Next week, on June 2, 2025, the final round of experimental results for muon g-2 will be announced. Ahead of that there is an update of the Muon g-2 White paper that got the Standard Model predicted value for muon g-2 badly wrong. The revised version acknowledges this mistake and remarks that the revised prediction is spot on with the experimental value of muon g-2.
The revised state of the art Standard Model prediction will still be about four times less precise than the experimentally measured value after June 3, 2025, however. The predicted value's uncertainty is greater than the experimentally measured uncertainty almost entirely due to the uncertainties in the QCD (quantum chromodynamics a.ka. strong force) calculation of the leading order hadronic vacuum polarization contribution to muon g-2.
These uncertainties are hard to reduce, since the values of the fundamental physical constants relevant to the calculation, like the value of the strong force coupling constant's value and the light quark masses, have uncertainties of the same magnitude as the total HVP calculation.
The consistency of the experimental value of muon g-2 and the value for it predicted in the Standard Model, is a broad global high precision measurement of the consistency of all parts of the low to medium energy scale Standard Model of Particle Physics with the real world.
The consistency which exists strongly disfavors the discovery of any beyond the Standard Model physics at a next generation particle collider (even though there one could cherry pick potential modifications of the Standard Model that haven't already been ruled out by other high energy physics data, that could have no impact on muon g-2, or would have an impact that is too negligible to discern).
This summary chart appears in the introduction to the paper:
A chart from the conclusion shows how the old White Paper Standard Model prediction for muon g-2 and the new one differ.
We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, aμ, updating the first White Paper (WP20) [1].
The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two.
The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the e+e−→π+π− cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%.
Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads a(SM)(μ) = 116592033(62) × 10^−11 (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1-3 of E989 at Fermilab, one finds a(exp)(μ)−a(SM)(μ) = 26(66) × 10^−11, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 is expected to be around 140 ppb, which is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.
R. Aliberti, et al., "The anomalous magnetic moment of the muon in the Standard Model: an update" arXiv:2505.21476 (May 27, 2025) (188 pages).
The conclusion explains that:
By comparing the uncertainties of Eq. (9.5) and Eq. (9.4) it is apparent that the precision of the SM prediction must be improved by at least a factor of two to match the precision of the current experimental average, which will soon be augmented by the imminent release of the result based on the final statistics of the E989 experiment at Fermilab. We expect progress on both data-driven and lattice methods applied to the hadronic contributions in the next few years. Resolving the tensions in the data-driven estimations of the HVP contribution is particularly important, and additional experimental results combined with further scrutiny of theory input such as from event generators should provide a path towards this goal. Further progress in the calculation of isospin-breaking corrections, from both data-driven and lattice-QCD methods, should enable a robust SM prediction from τ data as well. For lattice-QCD calculations of HVP continuing efforts by the world-wide lattice community are expected to yield further significant improvements in precision and, hopefully, even better consolidation thanks to a diversity of methods. The future focus will be, in particular, on more precise evaluations of isospin-breaking effects and the noisy contributions at long distances.
The role of aµ as a sensitive probe of the SM continues to evolve. We stress that, even though a consistent picture has emerged regarding lattice calculations of HVP, the case for a continued assessment of the situation remains very strong in view of the observed tensions among data-driven evaluations. New and existing data on e+e− hadronic cross sections from the main collaborations in the field, as well as new measurements of hadronic τ decays that will be performed at Belle II, will be crucial not only for resolving the situation but also for pushing the precision of the SM prediction for aµ to that of the direct measurement. This must be complemented by new experimental efforts with completely different systematics, such as the MUonE experiment, aimed at measuring the LO HVP contribution, as well as an independent direct measurement of aµ, which is the goal of the E34 experiment at J-PARC. The interplay of all these approaches, various experimental techniques and theoretical methods, may yield profound insights in the future, both regarding improved precision in the SM prediction and the potential role of physics beyond the SM. Finally, the subtleties in the evaluation of the SM prediction for aµ will also become relevant for the anomalous magnetic moment of the electron, once the experimental tensions in the determination of the fine-structure constant are resolved.
Basically, the conclusion calls for scientists to get to the bottom of why the experiments that were used as a basis for the first White Paper prediction were wrong, and hopes against all reasonable expectations that the process of doing that will reveal new physics.
The paper's claim that the uncertainty in the Standard Model prediction can be cut dramatically "in the next few years" is pretty much wishful thinking.
This paper doesn't address in detail how completely this result ruled out new physics, but further papers by unaffiliated scientists will no doubt do just that not long after the new experimental results are released next week.
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