Like electrons, muons have a negative electric charge and a quantum property called spin, which causes the particles to act like tiny, wobbling tops when placed in a magnetic field. The stronger the magnetic field, the faster a muon wobbles.
The Standard Model, developed in the 1970s, is humankind’s best mathematical explanation for how all the particles in the universe behave and predicts the frequency of a muon’s wobbling with extreme precision. But in 2001, the Brookhaven National Laboratory in Upton, New York, found that muons seem to wobble slightly faster than the Standard Model predicts.
Now, two decades later, Fermilab’s Muon g-2 experiment has done its own version of the Brookhaven experiment—and it has seen the same anomaly. When researchers combined the two experiments’ data, they found that the odds of this discrepancy simply being a fluke are roughly 1 in 40,000, a sign that extra particles and forces could be affecting the muon’s behavior.
“This has been a long time coming,” says University of Manchester physicist Mark Lancaster, a member of the Muon g-2 collaboration, a team of more than 200 scientists from seven countries. “Many of us have been working on it for decades.”
By the strict standards of particle physics, the results aren’t a “discovery” just yet. That threshold won’t be reached until the results achieve a statistical certainty of five sigma, or a 1-in-3.5 million chance that a random fluctuation caused the gap between theory and observation, rather than a true difference.
The new results—which will be published in the scientific journals Physical Review Letters, Physical Review A&B, Physical Review A, and Physical Review D—are based on just 6 percent of the total data the experiment is expected to collect. If Fermilab’s results stay consistent, reaching five sigma could take a couple of years. “The attitude to take is sort of cautious optimism,” says Nima Arkani-Hamed, a theoretical physicist at the Institute for Advanced Study in Princeton, New Jersey, who wasn’t involved with the research.
Already, Fermilab’s results amount to the biggest clue in decades that physical particles or properties exist beyond the Standard Model. If this disagreement with the Standard Model persists, then the work “is Nobel Prize-worthy, without question,” says Free University of Brussels physicist Freya Blekman, who wasn’t involved with the research.
A model of everything
The Standard Model is arguably the most successful scientific theory, capable of stunningly accurate predictions of how the universe’s fundamental particles behave. But scientists have long known that the model is incomplete. It’s missing a description of gravity, for one, and it says nothing about the mysterious dark matter that seems to be strewn throughout the cosmos.
To figure out what lies beyond the Standard Model, physicists have long tried to push it to its breaking point in lab experiments. However, the theory has stubbornly passed test after test, including years of high-energy measurements at the Large Hadron Collider (LHC), which in 2012 found a particle that had been predicted by the Standard Model: the Higgs boson, which plays a key role in giving mass to some other particles.
Unlike the LHC, which smashes particles together to make new kinds of particles, Fermilab’s Muon g-2 experiment measures known particles to extreme precision, searching for subtle deviations from Standard Model theory.
“The LHC, if you like, is almost like smashing two Swiss watches into each other at high speed. The debris comes out, and you try to piece together what’s inside,” Lancaster says. “We’ve got a Swiss watch, and we watch it tick very, very, very, very painstakingly and precisely, to see whether it’s doing what we expect it to do.”
The muon is just about the perfect particle to monitor for signs of new physics. It survives long enough to be studied closely in the lab—though still only millionths of a second—and while the muon is expected to behave a lot like the electron, it’s 207 times more massive, which provides an important point of comparison.
For decades, researchers have taken a close look at how muons’ magnetic wobbles are affected by the influence of other known particles. On the quantum scale—the scale of individual particles—slight energy fluctuations manifest as pairs of particles that pop in and out of existence, like suds in a vast bubble bath.
According to the Standard Model, as muons mingle with this foamy background of “virtual” particles, they wobble roughly 0.1 percent faster than you’d expect. This extra boost to the muon’s wobble is known as the anomalous magnetic moment.
The Standard Model’s prediction is only as good as its inventory of the universe’s particles, however. If the universe contains additional heavy particles, for example, they would tweak the anomalous magnetic moment of the muon—possibly even enough to measure in the lab.
Studying the muon is “almost the most inclusive probe of new physics,” says Muon g-2 team member Dominik Stöckinger, a theorist at Germany’s Dresden University of Technology.
Muon beams and magnetic fields
The Muon g-2 experiment starts with a beam of muons, which scientists make by smashing pairs of protons together and then carefully filtering through the subatomic debris. This muon beam then enters a 14-ton magnetic ring that originally was used in the Brookhaven experiment, shipped by barge and truck from Long Island to Illinois in 2013.
As the muons go round and round this storage ring, which has a uniform magnetic field, the wobbling muons decay into particles that smack into a set of 24 detectors along the track’s inner wall. By tracking how often these decay particles hit the detectors, researchers can figure out how quickly their parent muons were wobbling—a bit like figuring out a distant lighthouse’s rotation speed by watching it dim and brighten.
Muon g-2 is trying to measure the muon’s anomalous magnetic moment to an accuracy of 140 parts per billion, four times better than the Brookhaven experiment. At the same time, scientists had to make the best Standard Model prediction possible. From 2017 to 2020, 132 theorists led by the University of Illinois’s Aida El-Khadra worked out the theory’s prediction of muon wobble with unprecedented accuracy—and it was still lower than the measured values.
Because the experiment’s stakes are so high, Fermilab also took steps to eliminate bias. The experiment’s key measurements rely on the precise time that its detectors pick up signals, so to keep the scientists honest, Fermilab shifted the experiment’s clock by a random number. This change tweaked the data by an unknown amount that would be corrected for only after the analysis was complete.
The only records of this clock-shifting random number were on two handwritten pieces of paper that were kept in locked cabinets at Fermilab and the University of Washington in Seattle. In late February, these envelopes were opened and revealed to the team, which let them figure out the experiment’s true results on a live Zoom call.
“We were all really ecstatic, excited, but also shocked—because deep down, I think we’re all a little bit pessimistic,” says Muon g-2 team member Jessica Esquivel, a postdoctoral researcher at Fermilab.
The new Fermilab results provide an important clue to what might lie beyond the Standard Model—but theorists trying to find new physics don’t have endless space to explore. Any theory that tries to explain Muon g-2’s results must also account for the lack of new particles discovered by the LHC.
In some of the proposed theories that thread this needle, the universe contains several types of Higgs bosons, not just the one included in the Standard Model. Other theories invoke exotic “leptoquarks” that would cause new kinds of interactions between muons and other particles. But because many of these theories’ simplest versions have been ruled out already, physicists “have to kind of think in unconventional ways,” Stöckinger says.
Coincidentally, news of the Fermilab results comes two weeks after another lab—CERN’s LHCb experiment—found independent evidence of misbehaving muons. The experiment monitors short-lived particles called B mesons and tracks how they decay. The Standard Model predicts that some of these decaying particles spit out pairs of muons. But LHCb has found evidence that these muon-spawning decays occur less often than predicted, with odds of a fluke in the experiment at roughly one in a thousand.
Like Fermilab, LHCb needs more data before claiming a new discovery. But even now, the combination of the two results has physicists “jumping up and down,” El-Khadra says.
The next step is to replicate the results. Fermilab’s findings are based on the experiment’s first run, which ended in mid-2018. The team is currently analyzing two additional runs’ worth of data. If these data resemble the first run, they could be enough to make the anomaly a full-blown discovery by the end of 2023.
Theorists also are beginning to poke and prod at the Standard Model’s prediction, especially the parts that are notoriously tricky to calculate. New supercomputer methods called lattice simulations should help, but early results disagree slightly with some of the values that El-Khadra’s team included in its theoretical calculation. It will take years to sift through these subtle differences and see how they affect the hunt for new physics.
For Lancaster and his colleagues, the years of work ahead are well worth it—especially given how far they’ve come.
“When you go and tell people, I’m going to try to measure something to better than one part per million, they sometimes look at you a little bit odd … and then when you say, it’s gonna take 10 years, they go, You must be mad,” he says. “I think the message is: persevere.”