What Can Wobbling Muons Tell Us About the Particles in our Universe?

The Standard Model does not describe gravity, nor does it explain dark matter and dark energy, which constitute about 95% of the universe. It also doesn't explain particle mass differences or the absence of antimatter in the everyday world, suggesting a larger, more complete theory is needed.

The g-factor measures how strongly a particle interacts with a magnetic field. For a point-like particle, quantum mechanics predicts g=2. However, interactions with 'virtual particles' that constantly pop in and out of existence cause g to be slightly different from 2. The muon's heavier mass makes it more sensitive to these virtual particle corrections, including contributions from potential new physics.

Muons are injected into a magnetic storage ring where their spins precess. When a muon decays, it emits a positron. The energy of this positron is highest when emitted in the direction of the muon's spin. By counting positrons above an energy threshold, a 'wiggle plot' is created, showing oscillations whose frequency directly relates to the anomalous g-factor.

The Brookhaven experiment, conducted 20 years prior, measured a 3.7 sigma discrepancy between the muon's anomalous magnetic moment and the Standard Model prediction. While not a 'discovery' (which requires 5 sigma), it generated significant interest as a hint of new physics.

Fermilab aimed to achieve four times better precision than Brookhaven, delivering 20 times more muons and making numerous experimental improvements. The goal was to confirm Brookhaven's 3.7 sigma discrepancy and potentially reach the 5 sigma threshold for a new physics discovery.

The 50-foot diameter magnet, too fragile to break apart and too wide for typical roads, was moved on a custom-built frame. It traveled by barge down the Eastern Seaboard, around Florida, up the Gulf of Mexico, and into the Illinois river system, then was trucked the final 30 miles to Fermilab over three nights.

To prevent unconscious bias, the experiment was 'blinded.' A secret factor was applied to shift the data's time axis, preventing scientists from knowing the true g-factor result until all analyses were complete and unanimously approved. This ensures objectivity in the final reported value.

Fermilab's first result confirmed the Brookhaven finding, showing a value very close to the previous one. When combined with Brookhaven's data, the discrepancy with the Standard Model increased to 4.2 sigma, strengthening the evidence for new physics, though not yet a 5 sigma discovery.

The first result (Run 1) used only 6% of the total data planned. Fermilab has two more years of data (Run 2 and Run 3) in storage and is currently taking Run 4, with plans for Run 5 and potentially Run 6. They aim for 20 times the total data of Brookhaven, expecting to unblind Run 2 and 3 results in about a year.

The theoretical prediction for g-2 is produced by a large collaboration that scrutinizes different calculation methods and assigns uncertainties. While new lattice QCD calculations are emerging that pull the theoretical value closer to the experimental one, these are very new and still under intense community scrutiny, requiring validation.

Five sigma is the gold standard for proclaiming a discovery in particle physics. It means there's a 1 in 1.7 million chance that the observed result is a mere statistical fluctuation if the true answer were the Standard Model prediction. This extremely low probability provides high confidence in a discovery.