Finding From Particle Research Could Break Known Laws of Physics

Evidence is mounting that a tiny subatomic particle called a muon is disobeying the laws of physics as we thought we knew them, scientists announced on Wednesday.

The best explanation, physicists say, is that the muon is being influenced by forms of matter and energy that are not yet known to science, but which may nevertheless affect the nature and evolution of the universe. The new work, they said, could eventually lead to a breakthrough in our understanding of the universe more dramatic than the heralded discovery in 2012 of the Higgs boson, a particle that imbues other particles with mass.

Muons are akin to electrons but far heavier. When muons were subjected to an intense magnetic field in experiments performed at the Fermi National Accelerator Laboratory, or Fermilab, in Batavia, Ill., they wobbled like spinning tops in a manner slightly but stubbornly and inexplicably inconsistent with the most precise calculations currently available. The results confirmed results in similar experiments at the Brookhaven National Laboratory in 2001 that have tantalized physicists ever since.

“This quantity we measure reflects the interactions of the muon with everything else in the universe,” said Renee Fatemi, a physicist at the University of Kentucky. “This is strong evidence that the muon is sensitive to something that is not in our best theory.”

Dr. Fatemi is part of an international team of 200 physicists from 35 institutions and seven countries who have been operating the experiment, called Muon g-2, and who announced their first findings in a virtual seminar and news conference on Wednesday. The results are also published in a set of papers submitted to the Physical Review Letters, Physical Review A, Physical Review D and Physical Review Accelerators and Beams.

“Today is an extraordinary day, long awaited not only by us but by the whole international physics community,” Graziano Venanzoni, a spokesman for the Muon g-2 collaboration and a physicist at the Italian National Institute for Nuclear Physics, said in a statement issued by Fermilab.

Chris Polly of Fermilab, the other spokesman for the team, said, “It is so gratifying to finally be resolving this mystery.”

The measurements have about one chance in 40,000 of being a fluke, the scientists reported, a statistical status called “4.2 sigma.” That is still short of the gold standard — “5 sigma,” or about three parts in a million — needed to claim an official discovery by physics standards. Promising signals disappear all the time in science, but more data are on the way that could put their study over the top. Wednesday’s results represent only 6 percent of the total data the muon experiment is expected to garner in the coming years.

Those data could provide a major boost to particle physicists eager to build the next generation of expensive accelerators.

“This will help us understand things we don’t know yet,” said Marcela Carena, head of theoretical physics at Fermilab, who was not part of the experiment.

For decades, physicists have relied on a mathematical marvel of a theory called the Standard Model, which successfully explains the results of high-energy particle experiments in places like CERN’s Large Hadron Collider. But the model leaves deep questions about the universe unanswered: What exactly is dark matter, the unseen stuff that astronomers say makes up one-quarter of the universe by mass? Indeed, why is there matter in the universe at all?

Most physicists believe that a rich trove of new physics waits to be found, if only they could see deeper and further.

Theoretical candidates have arisen over the years: massive particles that go under the rubric of supersymmetry; lightweight wisps called axions; familiar particles lurking in hidden dimensions; and more.

In an email, Nima Arkani-Hamed, a particle theorist at the Institute for Advanced Study in Princeton who was not involved in the Fermilab experiment, called the result “most intriguing!” The precision of the measurements was “exquisite” and the efforts of the theorists “heroic,” he said, adding, “The situation should be decisively clarified in the coming years; the Fermilab result has certainly snapped us all to attention!”

Fabiola Gianotti, the director-general of CERN, sent her congratulations, saying, “The deviation of the muon’s behavior from the Standard Model expectation is truly intriguing, and we hope that more data and improved theoretical calculations will confirm that the cause is new physics.”

Dr. Carena said: “I’m very excited. I feel like this tiny wobble may shake the foundations of what we thought we knew.”

‘Who ordered that?’

Muons are an unlikely particle to hold center stage in physics. Sometimes called “fat electrons,” they resemble the familiar elementary particles that power our batteries, lights and computers and whiz around the nuclei of atoms; they have a negative electrical charge, and they spin, which makes them behave like tiny magnets. But they are 207 times as massive as their better-known cousins. They are also unstable, decaying radioactively into electrons and super-lightweight particles called neutrinos in 2.2 millionths of a second.

What part muons play in the overall pattern of creation is still a puzzle. “Who ordered that?” the Columbia University physicist I.I. Rabi said when they were first discovered in 1936. The particles are produced copiously at places like the Large Hadron Collider when more ordinary particles are crashed together at high energies.

Muons recently slipped onto center stage through a quirk of quantum mechanics, the nonintuitive rules that underlie the atomic realm and all of modern technology.

Among other things, quantum theory holds that empty space is not really empty but is in fact boiling with “virtual” particles that flit in and out of existence.

“You might think that it’s possible for a particle to be alone in the world,” Dr. Polly said in a biographical statement posted by Fermilab. “You might think the deepest, darkest reaches of outer space are a very lonely environment indeed for particles. But in fact, it’s not lonely at all. Because of the quantum world, we know every particle is surrounded by an entourage of other particles.”

According to the theory, anything allowed by the laws of nature can and will appear and disappear, tickling particles such as muons and influencing their behavior.

This affects a property of the muon called its magnetic moment, denoted in equations as g. According to a formula derived in 1928 by Paul Dirac, the English theoretical physicist and a founder of quantum theory, the magnetic moment of a lone muon should be 2.

But a muon is never alone. So Dirac’s formula must be corrected for the quantum buzz arising from all the other potential particles in the universe. That leads the factor g for the muon to be less than 2, hence the name of the experiment: Muon g-2.

The extent to which g-2 deviates from theoretical predictions is one indication of how much is still unknown about the universe.

In 1998 physicists at Brookhaven set out to explore this cosmic ignorance by measuring g-2. The group included Dr. Polly, then a graduate student; he made his mark, when things weren’t going well, by discovering that some delicate detectors had been smeared with fingerprints.

In the experiment, an accelerator called the Alternating Gradient Synchrotron created beams of muons and sent them into a 50-foot-wide storage ring, a giant racetrack controlled by superconducting magnets.

The value of g they obtained disagreed with the Standard Model’s prediction by enough to excite the imaginations of physicists — but without enough certainty to claim a solid discovery. Moreover, in a measure of how hard this work is, experts could not agree on the Standard Model’s exact prediction, further muddying hopeful waters.

At the time, redoing the experiment would not have increased the precision enough to justify the cost, Dr. Carena said, and in 2001 Brookhaven retired the 50-foot muon storage ring. The universe was left hanging.

The big move

Enter Fermilab, where a new campus devoted to muons was being built to replace the Tevatron — the world’s biggest particle collider at the time, but destined to be superseded by CERN’s Large Hadron Collider in 2009.

“That opened up a world of possibility,” Dr. Polly recalled in his biographical article. By this time, Dr. Polly was working at Fermilab; he and his colleagues could redo the g-2 experiment there, this time with more precision. He became the project manager for the experiment.

In order to do the experiment, however, they needed the 50-foot magnet racetrack from Brookhaven. And so in 2013, the magnet went on a 3,200-mile odyssey, mostly by barge, down the Eastern Seaboard, around Florida and up the Mississippi River, then by truck across Illinois to Batavia, home of Fermilab.

The magnet resembled a flying saucer, and it drew attention as it was driven south across Long Island at 10 miles per hour. There were rumors that a spaceship had landed at Brookhaven, Dr. Polly wrote: “I walked along and talked to people about the science we were doing. Moving it through the Chicago suburbs to Fermilab offered another chance for outreach. It stayed over one night in a Costco parking lot. Well over a thousand people came out to see it and hear about the science.”

The experiment started up in 2018 with a more intense muon beam and the goal of compiling 20 times as much data as the Brookhaven version.

Meanwhile, in 2020 a group of 170 experts known as the Muon g-2 Theory Initiative published a new consensus value of the theoretical value of muon’s magnetic moment, based on three years of workshops and calculations using the Standard Model. That answer reinforced the original discrepancy reported by Brookhaven.

Reached by phone on Monday, Aida X. El-Khardra, a physicist at the University of Illinois and a co-chair of the Muon g-2 Theory Initiative, said she did not know the result that Fermilab would be announcing two days later — and she didn’t want to, lest she be tempted to fudge in a lecture scheduled just before the official unveiling on Wednesday.

“I have not had the feeling of sitting on hot coals before,” Dr. El-Khadra said. “We’ve been waiting for this for a long time.”

On the day of the Fermilab announcement another group, using a different technique known as a lattice calculation to compute the muon’s magnetic moment, concluded that there was no discrepancy between the Brookhaven measurement and the Standard Model.

“Yes, we claim that there is no discrepancy between the Standard Model and the Brookhaven result, no new physics,” said Zoltan Fodor of Pennsylvania State University, one of the authors of a report published in Nature on Wednesday.

Dr. El-Khadra, who was familiar with that work, called it an “amazing calculation, but not conclusive.” She noted that the computations involved were horrendously complicated, having to account for all possible ways that a muon could interact with the universe, and requiring thousands of individual sub-calculations and hundreds of hours of supercomputer time.

These lattice calculations, she said, needed to be checked against independent results from other groups to eliminate the possibility of systematic errors. For now, the Theory Initiative’s calculation remains the standard by which the measurements will be compared.

Into the dark

The Fermilab had to accommodate another wrinkle. To avoid human bias — and to prevent any fudging — the experimenters engaged in a practice, called blinding, that is common to big experiments. In this case, the master clock that keeps track of the muons’ wobble had been set to a rate unknown to the researchers. The figure was sealed in a pair of envelopes that were locked in the office of Joe Lykken, deputy director of research at Fermilab, and at the University of Washington in Seattle.

In a ceremony on Feb. 25 that was recorded on video and watched around the world on Zoom, Dr. Polly opened the Fermilab envelope and David Hertzog from the University of Washington opened the Seattle envelope. The number inside was entered into a spreadsheet, providing a key to all the data, and the result popped out.

“That really led to a really exciting moment, because nobody on the collaboration knew the answer until the same moment,” said Saskia Charity, a Fermilab postdoctoral fellow who has been working remotely from Liverpool, England, during the pandemic. “So we all found that out together.”

The first reaction, she recalled, was pride that they had managed to perform such a hard measurement.

The second was that the results from Fermilab matched the previous results from Brookhaven. The muons, they found, were wobbling faster than expected, by a little less than three parts in a billion. This was great news to the physicists who had worried that the Brookhaven result was an anomaly that would evaporate with more data.

“This seems to be a confirmation that Brookhaven was not a fluke,” Dr. Carena, the theorist, said. “They have a real chance to break the Standard Model.”

And what will they find when they break it?

The muon anomaly, physicists said, has now given them new ideas for how to search for new particles. Dr. Lykken and Dr. Arkani-Hamed noted that among the prospective candidates were particles lightweight enough to be within the grasp of the Large Hadron Collider or its projected successor. Indeed, some might already have been recorded but are so rare that they have not yet emerged from the blizzard of data recorded by the instrument.

Another possibility, championed by Dan Hooper and Gordan Krnjaic, both of Fermilab, is a lightweight particle called Z; its existence could also explain why the cosmos appears to be expanding slightly faster than the standard cosmological models predict. Any Z particles would have decayed into lighter particles called neutrinos early in the Big Bang, pumping extra energy into the cosmic expansion and giving it a boost, and then disappeared.

Dr. Krnjaic said the g-2 result could set the agenda for particle physics for the next generation. “If the central value of the observed anomaly stays fixed, the new particles can’t hide forever,” he said. “We will learn a great deal more about fundamental physics going forward.”