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Scientists working on the Muon g-2 experiment, including University of Massachusetts Amherst professor of physics David Kawall and members of his lab, have released their third and final measurement of what’s known as the muon magnetic anomaly. That anomaly causes a small but detectable effect on how fast the spin axis of a fundamental particle called a muon rotates in a magnetic field, and could be the doorway to understanding some of the universe’s deepest secrets, like dark matter. The final result of the Muon g-2 experiment, which is hosted by the U.S. Department of Energy’s Fermi National Accelerator Laboratory, agrees with their published results from 2021 and 2023 but with a much better precision of 127 parts-per-billion, surpassing the original experimental design goal of 140 parts-per-billion.

This long-awaited result is a tremendous achievement of precision and will remain the world’s most precise measurement of the muon magnetic anomaly for many years to come. Despite recent challenges with the theoretical predictions that reduce evidence of new physics from muon g-2, this result provides a stringent benchmark for proposed extensions of the Standard Model of particle physics.

Physicists describe how the universe works at its most fundamental level with a theory known as the Standard Model. By making predictions based on the Standard Model and comparing them to experimental results, physicists can discern whether the theory is complete — or if there is physics beyond the Standard Model. 

“Though the Standard Model has been incredibly successful in describing essentially everything we see in the lab, we know that it is woefully incomplete,” says Kawall. “For instance, it doesn’t explain why there is more matter than antimatter in the universe, and it doesn’t account for dark matter, so we know there must be new physics and new particles just waiting to be discovered.”

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These particles blink in and out of existence and, like subatomic “dance partners,” grab the muon’s “hand” and change the way the muon interacts with the magnetic field. The Standard Model incorporates all known “dance partner” particles and predicts how the quantum foam changes g. But there might be more. Physicists are excited about the possible existence of as-yet-undiscovered particles that contribute to the value of g-2 — and would open the window to exploring new physics.

The Muon g-2 experiment looks at the wobble of the muon. Muons are similar to electrons but about 200 times more massive; like electrons, muons have a quantum mechanical property called spin that can be interpreted as a tiny internal magnet. In the presence of an external magnetic field, the internal magnet will wobble — or precess — like the axis of a spinning top. 

The precession speed in a magnetic field depends on properties of the muon described by a number called the g-factor. Theoretical physicists calculate the g-factor based on the current knowledge of how the universe works at a fundamental level.

Nearly 100 years ago, the value of g was predicted to be 2. But experimental measurements soon showed g to be slightly different from 2 by a quantity known as the magnetic anomaly of the muon. The Muon g-2 experiment gets its name from this relation.

The muon magnetic anomaly encodes the effects of all Standard Model particles, and theoretical physicists can calculate these contributions to an incredible precision. But previous measurements taken at Brookhaven National Laboratory in the late 1990s and early 2000s showed a possible discrepancy with the theoretical calculation at that time.

When experiment doesn’t align with theory, it could indicate new physics. Specifically, physicists wondered if this discrepancy could be caused by as-yet undiscovered particles pulling at the muon’s precession.

So physicists decided to upgrade the Muon g-2 experiment to make a more precise measurement. In 2013, Brookhaven’s magnetic storage ring was transported from Long Island, New York, to Fermilab in Batavia, Illinois. After years of significant upgrades and improvements, the Fermilab Muon g-2 experiment started up on May 31, 2017.

In parallel, an international collaboration of theorists formed the Muon g-2 Theory Initiative to improve the theoretical calculation. In 2020, the Theory Initiative published an updated, more precise Standard Model value based on a technique that uses input data from other experiments.

The discrepancy with the result from that technique continued to grow in 2021 when Fermilab announced its first experimental result, confirming the Brookhaven result with a slightly improved precision. At the same time, a new theoretical prediction came out based on a second technique that heavily relies on computational power. This new number was closer to the experimental measurement, narrowing the discrepancy.

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To make the measurement, the Muon g-2 collaboration repeatedly sent a beam of muons into a 50-foot-diameter superconducting magnetic storage ring, where they circulated about 1,000 times at nearly the speed of light. Detectors lining the ring allowed scientists to determine how rapidly the muons were precessing. Physicists must also precisely measure the strength of the magnetic field to then determine the value of g-2.

This is where Kawall and his students, including postdoctoral researcher Matthew Bressler, graduate student David Kessler, and undergrads Johnny Ayoub and Mor Evron, come in. His group worked on measuring the strength of the magnetic field through which the muons passed, as well as preparing the magnet itself, a feat requiring almost unimaginable precision. The team also spent years developing special calibration probes of incredible fidelity, accurate down to 15 parts per billion.

“One of the major contributions that Bressler and Kessler made was to the absolute calibration of the magnetic field,” said Kawall. “This was essential for the determination of g-2 and required months of dedicated measurements and years of careful thought and analysis. The result they achieved was more precise and more robust than I thought was possible when we were designing the Fermilab experiment. They did an absolutely fantastic job.”

The latest experimental value of the magnetic moment of the muon from the Fermilab experiment is: am = (g-2)/2 (muon, experiment) = 0.001 165 920 705 +- 0.000 000 000 114(stat.)    +- 0.000 000 000 091(syst.)

“This is a very exciting moment because we not only achieved our goals but exceeded them, which is not very easy for these precision measurements,” said Peter Winter, a physicist at Argonne National Laboratory and co-spokesperson for the Muon g-2 collaboration. “With the support of the funding agencies and the host lab, Fermilab, it has been very successful overall, as we reached or surpassed pretty much all the items that we were aiming for.”

“For over a century, g-2 has been teaching us a lot about the nature of nature,” said Lawrence Gibbons, professor at Cornell University and analysis co-coordinator for this result. “It’s exciting to add a precise measurement that I think will stand for a long time.”

This final measurement is based on the analysis of the last three years of data, taken between 2021 and 2023, combined with the previously published datasets. This more than tripled the size of the dataset used for their second result in 2023, and it enabled the collaboration to finally achieve their precision goal proposed in 2012.

The Muon g-2 collaboration is made up of nearly 180 scientists from 37 institutions in seven countries. Marco Incagli, a physicist with the Italian National Institute for Nuclear Physics at Pisa and co-spokesperson for Muon g-2, emphasized that the internationality of the collaboration was key to the success of the experiment.

“It’s extraordinary that physics has progressed to the point where we’re able to make predictions and measurements that agree to 8 significant figures, and that such measurements can provide a window into solving some of the most important mysteries in physics,” says Kawall. “It’s been an absolute joy working on such interesting and challenging physics with so many amazing scientists from all over the world. I’m especially thankful for the opportunity to have worked closely with a set of very talented UMass Amherst students and postdocs without whom this result, which is certain to appear in future textbooks, would not have been possible.”