The Muon g-2 experiment (pronounced “gee minus two”) is designed to look for tantalizing hints of physics beyond the Standard Model of particle physics. It does this by measuring the magnetic field (aka the magnetic moment) generated by a subatomic particle known as the muon. Back in 2001, an earlier run of the experiment at Brookhaven National Laboratory found a slight discrepancy, hinting at possible new physics, but that controversial result fell short of the critical threshold required to claim discovery.
Now, Fermilab physicists have completed their initial analysis of data from the updated Muon g-2 experiment, showing “excellent agreement” with the discrepancy Brookhaven recorded. The results were announced today in a new paper published in the journal Physical Review Letters.
As I wrote at Nautilus in 2013, before the muon was first discovered in 1936, physicists thought their model of particle physics was pretty much complete. Then Caltech physicists Carl Anderson and Seth Neddermeyer, who were studying cosmic rays, noticed that some particles didn’t curve as expected when they passed through a magnetic field. A year later, cloud chamber experiments confirmed that these particles were, indeed, new. It was such a surprising development that I.I. Rabi famously declared, “Who ordered that?”
That discovery led to a much more complicated version of the Standard Model of particle physics, with not one, not two, but three generations of matter particles (quarks and leptons), not to mention three varieties of force-carrying particles (gauge bosons)—a veritable particle zoo. We just don’t encounter those second and third generations very often outside of particle accelerators because they are so heavy that they decay into their first-generation cousins almost immediately. The Nobel Prize-winning discovery of the Higgs boson in 2012 was the final piece of the Standard Model’s particle zoo to be experimentally verified.
But that is not the end of the story. The Standard Model works just fine at the subatomic scale, but it pretty much ignores gravity (which is too weak to have much of an impact on the quantum realm). Physicists have yet to come up with a theory of quantum gravity that works within that framework, so we essentially have two different “rule books” for the subatomic and macro scale worlds: quantum mechanics and general relativity, respectively. The model also doesn’t account for dark matter. And while physicists hoped ongoing experiments at the Large Hadron Collider would find evidence for more exotic particles and forces (such as supersymmetry), to date there have only been—at best—tiny hints of physics beyond the Standard Model. That’s where the latest muon-related results come in.
The muon (a member of the lepton classification) is the heavier second-generation cousin of the electron—the tau is the third-generation cousin—and that makes muons particularly sensitive to virtual particles popping in and out of existence in the quantum vacuum, since they can briefly interact with those virtual particles. “Muons are special,” Fermilab physicist Chris Polly—a co-author of the new paper and co-spokesperson for the Muon g-2 collaboration—told Symmetry magazine in 2012. “They are light enough to be produced copiously, yet heavy enough that we can use them experimentally to uniquely probe the accuracy of the Standard Model.”
The muon has an internal magnet, as well as an angular momentum (spin); “g” (the “proportionality constant”) refers to the ratio between the internal magnet’s strength and the rate of gyration. The muon’s magnet would typically rotate to align along the axis of the magnetic field, much like a compass does in Earth’s magnetic field. But because of the muon’s angular momentum, this doesn’t happen; instead, the field exerts a torque on the muon’s spinning magnetic moment, causing it to precess around the axis of the field. Because the muon can interact with virtual particles, the value for g differs from the classical value of 2 by about 0.1 percent—hence it’s technically known as the anomalous magnetic moment of the muon.
When Polly was still a graduate student, he worked on the original Muon g-2 experiment at Brookhaven, which ran from 1997 to 2001. The experiment was designed to make precise measurements of the wobble that occurs when a muon is placed in a magnetic field in response to all the virtual particles popping in and out of existence. If the value of the wobble disagrees with the exacting prediction of the Standard Model, that’s a strong hint that some new physics might be involved.
The final result, announced in 2006, found an intriguing discrepancy with the predicted value of the Standard Model: the muon’s measured magnet moment came in at a smaller value. Even more intriguing, that result was deemed a 3.7-sigma effect. (A signal’s strength is determined by the number of standard statistical deviations, or sigmas, from the expected background in the data, producing a telltale “bump.” This metric is often compared to a coin landing on heads several tosses in a row. A three-sigma result is a strong hint. The gold standard for claiming discovery is a five-sigma result, comparable to tossing 21 heads in a row, for example.)
That said, three-sigma results, while tantalizing, pop up all the time in particle physics, and more often than not, they disappear once more data is added to the mix. So Fermilab revived the Muon g-2 experiment in hopes of either confirming or refuting the discrepancy once and for all.
Since it would have been financially prohibitive to build the massive storage ring magnet from scratch, Fermilab opted to re-use Brookhaven’s (as well as several subsystems). Moving such a massive piece of equipment (it measures 50 feet in diameter) required travel by barge, looping around Florida, going up the Tennessee-Tombigbee waterway, and finally maneuvering up the Illinois River to Lemont, Illinois. Then the storage ring was transferred to a specially designed truck to make its final trip to Fermilab.
Fermilab’s accelerators smash a beam of protons into a fixed target, producing a shower of subatomic particles. Some of these are pions, which quickly decay into muons with spins all pointing in the same direction. Magnets then steer those decaying pions into a triangular tunnel, and once all the pions have decayed, the resulting muons are fed into the massive storage ring. Muons don’t stick around for long; while circulating within the storage ring, they can last for about 64 microseconds—just long enough to enable physicists to make precision measurements.
All those muons orbit the ring at velocities approaching the speed of light, eventually decaying into neutrinos and positrons. Neutrinos (aka ghost particles) rarely interact with anything, so they are not detected. But the positrons can be detected. And they will all be traveling in whatever direction the muons’ internal magnets were pointing, giving physicists a means to measure just how much that magnetic moment was precessing.
These latest results from Fermilab are drawn from data collected during the first year that the Muon g-2 experiment was operational, so the margin for error is roughly the same right now as the earlier Brookhaven measurement. However, the two results match quite closely, and taken together, they boost the statistical significance to 4.2 sigma—teetering just on the verge of the threshold required for discovery. That means there is only a 1 in 40,000 chance that this is due to a statistical fluctuation. “After the 20 years that have passed since the Brookhaven experiment ended, it is so gratifying to finally be resolving this mystery,” said Polly.
Fermilab is also using the same storage ring as Brookhaven, albeit with multiple upgrades in place to achieve a fourfold improvement in the accuracy of the measurements (a precision of 140 parts per billion). The next step would be to try to find independent confirmation from an experiment that measures the muon’s magnetic moment via very different means—perhaps at the Japan Proton Accelerator Research Complex (J-PARC), whose Rapid Cycling Synchrotron (RCS) also boasts powerful proton beams designed to create beams of muons for particle experiments.
For those hungry for the hardcore technical details, there were two accompanying papers from the collaboration. One, published in Physical Review A, focuses on the intensive monitoring, calibration, and weighting that was done to make such a precise measurement possible. The second, published in Physical Review D, gives technical details on the calculations performed to extract the measurement from four different data sets.
Fermilab’s announcement already has particle theorists scrambling to incorporate those findings into their models. At least one group of theorists has calculated a new estimate of the muon’s magnetic moment to bring it more in line with the Standard Model, according to a new paper published in the journal Nature. That makes the muon’s magnetic moment less mysterious, since there is no need for new physics to explain the Brookhaven and Fermilab measurements.
“If our calculations are correct and the new measurements do not change the story, it appears that we don’t need any new physics to explain the muon’s magnetic moment—it follows the rules of the Standard Model,” said co-author Zoltan Fodor, a physicist at Penn State University. “Although the prospect of new physics is always enticing, it’s also exciting to see theory and experiment align. It demonstrates the depth of our understanding and opens up new opportunities for exploration. Our finding means that there is a tension between the previous theoretical results and our new ones. This discrepancy should be understood. We have many years of excitement ahead of us.”