections, refining theoretical predictions to match experimental precision.

Contribution

It provides the first computation of next-to-next-to-leading-order hadronic contributions and analytical four-loop heavy-lepton corrections for the muon g-2.

Findings

The NNLO hadronic contribution is $1.24 imes 10^{-10}$ with small uncertainty.

Four-loop heavy-lepton corrections are analytically obtained and compared with existing results.

Results are significant for precision tests of the Standard Model.

Abstract

We report about recent results obtained for the muon anomalous magnetic moment. Three-loop kernel functions have been computed to obtain the next-to-next-to-leading-order hadronic vacuum polarization contributions. The numerical result, $a_\mu^{\rm{had,NNLO}}=1.24\pm 0.01 \times 10^{-10}$, is of the same order of magnitude as the current uncertainty from the hadronic contributions. For heavy-lepton corrections, analytical results are obtained at four-loop order and compared with the known results.