A Muon g-2 Recap

The introduction of an otherwise unimpressive new muon g-2 paper provides a nice recap of where the physics world is in terms of experimental measurements and theoretical calculations of the anomalous magnetic moment of the muon, muon g-2.

In particular, it notes the not widely known fact that the data underlying the "data driven" Standard Model predicted value showing a 4.2 sigma discrepancy with the experimental value itself shows large discrepancies that bely the claimed low uncertainty associated with this method.

The experimental value of the muon anomalous magnetic moment measured recently by the FNAL Muon g-2 experiment confirms the old BNL result and adds significance to the long standing discrepancy between the measured value and the standard model (SM) prediction, now raised to 4.2 σ. Currently, the world average for this discrepancy is 

∆aµ ≡ a exp µ − a SM µ = (2.51 ± 0.59) · 10^−9 . (1.1) 

The SM estimate recommended by the Muon g-2 Theory Initiative relies on a data-driven approach that makes use of experimental measurements of the σhad = σ(e +e − → hadrons) cross section to determine the hadronic vacuum polarization contribution a HVP µ. This is the most uncertain input in the prediction for aµ and, due to its non-perturbative nature, improving in precision is a difficult task. Apart for the uncertainty, one can also wonder to which level the adopted value can be considered reliable, since determinations of a HVP µ using data from different experiments exhibit a certain disagreement. In particular, KLOE and BaBar disagree at the level of 3σ, especially in the π +π − channel that accounts for more than 70% of the value of a HVP µ, and while BaBar data favour smaller values of ∆aµ, KLOE data pull to increase the discrepancy. 

[1] Due to relatively larger errors, there is instead agreement within 1.5 σ between KLOE and CMD-2, SND, BES-III. 

The HVP contribution can also be determined from first principles by means of lattice QCD techniques. However, until recently, the uncertainties in lattice results were too large to allow for useful comparisons with the data-driven results. A first lattice QCD determination of a HVP µ with subpercent precision was recently obtained by the BMW collaboration a HVP µ = 707.5(5.5) × 10^−10. It differs from the world average obtained from the data-driven dispersive approach by 2.1 σ and, in particular, it would yield a theoretical prediction for aµ only 1.3 σ below the measurement.[2] 

[2] Other lattice determinations also tend to give larger a HVP µ central values although with considerably larger errors. 

. . . [N]ew high statistics measurements of σhad, and in particular in the π +π − channel, that might be soon provided by the CMD-3 collaboration, as well as new high precision lattice evaluations, which might confirm or correct the BMW result, will be of crucial importance not only to strengthen or resize the evidences for a (g − 2)µ anomaly, but also to asses the status of the related additional discrepancies. 

From arXiv:2112.09139.

Personally, I am quite confident that the BMW result, with minor modifications, will turn out to be the correct Standard Model prediction. But it will take time for the scientific consensus to catch up.

If this is true, there is no muon g-2 anomaly and hence, no hint from it of new physics by this very global measure of discrepancies from the Standard Model. This basically rules out most kinds of new physics at the electro-weak scale or anywhere close to it at higher energies.