Tightening the screws on the Standard Model: theory predictions for the anomalous magnetic moment of the muon

The muon, a heavier cousin of the electron, has electric charge and spin and therefore a magnetic moment. The muon’s magnetic moment is related to its spin via a factor g which would take the value 2 from the Dirac equation. However, g differs from 2 by a small amount because of quantum field theory effects in which the muon interacts with virtual particles produced by energy fluctuations in the vacuum. The combination (g-2)/2 is known as the ‘anomalous magnetic moment of the muon’, a_mu, and it can be determined very accurately by experiment. The Muon g-2 experiment at Fermilab (near Chicago, USA) has recently unveiled a new determination of a_mu. This has confirmed the tantalising discrepancy (4 sigma) that existed earlier between experiment and Standard Model expectations; a larger data sample will further improve the experimental uncertainties. Such a discrepancy could be a signal for the existence of previously unseen (i.e. non-Standard Model) particles present in the vacuum. At the same time the race is on to improve the theoretical uncertainties from the Standard Model. The largest Standard Model uncertainty comes from the hadronic vacuum polarisation (HVP) contribution, in which the muon interacts with virtual quark-antiquark pairs. The computational approach to handling quarks and strong-interaction physics, known as Lattice QCD, is now starting to weigh in on determination of the HVP. In the process it has added more questions to the conundrum of a_mu … After a general introduction to the experiment and theoretical inputs to the Standard Model determination of a_mu, I will go on to discuss recent lattice QCD results in this area and where things are heading.