Muon g-2 collaboration doubles precision with latest measurement

Uncharted territory explored in search of new physics

11 August 2023

The muon g-2 collaboration today announced a highly anticipated brand new result from its measurement of the muon's anomalous magnetic moment. The result is consistent with the result of the first round of measurements, but the accuracy is improved by a factor of 2 compared to the earlier result. This most precise measurement of the anomalous magnetic moment of the muon to date was presented at a seminar at Fermilab (FNAL) and submitted to the prestigious journal Physical Review Letters for publication.

The research group of Prof. Dr. Martin Fertl, who has been conducting research in the field of low-energy particle physics at the Cluster of Excellence PRISMA+ at Johannes Gutenberg University Mainz (JGU) since 2019, is the only one in Germany that is involved in the muon g-2 collaboration with experimental contributions. Martin Fertl himself already started working on the muon g-2 experiment in 2014 as a postdoctoral researcher at the University of Washington, Seattle, and today is a very special day for him. "The new value we were able to announce today underpins the first result we announced in April 2021," said Martin Fertl. "It brings particle physics closer to the ultimate showdown between theory and experiment that could reveal new particles or forces. This is what we've been waiting for more than 20 years."

New result doubles precision

The new experimental result for g-2 (see below for explanation) is based on the first three years of data since 2018, i.e., it contains the newly evaluated data from run two and three, as well as the data from run one already published in 2021. In total, more than 40 billion muons were measured for this purpose. The result is:

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

The g-2 measurement thus corresponds to an overall precision of 200 parts per billion - compared to 460 parts per billion achieved with the analysis of the first 6 percent of the data and announced in April 2021. With this latest measurement, the muon g-2 collaboration has already achieved ahead of schedule one of its most important goals, namely, to decrease a specific type of uncertainty: the uncertainty caused by experimental imperfections, known as systematic uncertainty.

"This is a great experimental achievement," says a delighted Dr. René Reimann, postdoc in the research group of Martin Fertl and, together with PhD student Mohammad Ubaidullah Hassan Qureshi, significantly involved in the analysis of the magnetic field in the experimental setup. While the systematic uncertainty of 68 parts per billion has thus already surpassed the design goal, the larger aspect of the uncertainty — the statistical uncertainty — is driven by the amount of data analyzed. Thus, the result announced today already adds 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. "Our goal of ultimately achieving an overall accuracy of 140 parts per billion with the new muon g-2 experiment, which is a factor of four higher than the previous experiment at Brookhaven National Laboratory, therefore seems very realistic," Mohammad Ubaidullah Hassan Qureshi concludes.

Muons as Test Objects for New Physics — What does g-2 mean?

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. The anomalous magnetic moment of the muon is a very important precision observable in this context, which provides one of the most promising tests of the Standard Model. For many years there has been a discrepancy here and the big question is whether this is "real" or "merely" a consequence of systematic uncertainties in theory and experiment.

Muons are fundamental particles that are similar to electrons but about 200 times as massive and live only for the millionth fraction of a second. Like the electron, the muon has a magnetic moment, a kind of miniature internal bar magnet that precesses or wobbles in the presence of a magnetic field, 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 muon g-2 experiment gets its name from the fact that the "g" of the muon always deviates a little — by about 0.1 percent — from the simple expectation g=2. This anomaly is commonly called the anomalous magnetic moment of the muon (a = (g-2)/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," 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.

Racetrack for muons

The muon g-2 experiment measures the rotation frequency of the "internal compass needle" of the muons in a magnetic field, as well as the magnetic field itself, and determines the anomalous magnetic moment from it. The muon beam is generated at FNAL's muon campus specifically for the experiment — it has a purity never achieved before.

To make the measurement, the muon g-2 collaboration repeatedly sent this beam of muons into a 50-foot-diameter superconducting magnetic storage ring, where they circulated on average about 1,000 times at nearly the speed of light. Using detectors lining the ring, the researchers were able to determine how fast the muons' compass needles were moving relative to their trajectories. Physicists must also precisely measure the strength of the magnetic field to then determine the value of g-2. And this is where the expertise of Martin Fertl and his research group lies: the extremely precise measurement of the magnetic field in the muon storage ring over the entire measurement period of several years. Already at his former place of work, Martin Fertl led the development of an array of highly sensitive magnetometers based on the principle of pulsed nuclear magnetic resonance for this purpose. Several hundred of these measuring heads are installed in the walls of the vacuum chambers surrounding the muons. Another 17 measuring heads remotely orbit the storage ring, which has a diameter of 50 foot, to measure the applied magnetic field even more comprehensively. "To achieve our precision goal, we must be able to measure the magnetic field in which the muons move to an accuracy of 70 parts per billion," Martin Fertl calculates.

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. After four years of construction, data collection began in 2018, and the experiment has continued to improve since then.
In addition to the now published measurements from the first three years, the experiment collected data for another three years. Finally, on July 9, 2023, 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.

Is there a discrepancy between theory and experiment?

Physicists can calculate the effects of the known Standard Model “dance partners” 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 a very challenging. In 2017, more than 130 physicists worldwide therefore joined forces in the "Muon g-2 Theory Initiative" to jointly address this challenge, among them Prof. Dr Hartmut Wittig, theoretical physicist and also speaker of the Cluster of Excellence PRISMA+, who represents the Mainz activities in the field of theory prediction as a member of the Steering Committee. In 2020, the initiative announced the best Standard Model prediction for muon g-2 available at that time. 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.

The Muon g-2 collaboration

The Muon g-2 collaboration comprises close to 200 scientists from 33institutions 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 finally expect another factor of two in precision. 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.