Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment

TL;DR

This paper introduces a lattice QCD method to compute the hadronic contribution to the muon's magnetic moment directly in Euclidean space, offering a systematic approach that can be improved with current computational resources.

Contribution

It presents a novel Euclidean space lattice calculation method for the hadronic vacuum polarization contribution to the muon g-2, avoiding reliance on experimental data.

Findings

Initial lattice calculation of the hadronic contribution

Methodology for systematic improvement in quenched approximation

Framework for including dynamical quarks in future work

Abstract

We present a quenched lattice calculation of the lowest order (alpha^2) hadronic contribution to the anomalous magnetic moment of the muon which arises from the hadronic vacuum polarization. A general method is presented for computing entirely in Euclidean space, obviating the need for the usual dispersive treatment which relies on experimental data for e^+e^- annihilation to hadrons. While the result is not yet of comparable accuracy to those state-of-the-art calculations, systematic improvement of the quenched lattice computation to this level of accuracy is straightforward and well within the reach of present computers. Including the effects of dynamical quarks is conceptually trivial, the computer resources required are not.