A couple of weeks ago, a new lattice QCD calculation by a group known as BMW tried to tip the BSM community into depression by reporting that they could resolve the tension between theory and experiment. Their new result had a tiny uncertainty (of 0.6%), much smaller than any previous lattice computation.
As I've mentioned here several times, the anomalous magnetic moment of the muon is one of the most precisely measured quantities in the world, and its prediction from theory has for several years been believed to be slightly different from the measured one. Since the theory was thought to be well understood and rather "clean", with uncertainty similar to the experimental one (yet the two values being substantially different) it has long been a hope that the Standard Model's cracks would be revealed there. Two new experiments should tell us about this, including an experiment at Fermilab that should report data this year with potentially four times smaller experimental uncertainty than the previous result; An elementary decription of the physics and experiment is given on their website.
However, there were always two slightly murky parts of the theory calculation, where low-energy QCD rears its head appearing in loops. A nice summary of this is found in e.g. this talk from slide 33 onwards, and I will shamelessly steal some figures from there. These QCD loops appear as
The calculation of both of these is tricky, and the light-by-light contribution is believed to be under control and small. The disagreement is in the HVP part. This corresponds to mesons appearing in the loop, but there is a clever trick called the R-ratio approach, where experimental cross-section data can be used together with the optical theorem to give a very precise prediction. Many groups have calculated this with results that agree very well.
On the other hand, it should be possible to calculate this HVP part by simulating QCD on the lattice. Previous lattice calculations disagreed somewhat, but also estimated their uncertainties to be large, comparable to the difference between their calculations and the experimental value or the value from the R-ratio. The new calculation claims that, with their new lattice QCD technique, they find that the HVP contribution should be large enough to remove the disagreement with experiment, with a tiny uncertainty. The paper is organised into a short letter of four pages, and then 79 pages of supplementary material. However, they conclude the letter with "Obviously, our findings should be confirmed –or refuted– by other collaborations using other discretizations of QCD."
Clearly I am not qualified to comment on their uncertainty estimate, but if the new result is true then, unless there has been an amazing statistical fluke across all groups performing the R-ratio calculation, someone has been underestimating their uncertainties (i.e. they have missed something big). So it is something of a relief to see an even newer paper attempting to reconcile the lattice and R-ratio HVP calculations, from the point of view of lattice QCD experts. The key phrase in the abstract is "Our results may indicate a difficulty related to estimating uncertainties of the continuum extrapolation that deserves further attention." They perform a calculation similar to BMW but with a different error estimate; they give a handy comparison of the different calculations in this plot:
Update 12/03/20: A new paper yesterday tries to shed some new light on the situation: apparently it has been known since 2008 that an HVP explanation of the muon anomalous magnetic moment discrepancy was unlikely, because it leads to other quantities being messed up. In particular, the same diagrams that appear above also appear in the determination of the electroweak gauge coupling, which is precisely measured at low energies from Thomson scattering, and then run up to the Z mass: $$ \alpha^{-1} (M_Z) = \alpha^{-1} (0) \bigg[ 1 - ... - \Delta \alpha^{(5)}_{\mathrm{HVP}} (M_Z) + ... \bigg] $$ where the ellipsis denotes other contributions. Adding the BMW lattice contribution there at low energies and extrapolating up, the new paper finds that the fit is spoiled for the W-boson mass and also an observable constructed from the ratio of axial and vector couplings to the Z-boson: $$ A_{\ell} = \frac{2 \mathrm{Re}[ g_V^{\ell}/g_A^{\ell}]}{1 + (\mathrm{Re} [g_V^{\ell}/g_A^{\ell}])^2}$$ The key plot for this observable is:
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