New muon g-2 calculation consistent with experiment

[ohwilleke]

TL;DR Summary

A July 2024 higher precision lattice QCD calculation of muon g-2 is closer than ever to the experimental measurement of muon g-2 last updated in August of 2023.

The updated BMW calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment a(μ) in the Standard Model is squarely consistent, at 0.9 sigma with the experimental measurement of muon g-2.

This agreement is found to be present despite the fact that its uncertainty in this new and improved HVP calculation is 40% smaller (producing a 31% reduction in the uncertainty of the overall theoretical calculation) and the fact that the 2023 experimental measurement has 55% less uncertainty, making agreement of the two values a harder to hit target.

The experimental value is based upon the first three phases of a six phase experiment. Phase four, whose results are tentatively expected late in 2024, will significantly reduce the uncertainty in the experimental result. The improvements from phases five and six are expected to be much smaller. The uncertainty in the experimental result is already about 42% smaller than the uncertainty in the calculation of the Standard Model predicted value. The experimentally measured value will probably continue to have less uncertainty than the Standard Model predicted value calculation for at least several years to come.

The bottom line value for the new 2024 BMW calculation is:

aµ = 116,592,019(38) × 10⁻¹¹.

Partial calculations confirm the BMW result vis-a-vis the partially experimentally based analysis in the so called "window" part of the calculation (as does the recent CMD-3 experimental measurement of the same experimental inputs that went into the "Theory Initiative" calculation):

The apparent discrepancy between the Theory Initiative calculation of the Standard Model prediction and the experimental results has been the source out countless papers proposing proposals for new physics. this discrepancy was a result of an inaccurate calculation of the Standard Model prediction for muon g-2 by the Theory Initiative. This was mostly a result of the incorporation of slightly inaccurate experimental data (regarding electron-positron annihilations that produce pion pairs) into their hadronic vacuum polarization calculation.

Muon g-2 is important because it a strong global test, at high precision, of the accuracy of all parts of the Standard Model at once. And, in this test, the experimentally measured result matches the theoretical calculation of muon g-2's value (at a precision of about 4 parts per ten million).

This rules out many kinds of new physics that a next generation particle collider could detect. But muon g-2 is less sensitive to new physics at energy scales higher than those of any of the proposed next generation particle colliders.

The paper presenting the new lattice QCD calculation of muon g-2 and its abstract are as follows:

We present a new lattice QCD calculation of the leading order hadronic vacuum polarization contribution to the muon anomalous magnetic moment a(μ). We reduce uncertainties compared to our earlier computation by 40%, arXiv:2002.12347. We perform simulations on finer lattices allowing for an even more accurate continuum extrapolation. We also include a small, long-distance contribution obtained using input from experiments in a low-energy regime where they all agree. Combined with other standard model contributions our result leads to a prediction that differs from the measurement of a(μ) by only 0.9 standard deviations. This provides a remarkable validation of the standard model to 0.37ppm.

A. Boccaletti, et al., "High precision calculation of the hadronic vacuum polarisation contribution to the muon anomaly" arXiv:2407.10913 (July 15, 2024).

The new paper also notes that:

In the near future we expect that other lattice collaborations will also provide precise calculations of a(LO-HVP)(µ) that can confirm or refute our results. Also, more data for the e+e− → π+π− cross section is expected soon.

For those of you who aren't visual learners (with values times 10^-11 shown below):

New BMW calculation (2024): 116,592,019(38)
Theory Initiative calculation (2020): 116,591,810(43)
BMW calculation (2020): 116,591,954(55)
World Experimental Average (2023) : 116,592,059(22)
Fermilab Run 1+2+3 data (2023): 116,592,055(24)
Combined measurement (2021): 116,592,061(41)
Brookhaven's E821 data (2006): 116,592,089(63)

QCD v. Non-QCD Calculations In Muon g-2

The QED + Electroweak (EW) predicted value (omitting the Hadronic Vacuum Polarization (HVP) and Hadronic Light by Light (HLbL) components, and before the latest QED component tweak) is: 116,584,872.53 (101). Thus, it accounts for only about 3% of the total uncertainty in the value of muon g-2. Given the experimental results, the implied combined hadronic (i.e. QCD) contribution to the total is about 7186.47 times 10^-11. This is 0.00616% of the total value, despite the fact that it is the source of 97% of the uncertainty in the calculation, because QCD calculations are vastly less precise than QED and weak force calculations.

Within the two QCD calculations, the Hadronic Vacuum Polarization calculation has a relative uncertainty of about 0.5% and accounts for the bulk of the QCD contribution, while the Hadronic Light by Light calculation has a relative uncertainty of a little less than 20%, but involves a much smaller total contribution to the whole.

Other Tweaks To The Muon g-2 Calculation

Two other tweaks in parts of the muon g-2 calculation have also been made and aren't included in the new paper. They reduce the difference between the theoretical calculation and the experimentally measured calculation to about 0.6 sigma, which is a precision of about 0.22 parts per million.

One is an increase of 14.8 x 10^-11, in the Hadronic light-by-light calculation from 2021, and also reduces the uncertainty in the latest BMW calculation of the total muon g-2 value (including its new HVP calculation) from ±38 x 10^-11 to ±37 x 10^-11.

The other is a reduction of about 0.06 x 10^-11 in the QED part of the calculation from April of 2024, which is a five sigma downward shift in that calculation. But it is immaterial to the overall muon g-2 calculation because the original calculation was already so precise.