There are two leading calculations of the Standard Model prediction for the anomalous magnetic moment of the muon, called muon g-2, which is an inherent electromagnetic property of muons (a "heavy" electron) that can, in theory, be calculated exactly in the Standard Model.
This calculation has three main components, the electromagnetic contribution, which is the primary contribution to the overall value and is easy to calculate and extremely precise, the weak force contribution, which is much smaller contribution which is harder to calculate and not quite as precise (to a great extent because some of the physically measured constants that go into that calculation haven't been measured as precisely), and the strong force (i.e. QCD) contribution which is like the weak force contribution a small part of the total in absolute terms, that is profoundly difficult to calculate and is the source of the lion's share of the uncertainty in the calculation of muon g-2.
The small contribution to the muon g-2 which involves considering virtual quarks and gluons that impact the electromagnetic properties of muons when you are being exceedingly rigorous is hard to determine because QCD calculations are exceedingly difficult (for reasons I've explained in prior posts at this blog) and the because the underlying physical constants that go into them (such as the strong force coupling constant and light quark masses) haven't been measured very precisely. The hadronic vacuum polarization (HVP) part of the muon g-2 calculation is particularly difficult to calculate and is a QCD component of the muon g-2 calculation.
Both theoretical calculations agree on the electromagnetic and weak force contributions, are reasonably close to each other (although the differences are statistically very significant), and match the experimentally measured results at roughly the part per hundred million level.
One of the calculations (by the BMW group) matches the experimental result and is purely theory driven, the other (by the Theory Initiative group) is "data driven" and replaces some of the HVP calculations needed to determine muon g-2 in the Standard Model with experimental data that they think should replicate the theoretical calculations that this approach doesn't calculate directly.
A new (admittedly quite technical) lattice QCD study suggests that the data driven component is of the Theory Initiative calculation is inaccurately determining the Standard Model contribution to the HVP contribution to muon g-2 for which it attempts to substitute experimentally data for some reason.
Muon g-2 is an observable quantity that is sensitive globally to almost everything in the Standard Model, at least at "low energies" at the scale of what can be seen at particle colliders and below, although new physics at the extremely high energies of the time immediately after the Big Bang "decouple" from this observable.
If the correct Standard Model prediction for muon g-2 is consistent with the experimental measurement of muon g-2 (which has now been replicated at high precision), then there is very little room for "low energy" beyond the Standard Model physics (although they aren't entirely ruled out so long as their contributions to muon g-2 net out to zero), and the case for the completeness of the existing Standard Model is greatly heightened.
In contrast, if the correct Standard Model prediction for muon g-2 is significantly different from the experimental measurement of muon g-2 then there have to be "low energy" beyond the Standard Model physics out there to be discovered that give rise to the discrepancy of a well quantified magnitude, that should be accessible at the energy scales of current or next generation particle accelerators. The energy scales at which these new physics should arise is further constrained by the fact that, apart from potential lepton universality violations, we haven't seen them at the LHC so far.
Thus, if this discrepancy is real, "new physics" are just around the corner and there is a strong scientific motivation for building a next generation collider and for choosing the design more likely to identify the source of a muon g-2 anomaly with a particular magnitude.
This new study suggests that the "muon g-2 anomaly" arises because of a flawed calculation of the Standard Model prediction for this observable, arising from the "data driven" part of that prediction of the HVP contribution to muon g-2, and not new physics that is waiting to be imminently observed.
The paper and its abstract are as follows:
Euclidean time windows in the integral representation of the hadronic vacuum polarization contribution to the muon g−2 serve to test the consistency of lattice calculations and may help in tracing the origins of a potential tension between lattice and data-driven evaluations.
In this paper, we present results for the intermediate time window observable computed using O(a) improved Wilson fermions at six values of the lattice spacings below 0.1 fm and pion masses down to the physical value. Using two different sets of improvement coefficients in the definitions of the local and conserved vector currents, we perform a detailed scaling study which results in a fully controlled extrapolation to the continuum limit without any additional treatment of the data, except for the inclusion of finite-volume corrections. To determine the latter, we use a combination of the method of Hansen and Patella and the Meyer-Lellouch-Lüscher procedure employing the Gounaris-Sakurai parameterization for the pion form factor. We correct our results for isospin-breaking effects via the perturbative expansion of QCD+QED around the isosymmetric theory.
Our result at the physical point is a^win(μ)=(237.30 ± 0.79 stat ± 1.22 syst) × 10^−10, where the systematic error includes an estimate of the uncertainty due to the quenched charm quark in our calculation. Our result displays a tension of 3.8σ with a recent evaluation of a^win(μ) based on the data-driven method.
Marco Cè, et al., "Window observable for the hadronic vacuum polarization contribution to the muon g−2 from lattice QCD" arXiv:2206.06582 (June 14, 2022) (report number MITP-22-038, CERN-TH-2022-098).