It has been 12 years since physicists transported a giant magnetic ring down the Atlantic coast, around Florida, up the Mississippi River and across two interstates to Batavia, Ill. On Tuesday, the team behind that ring unveiled their final result: the most precise value yet recorded for the tiny wobble of a subatomic particle called the muon.
Physicists hoped that the measurement, submitted to the journal Physical Review Letters, would open a window to new types of energy and matter that so far have only been theorized.
“We want to know how our universe formed, what it’s made out of and how it interacts,” said Peter Winter, a physicist at Argonne National Laboratory and a spokesman for the Muon g-2 Collaboration, which ran the experiment at Fermi National Accelerator Laboratory, or Fermilab. The new result, he said, “will stand as a benchmark for years to come.”
But a glaring problem remains. Physicists have predicted two distinct values for the muon’s wobble but aren’t sure which is correct. The new result matches one prediction, but until the other prediction can be satisfyingly explained away, scientists won’t know if they have uncovered evidence of new physics.
“The Fermilab experiment is hugely successful, they did their job,” said Aida El-Khadra, a physicist at the University of Illinois Urbana-Champaign who leads the Muon g-2 Theory Initiative. “We theorists, we still need to follow up.”
Until the dust settles, Dr. El-Khadra added, “the jury is still out.”
Muons are similar to electrons but far heavier and unstable in nature. When placed in a magnetic field, they precess, or wobble, like a spinning top. The speed of that wobble depends on a property of the muon related to its internal magnetism, known to physicists as g.
Absent any nearby particles, g should equal exactly 2. But according to quantum theory, even empty space isn’t truly empty: It brims with so-called “virtual” particles of all kinds, blipping in and out of existence. They persist long enough to interact with the muon, slightly changing its wobble and pulling g away from 2.
Dr. Winter likened the effect to the way that leaves on a tree shift in the wind. The force is unseen, but its interaction with the leaves is predictable depending on the strength and direction of the wind. Measuring whether the leaves moved as expected, he said, would indicate whether your wind model was correct.
Physicists rely on the collection of particles and forces encapsulated in the Standard Model — their best theory for how the universe looks and behaves at subatomic scales — to predict how much g deviates from 2. They call this deviation g-2 (pronounced “g minus 2”). Their hunch, however, is that the Standard Model is incomplete because it lacks an explanation for key puzzles in physics, like the nature of dark matter or why certain particles known as neutrinos can have mass.
If there are undiscovered particles or forces at play, measuring g-2 will help physicists find them, because its value will be different from what the Standard Model predicts. But calculating a prediction has proved notoriously difficult. Traditionally, theorists have avoided a direct calculation, instead compiling relevant data from particle experiments around the world and working backward to achieve a theoretical prediction for g-2.
“In some sense, if you’re a theorist like me, this is cheating,” Dr. El-Khadra said, because it avoids a direct calculation from theory. “But it is a completely well-founded approach.”
In the meantime, experimentalists have been busy measuring. In the 1990s, scientists at Brookhaven National Laboratory in New York began operating a 50-foot-diameter magnet shaped like a ring. Muons raced around that ring, their wobbles recorded by detectors along its edge.
The outcome of that experiment was a tantalizing result for g-2 — the deviation of g from 2 — that seemed to defy the theoretical prediction. The discrepancy between what they measured and the theoretical prediction for g-2 was at a level of 3.7 sigma, in the units of uncertainty used by physicists. (A 5-sigma discrepancy is the general standard for claiming a discovery.)
A dozen years later, in a grand feat of logistics, physicists spent 35 days inching the magnetic ring by barge and truck from Brookhaven to Fermilab, where a more powerful source of muons would allow them to gather more data with higher precision. In 2021, the scientists confirmed the g-2 value initially measured at Brookhaven. The mismatch between the experiment and prediction rose to 4.2 sigma and then over 5 sigma in 2023.
But physicists stopped short of claiming a discovery because a different, more direct way to predict g-2 from the Standard Model had surfaced. The method, which involves using supercomputers to simulate the universe as a four-dimensional grid of space-time points, relies on no data at all. That is advantageous over the earlier prediction, which did rely on experimental data, some of which are now contradictory.
Comparing the newer prediction to the g-2 value measured ever more precisely at Fermilab shows no discrepancy between theory and experiment, suggesting no discovery at all.
Theorists have tried to reconcile their two predictions ever since, even as Fermilab scientists forged ahead with ever more precise measurements of the muon’s wobble. Announced to the world on Tuesday, their final value for g-2, calculated from hundreds of billions of observed muons, is 0.00233184141.
It is the same value measured at Brookhaven more than two decades ago, but with a much higher precision of 127 parts per billion. That is as precise as measuring the length of a football field with an error less than the width of a hair.
Now the ball is in the theorists’ court, said Marco Incagli, a physicist at the National Institute of Nuclear Physics in Italy and a spokesman for the Fermilab collaboration.
With the Muon g-2 Collaboration officially completed, “I am relieved and I am sad at the same time,” Dr. Incagli said. Other results from the collaboration, including searches for dark matter, are forthcoming. The team also looks forward to an upcoming measurement of g-2 by Japanese scientists using a different experimental technique.
And the theorists march on. New physics could perhaps explain the persistent gap between their predictions. But even if no discovery is made, the effort was not in vain, said Dr. El-Khadra. Knowing what kinds of physics can’t exist would help theorists to imagine which kinds can, and to further make sense of the universe.
“It is really important to have both methods, to confront them with each other, to finish what we started,” Dr. El-Khadra said. “That continuing work is bound to yield profound insights.”
Katrina Miller is a science reporter for The Times based in Chicago. She earned a Ph.D. in physics from the University of Chicago.
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