## Muon collaboration explores uncharted territory in search of new physics

A subatomic particle called the muon, a particle similar to an electron but about 200 times heavier, could unlock how the physicists’ model that describes how the universe works at a fundamental level is incomplete.

Now, scientists have a brand-new measurement of a property of the muon called the anomalous magnetic moment that improves the precision of their previous result by a factor of 2.

An international collaboration of scientists working on the Muon g-2 experiment at the U.S. Department of Energy’s Fermi National Accelerator Laboratory announced the updated measurement Aug. 10. This new value bolsters the first result they announced in April 2021 and sets up a showdown between theory and experiment over 20 years in the making.

“Our goal as experimenters has been to improve the experimental precision and our confidence in that measurement,” said University of Michigan physicist Tim Chupp. “So far, we’ve shown that we can measure this fundamental property of the muon accurately and precisely. We have more data still to analyze over the next couple of years, and expect another factor of 2 improvement. The precision of our measurement is going to be a significant challenge to the Standard Model.”

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.

Like electrons, muons have a tiny internal magnet that, in the presence of a magnetic field, precesses or wobbles like the axis of a spinning top. The precession speed in a given magnetic field depends on the muon magnetic moment, typically represented by the letter g; at the simplest level, theory predicts that g should equal 2.

The difference of g from 2—or g minus 2—can be attributed to the muon’s interactions with particles in a quantum foam that surrounds it. These particles blink in and out of existence and, like subatomic “dance partners,” change the way the muon interacts with the magnetic field.

The Standard Model incorporates all known 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 new experimental result announced by the Muon g-2 collaboration is:

g-2 = 0.00233184110 +/- 0.00000000043 (stat.) +/- 0.00000000019 (syst.)

This corresponds to a measurement of g-2 with precision 0.20 parts-per-million. The Muon g-2 collaboration describes the result in a paper submitted to Physical Review Letters. With this measurement, the collaboration has already reached its goal of decreasing one particular type of uncertainty: uncertainty caused by experimental imperfections, known as systematic uncertainties labeled “syst.”

Due to the large amount of additional data that is going into the 2023 analysis announcement, the Muon g-2 collaboration’s latest result is more than twice as precise as the first result announced in 2021.

While the total systematic uncertainty has already surpassed the design goal, the larger aspect of uncertainty—statistical uncertainty or “stat”—is driven by the amount of data analyzed. The new result adds an additional two years of data to the first result. The Fermilab experiment will reach its ultimate statistical uncertainty once scientists incorporate all six years of data in their analysis, which the collaboration aims to complete in the next couple of years.

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.

Chupp leads a group of U-M graduate and undergraduate students who have become experts at measuring the magnetic field that confines the muons in the Fermilab magnet. The magnetic field is the reason the muons wobble.

“It has been truly amazing to work with so many scientists across the world. The new measurement is the result of the fusion of all scientists’ efforts, achieving it has been a real challenge but also extremely rewarding,” said Harriet Shi, a U-M undergraduate concentrating in physics and math, who has been working on understanding subtle effects of the magnetic field measurement.

Graduate student David Aguillard worked on calibrating all the magnetic field measurement instruments using a novel helium-3 magnetometer.

“It’s been an amazing effort to measure g-2 with the statistical precision to test the standard model; achieving that precision is an accomplishment in its own right,” he said.

The Fermilab experiment reused a storage ring originally built for the predecessor Muon g-2 experiment at DOE’s Brookhaven National Laboratory that concluded in 2001. In 2013, the collaboration transported the storage ring 3,200 miles from Long Island, New York, to Batavia, Illinois. Over the next four years, the collaboration assembled the experiment and improved their techniques, instrumentation and simulations. The main goal of the Fermilab experiment is to reduce the uncertainty of g-2 by a factor of 4 compared to the Brookhaven result.

The experiment was “really firing on all cylinders” for the final three years of data-taking, which came to an end in July 2023. That’s when the collaboration shut off the muon beam, concluding the experiment after six years of data collection. They reached the goal of collecting a data set that is more than 21 times the size of Brookhaven’s data set.

Physicists can calculate the effects of the known Standard Model on Muon g-2 to incredible precision. The calculations consider the electromagnetic, weak nuclear and strong nuclear forces, including photons, electrons, quarks, gluons, neutrinos, W and Z bosons, and the Higgs boson. If the Standard Model is correct, this ultra-precise prediction should match the experimental measurement.

Calculating the Standard Model prediction for Muon g-2 is very challenging. In 2020, the Muon g-2 Theory Initiative announced the best Standard Model prediction for Muon g-2 available at that time. The new g-2 result combined with the data from earlier measurements at Fermilab and Brookhaven shows disagreement with the 2020 Theory Initiative value by five-times the combined uncertainties, or 5-sigma. But a new experimental measurement of the data that feeds into the prediction and a new calculation based on a different theoretical approach—lattice gauge theory—are in tension with the 2020 calculation. Scientists of the Muon g-2 Theory Initiative aim to have a new, improved prediction available in the next couple of years that considers both theoretical approaches.

“Our new result is exciting even without a clear theoretical prediction to compare to, because it confirms the previous result of run 1 and shows that there is consistency in the experimental result,” said U-M graduate student Eva Krageloh.

The Muon g-2 collaboration comprises 181 scientists from 33 institutions in seven countries and includes nearly 40 students so far who have received their doctorates based on their work on the experiment. Collaborators will now spend the next couple of years analyzing the final three years of data, and expect another factor of 2 in precision when they finish.

The collaboration anticipates releasing their final, most precise measurement of the muon magnetic moment in 2025—setting up the ultimate showdown between Standard Model theory and experiment. Until then, physicists have a new and improved measurement of Muon g-2 that is a significant step toward its final physics goal.