Fermilab scientists are measuring the muon’s behavior to such extraordinary precision because the particle provides a powerful test of the Standard Model, the modern theory that describes how the universe’s known particles and forces work on a fundamental level.

For all its success, the Standard Model is jarringly incomplete. It offers no description of gravity, nor does it account for “dark matter,” the mysterious stuff that gravitationally outmuscles ordinary matter at cosmic scales. And according to the Standard Model, the universe ought to contain equal amounts of regular matter and its counterpart, antimatter. But those substances annihilate on contact, so if this were true, none of our atoms would exist.

“All we’re trying to do is try to identify solid evidence — you know, a pointer — for what these new types of interactions or particles are,” said Muon g-2 member Mark Lancaster, a physicist at the University of Manchester. “We know they have to exist, because if they didn’t exist, we wouldn’t be here.”

The latest data from Fermilab’s Muon g-2 experiment has been analyzed by an international team of more than 180 scientists. It backs up previous results seen as evidence that the muon could be disobeying the Standard Model. If such misbehavior were confirmed, it would provide a tantalizing, long-sought clue as to what lies beyond our current understanding.

However, as precise as Fermilab’s new measurement is, today isn’t a champagne moment for physicists seeking the unknown. To claim an ironclad deviation from the Standard Model, everyone has to agree on what that theory predicts, and in a dramatic twist, they no longer do.

A flurry of papers published since 2021 has unsettled the previous Standard Model prediction for the muon, leaving theorists with several gnarly discrepancies to resolve — and experimentalists ready to watch the show.

“I’m sort of, like, leaning back on my chair with my popcorn,” said Muon g-2 member Paolo Girotti, a postdoctoral researcher at Italy’s National Institute of Nuclear Physics.

The way a muon wobbles

Developed in the early 1970s, the Standard Model of particle physics generates extremely accurate predictions for three of the known fundamental forces, such as electromagnetism, and the 17 known types of particles that make up the universe’s building blocks, including the electron, the photon and the muon.

To probe the Standard Model’s limits, scientists have turned to the muon. These particles have electrical charge like electrons, and they have a quantum property called spin. Combined, the two traits make muons act like small magnets, which causes them to wobble like spinning tops when placed in a magnetic field.

The rate of the muon’s wobble depends on how it interacts with all the other known particles and forces, so if there’s something in the universe the Standard Model currently doesn’t account for, it could be nudging the muon, too — giving it extra oomph that Fermilab could detect.

For the past two decades, physicists have seen hints of such extra nudges of the muon, including evidence collected between 1997 and 2001 by Brookhaven National Laboratory in New York. Fermilab, founded in 1967 and named for physicist Enrico Fermi, proposed a follow-on search in 2008. In 2013, the facility acquired a key piece of the Brookhaven experiment: a 50-foot-wide ring lined with superconducting magnets, designed to function as a track of sorts for a beam of circling muons.

After five years of major upgrades to the ring and its facilities, Fermilab started collecting its first run of muon data in 2018. Three years later, Fermilab announced its first results from the experiment — and excitement intensified. Researchers not only saw signs that the muon was wobbling weirdly in comparison to the Standard Model prediction at that time, but their data also fell in line with Brookhaven’s numbers.

The new results unveiled Thursday, which follow another round of intensive upgrades to the experiment, also match Fermilab’s 2021 results and the earlier Brookhaven ones, reducing the chances that they are seeing errors in their measurements.

“This is the most precise measurement of a quantity in particle physics ever [done] using an accelerator, which is brilliant. I mean, it’s an amazing achievement,” said Muon g-2 member Alex Keshavarzi, a physicist at the University of Manchester.

But there is a catch: Even as the Muon g-2 team members were hard at work on their experiment, theorists were taking another crack at the math underlying the Standard Model’s prediction — and now it’s the theory that needs adjustment.

‘Ready for the showdown’

The Standard Model’s math can be astonishingly complex. To understand a particle’s property to extreme precision, physicists must compute all the relevant ways that the known particles and forces can interact with each other, no matter how rare or Rube Goldberg-esque those dalliances may be.

For the muon’s wobble in particular, the Standard Model’s prediction must account for a subtle, mind-bending process known prosaically as “hadronic vacuum polarization.”

The gist is that in an instant, muons can emit and reabsorb photons of light that can get up to all sorts of mischief before they get reabsorbed. Most annoyingly of all, one of these photons can temporarily split into a particle called a quark and its antimatter equivalent, which can strongly interact with themselves and any other fleeting particles nearby in a dizzyingly large number of ways, nudging the muon in the process.

Theorists have devised two main ways to solve the problem. The last major Standard Model prediction of the muon’s wobble, which was published in 2020 by a team of more than 130 physicists, used the more traditional “dispersive” approach, which relies on reams of data collected on electrons as they annihilate their antimatter equivalents. But since 2020, theorists have refined a newer method called the “lattice” approach, which estimates aspects of the muon’s behavior using supercomputer simulations.

Bizarrely, most of the dispersive and lattice calculations done so far seem to disagree on parts of the Standard Model prediction for the muon’s behavior, and nobody quite knows why. Most dispersive results in combination suggest a fairly glaring mismatch between theory and experiment (with one recent, vexing exception). By contrast, today’s most precise, full-bore lattice calculation suggests a Standard Model prediction that’s closer to the muon’s observed wobble.

“We can’t take that lying down — we need to figure out what’s happening there,” said University of Illinois at Urbana-Champaign physicist Aida El-Khadra, the steering committee chair of the Muon g-2 Theory Initiative, the group that developed the 2020 prediction. El-Khadra wasn’t involved with the new Fermilab results.

Where the theory will settle out “is the million-dollar question right now,” added University of Regensburg physicist Christoph Lehner, a steering committee co-chair of the Muon g-2 Theory Initiative who also wasn’t involved with the Fermilab results. “Unfortunately, the answer very likely is that we have to wait a little bit.”

It’s perhaps a more frustrating situation than physicists had hoped for. But as they attempt to peer into the universe’s unknown corners, researchers say they can’t be too careful. The Fermilab Muon g-2 experiment stopped collecting data last month, and by the end of 2025, it plans to deliver a final result up to twice as precise as Thursday’s measurement, with roughly four times more data backing it up.

Meanwhile, theorists hope to understand and partially resolve the mismatched calculations by 2025 in hopes of catching up with experiments and possibly revealing, if the universe wills it, hidden worlds within the quantum realm.

“We’ll be ready for the showdown,” El-Khadra said.