Ref. [8] is R. Aliberti et al., The anomalous magnetic moment of the muon in the Standard Model: an update, Phys. Rept. 1143 (2025) 1 [arXiv:2505.21476].
A paper on the latest developments of calculating muon g-2 (the anomalous magnetic moment of the muon which can be calculated in the Standard Model from first principles) in the latest BMW group calculation not only updates their calculation to be more precise (and consistent with the high precision experimental results), but also provide excellent background for the entire enterprise of calculating muon g-2 and comparing it to the experimental results.
The overview of the paper is as follows:
Almost twenty years ago, physicists at Brookhaven National Laboratory measured the magnetic moment of the muon with a remarkable precision of 0.54 parts per million (ppm) [20]. Since that time, the reference Standard Model prediction forth is quantity has exhibited a persistent discrepancy with experiment of more than three sigma [9]. This raises the tantalising possibility of undiscovered forces or elementary particles. The attention of the world was drawn to this discrepancy when Fermilab presented a brilliant confirmation of Brookhaven’s measurement, which brought the discrepancy to 4.2 sigma [21]. In the meantime a very large-scale lattice QCD calculation of a key theoretical contribution was performed by the Budapest-Marseille-Wuppertal (BMW) collaboration [3], as seen in Fig. 1. This result significantly reduces the difference between theory and experiment, suggesting that new physics may not be needed to explain the experimental results. However, it simultaneously introduces a new discrepancy with the existing data-driven determination of this contribution.
Since then, the experimental [2] results have been updated with significantly improved precision, and the lattice result has been independently confirmed by other lattice collaborations. At the same time, new developments in the data-driven inputs that the lattice calculations replace [17–19] lead to a significant spread in the results depending on what inputs are taken. This has culminated in an updated theory prediction based on the lattice results instead of the data-driven determinations, as seen in Fig. 1.
In these proceedings, I present a new hybrid calculation that combines an update to the most precise lattice results with data-driven inputs in a low-energy region where the observed discrepancies are not present. This new result leads to aprediction that differs from the experimental measurement by only 0.5𝜎, providing a remarkable validation of the Standard Model to 0.31 ppm.
As Table 1 shows, the main problem is how to more precisely measure the Hadronic Vacuum Polarization (HVP) component more precisely.
According to the abstract:
The latest results from the Budapest-Marseille-Wuppertal (BMW) and DMZ collaborations, . . . [make] a determination of the hadronic vacuum polarisation contribution to a precision of 0.45%. [i.e. from ± 6.1 to ± 3.2.]
This new calculation is about twice as precise as the previous HVP calculation.
The conclusion of the paper states that:
Recent lattice QCD results have surpassed the precision of all other theoretical predictions of the hadronic vacuum polarisation contribution to the muon magnetic moment. When taken together with the latest theory consensus for the other contributions [8], these results show excellent agreement with the latest experimental measurements [2]. This a remarkable success for quantum field theory, bringing together diverse computational tools to include all aspects of the Standard Model in a single calculation that validates the Standard Model to 0.31 ppm.
As a practical matter, this further tightens global constrains on low to medium energy deviations from the Standard Model.
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