The Standard Model (SM) of Particle Physics is a highly successful theory for describing and predicting the properties of the known elementary particles and the fundamental forces that act between those particles. However, it leaves many open questions such as “What is dark matter?” or “What happened directly after the Big Bang?”. Answering such questions requires the discovery of new physics beyond the Standard Model. Due to quantum effects, such new physics is expected to influence the properties of the known particles by small amounts, and therefore could be discovered by observing small deviations between experimental results and theoretical predictions made within the Standard Model. 

A quantity that continues to receive a lot of attention is the anomalous magnetic moment of the Muon (“Muon g-2”), which describes the behaviour of a muon (a heavier version of the electron) inside a magnetic field. Muon g-2 has recently been measured at Fermilab (USA) to an impressive precision of 0.2 parts per million [1] and a further reduction of uncertainties is expected in the near future. The current SM prediction from the white paper of the Muon g-2 Theory initiative [2], with a precision of 0.37 parts per million, is in 5 sigma tension with the experimental measurement, giving rise to a potential discovery of new physics. In the current SM prediction, the leading contribution to Muon g-2 arising from the strong nuclear force, the hadronic vacuum polarisation (HVP), is determined by replacing a part of the calculation by supplementary experimental data (“R-ratio”). However, recent advances have made it possible to calculate the HVP numerically from first principles using supercomputer simulations (“lattice QCD”) to competitive precision with the R-ratio results [3].  

Several groups working in Lattice QCD have recently been focussing on determining a specific part of the HVP (“window observable” [4]). This window observable is particularly suitable for high-precision lattice calculations, and can provide an important comparison between R-ratio and lattice QCD determinations of the HVP. As part of the international RBC/UKQCD collaboration, researchers from the Universities of Edinburgh and Southampton, with the help of DiRAC resources, have published the most precise result for the window observable to date [5]. This result is in good agreement with independent lattice QCD determinations by other collaborations (see blue squares in Figure 2). However, lattice QCD results are in tension with the same quantity determined from the R-ratio (green circle in Figure 2), indicating that the SM prediction for Muon g-2 may be larger than the value obtained using the R-ratio approach, which would bring the SM prediction for Muon g-2 closer to the experimental measurement.   

Going forward, it will be crucial to have several independent lattice QCD calculations of the full HVP with competitive precision to the R-ratio determination, to reliably scrutinise the SM prediction of Muon g-2. Further reduction of uncertainties are also required to match the experimental target precision, and will provide a stringent test of the Standard Model of Particle Physics. DiRAC resources will continue to play an important role in this endeavour.  

References 

[1] Muon g-2 Collaboration, Phys.Rev.Lett. 131 (2023) 16, 161802 

[2] T. Aoyama et al, Phys.Rept. 887 (2020) 1-166 

[3] Sz. Borsanyi et al, Nature 593 (2021) 7857, 51-55 

[4] RBC and UKQCD Collaborations, Phys.Rev.Lett. 121 (2018) 2, 022003 

[5] RBC and UKQCD Collaborations, Phys.Rev.D 108 (2023) 5, 054507