Muon $g-2$: Lattice calculations of the hadronic vacuum polarization

TL;DR

This paper reviews lattice QCD calculations of the hadronic vacuum polarization contribution to the muon g-2, emphasizing the need for high-precision ab initio predictions to match experimental accuracy.

Contribution

It provides a comprehensive review of current lattice QCD methods and identifies key sources of uncertainty for achieving sub-percent precision in HVP calculations.

Findings

Lattice QCD can potentially match experimental precision in muon g-2 predictions.

Major uncertainties stem from statistical errors and systematic effects in lattice calculations.

Controlling these uncertainties is crucial for reliable Standard Model tests.

Abstract

The experimental uncertainty on the anomalous magnetic moment of the muon has been significantly reduced with the recent results of the Fermilab $g-2$ experiment, and a further reduction is expected in the near future. The precision of the Standard Model prediction needs to improve correspondingly to increase the sensitivity of tests for physics beyond the Standard Model. The largest uncertainty is due to contributions from the strong interaction, in particular the hadronic vacuum polarization (HVP) contribution. Lattice QCD calculations have the potential to provide precise ab initio predictions of the HVP contribution. We review the state of lattice QCD calculations, focusing on the dominant sources of uncertainty that need to be controlled to provide results with sub-percent precision.