The first results from the Muon g-2 experiment at the U.S. Department of Energy’s Fermi National Accelerator Laboratory show fundamental particles called muons behaving in a way that is not predicted by scientists’ best theory, the Standard Model of particle physics.

This landmark result, published in Physical Review Letters, confirms a discrepancy that has been gnawing at researchers for decades.

“The result of our first year of data is the most highly anticipated particle physics result in nearly a decade, and an exceptional accomplishment for the incredibly talented collaboration of experimenters,” said Tim Chupp, a University of Michigan professor of physics, who leads a group of U-M undergrads, graduate students and postdoctoral researchers who have collaborated on the Fermilab effort from the start.

The strong evidence that muons deviate from the Standard Model calculation hints at exciting new physics. One potential explanation would be the existence of undiscovered particles or forces. Muons act as a window into the subatomic world and could be interacting with yet undiscovered particles or forces.

A muon is about 200 times as massive as its cousin, the electron. Muons occur naturally when cosmic rays strike the Earth’s atmosphere, and particle accelerators at Fermilab can produce them in large numbers.

Like electrons, muons act as if they have a tiny internal magnet. In a strong magnetic field, the direction of the muon’s magnet precesses, or wobbles, much like the axis of a spinning top or gyroscope. The strength of the internal magnet determines the rate of the muon precession and is described by a number that physicists call the g-factor. The Standard Model can be used to calculate the g-factor with ultra-high precision based on known particles and forces.

The Muon g-2 experiment sends a beam of muons into a ring of magnets, where they circulate thousands of times at nearly the speed of light. Detectors lining the ring allow scientists to determine how fast the muons are precessing.

The Muon g-2 ring sits in its detector hall amidst electronic racks, the muon beamline and other equipment. The experiment operates at negative 450 degrees Fahrenheit. Image credit: Reidar Hahn

As the muons circulate in the Muon g-2 magnet, they also interact with a quantum foam of subatomic particles popping in and out of existence. Interactions with these short-lived particles affect the value of the g-factor, causing the muons’ precession to speed up very slightly. The Standard Model predicts this so-called anomalous magnetic moment extremely precisely. But if the quantum foam contains additional forces or particles not accounted for by the Standard Model, that would tweak the muon g-factor further.

“This quantity we measure reflects the interactions of the muon with everything else in the universe. But when the theorists calculate the same quantity, using all of the known forces and particles in the Standard Model, we don’t get the same answer,” said Renee Fatemi, a physicist at the University of Kentucky and the simulations manager for the Muon g-2 experiment. “This is strong evidence that the muon is sensitive to something that is not in our best theory.”

The predecessor experiment at DOE’s Brookhaven National Laboratory, which concluded in 2001, offered hints that the muon’s behavior disagreed with the Standard Model. The new measurement from the Muon g-2 experiment at Fermilab, the most precise measurement to date, is in close agreement with the value found at Brookhaven and also diverges from theory.

The Fermilab experiment reuses the main component from the Brookhaven experiment, a 50-foot-diameter superconducting magnetic storage ring. In 2013, it was transported 3,200 miles by land and sea from Long Island to the Chicago suburbs, where scientists could take advantage of Fermilab’s particle accelerator and produce the most intense beam of muons in the United States. Over the next four years, researchers assembled the experiment, tuned and calibrated an incredibly uniform magnetic field, developed new techniques, instrumentation and simulations, and thoroughly tested the entire system.

“The absolute strength of the magnetic field must be determined to connect the muon’s wobble frequency to the theory prediction, a unique challenge in a particle physics experiment,” Chupp said. “We are part of the team of experts in atomic physics and precision measurements that developed new approaches to accomplish this.”

The combined results from Fermilab and Brookhaven show a difference with theory at a significance of 4.2 sigma, a stronger signal than provided by the Brookhaven result, but a little shy of the 5 sigma (or standard deviations) that scientists favor to claim a discovery but still compelling evidence of new physics. The chance that the results are a statistical fluctuation is about 1 in 40,000.

As a U-M graduate student, Alec Tewsley-Booth developed new analysis methods that allowed the researchers to measure not just the size of the magnetic field, but also the shape and how it changes over time.

“There’s been a lot of tension in the field caused by the previous results. They were just so tantalizing that many theorists began working on extensions to the Standard Model to explain the discrepancy. However, when you get results disagreeing with the theory, there are always lingering questions about whether the difference might be caused by a mistake in the experiment,” said Tewsley-Booth, now a U-M postdoctoral researcher.

“Before these results, it was unknown whether our results would push back in favor of the old theory or new physics. Our Run-1 results go a long way toward indicating new physics and validating the previous experiment.”

U-M graduate student Eva Krägeloh compared different representations of the magnetic field data in order to help understand the accuracy and determine the uncertainties of the scientists’ measurements. A crucial cross check of the magnetic field measurements used a new instrument called the helium-3 magnetometer developed by Chupp and graduate student Midhat Farooq.

U-M graduate student Midhat Farooq in the Chupp lab works on development of the 3He magnetometer used to confirm calibration of measurements of the storage ring magnetic field. Image credit: Chupp Lab

“There are hundreds of devices used to measure the magnetic field, but they are all referenced to one device that was calibrated to Midhat’s magnetometer with amazing precision,” Chupp said.

In its first year of operation, 2018, the Fermilab experiment collected more data than all prior muon g-factor experiments combined. With more than 200 scientists from 35 institutions in seven countries, the Muon g-2 collaboration has now finished analyzing the motion of more than 8 billion muons from that first run.

So far, the researchers have analyzed less than 6% of the data the experiment will eventually collect. Data analysis on the second and third runs of the experiment, led in part by Tewsley-Booth and Chupp, is underway; the fourth run is ongoing; and a fifth run is planned. Combining the results from all five runs will give scientists a four-times more precise measurement of the muon’s g-factor, probing with greater certainty whether new physics is hiding within the quantum foam.

“Particle physicists are again going to turn their attention to what this new physics could be. For physics, this finding is quite profound because it gives us a much better idea of a specific signal to examine,” Chupp said. “It’s beautiful physics, it challenges us experimentally, and it probes the deepest questions of particle physics.”

The U-M group’s Muon g-2 research is funded by the National Science Foundation.

More information:

• Study: Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• Tim Chupp
• Midhat Farooq
• Alec Tewsley-Booth
• Eva Krägeloh
• Muon g-2