Hadronic contributions to the anomalous magnetic moment of the muon from Lattice QCD

Abstract

The recently reported new measurement of the anomalous magnetic moment of the muon, 𝑎𝜇, by the E989 collaboration at Fermilab has increased the tension with the Standard Model (SM) prediction to 4.2 standard deviations. In order to increase the sensitivity of SM tests, the precision of the theoretical prediction, which is limited by the strong interaction, must be further improved. In our project we employ lattice QCD to compute the leading hadronic contributions to 𝑎𝜇 and various other precision observables, such as the energy dependence (“running”) of the electromagnetic coupling, 𝛼, and the electroweak mixing angle, sin² 𝜃W. Here we report on the performance of our simulation codes used for the generation of gauge ensembles at (near-)physical pion masses and fine lattice spacings. Furthermore, we present results for the hadronic running of 𝛼, the electroweak mixing angle, as well as the hadronic vacuum polarisation and light-by-light scattering contributions to 𝑎𝜇. Results from an ancillary calculation of the spectrum in the isovector channel are crucial in order to further increase the precision of our determination of the hadronic vacuum polarisation contribution.