One tiny particle could complicate predictions of physics theorists

Scientists working on the Muon g-2 experiment, hosted by the U.S. Department of Energy’s Fermi National Accelerator Laboratory, have released their third and final measurement of the muon magnetic anomaly. This value is related to g-2, the experiment’s namesake measurement. The final result 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.

“The anomalous magnetic moment, or g–2, of the muon is important because it provides a sensitive test of the Standard Model of particle physics. This is an exciting result and it is great to see an experiment come to a definitive end with a precision measurement,” said Regina Rameika, the U.S. Department of Energy’s Associate Director for the Office of High Energy Physics.

“This is a very exciting moment because we not only achieved our goals but exceeded them …”

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.

“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.”

The Muon g-2 (pronounced “gee minus two”) experiment looks at the wobble of a fundamental particle called 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, which is contained in the Standard Model of particle physics.

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, a_μ, calculated with (g-2)/2. 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.

Recently, the Theory Initiative published a new prediction combining the results of several groups that used the new computational technique. This result remains closer to the experimental measurement, dampening the possibility of new physics. However, the theoretical effort will continue to work to understand the discrepancy between the data-driven and computational approaches.

The latest experimental value of the magnetic moment of the muon from the Fermilab experiment is:

a_μ = (g-2)/2 (muon, experiment) = 0.001 165 920 705 +- 0.000 000 000 114(stat.)
                                                                                                              +- 0.000 000 000 091(syst.)

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.

It also represents an analysis of the experiment’s best-quality data. Toward the end of their second data-taking run, the Muon g-2 collaboration finished tweaks and enhancements to the experiment that improved the quality of the muon beam and reduced uncertainties.

The Muon g-2 collaboration describes the result in a paper that they submitted today to Physical Review Letters.

“As it has been for decades, the magnetic moment of the muon continues to be a stringent benchmark of the Standard Model,” said Simon Corrodi, assistant physicist at Argonne National Laboratory and analysis co-coordinator. “The new experimental result sheds new light on this fundamental theory and will set the benchmark for any new theoretical calculation to come.”

A future experiment at the Japan Proton Accelerator Research Complex will likely make another measurement of the muon magnetic anomaly in the early 2030s, but, initially, they won’t achieve the same precision as Fermilab.

Meanwhile, the Theory Initiative will continue working to resolve the inconsistency between their two theoretical predictions.

The Muon g-2 collaboration is made up of nearly 176 scientists from 34 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.

Unusually, the scientists also represent a variety of physics areas. “This experiment is quite peculiar because it has very different ingredients in it,” said Incagli. “It is really done by a collaboration among communities that normally work on different experiments.”

Unlike other high-energy physics experiments, Muon g-2 needed more than just high-energy physicists; the collaboration is also composed of accelerator physicists, atomic physicists and nuclear physicists. “It was very valuable to see that, when we had all these different experts come together, we could solve items that probably one group could not have done alone,” said Incagli.

It was very valuable to see that, when we had all these different experts come together, we could solve items that probably one group could not have done alone.

While the experiment’s main analysis has come to an end, there is more to be mined from the six years of Muon g-2 data. In the future, the collaboration will produce measurements of a property of the muon called the electric dipole moment, as well as tests of a fundamental property of physical laws known as charge, parity, and time-reversal symmetry.

“It’s a really beautiful experiment,” said Gibbons. “The data that comes out is really exquisite. It’s been a privilege to have access to this data and analyze it.”

“Of course, it’s sad to end such an endeavor because it’s been a large part of many of our collaborators’ lives,” said Winter, who has been part of the collaboration since 2011. “But we also want to move to the next physics that’s out there, to do our best to advance the field in other areas.

“I think it will be a textbook experiment that will be a long-lasting reference for many future decades to come,” Winter added.

Fermilab editor’s note: This press release was originally published by the U.S. Department of Energy’s Argonne National Laboratory. Fermi National Accelerator Laboratory and Argonne are collaborating to develop a practical approach to reduce the size and cost of superconducting linear accelerators — technology with great potential for addressing the challenge of long-lived radioactive isotopes in used nuclear fuel. Fermilab is contributing its expertise in superconducting accelerator cavities and cryogenic systems, including the development of advanced niobium-three-tin coatings.

The U.S. Department of Energy’s (DOE) Argonne National Laboratory and Fermi National Accelerator Laboratory (Fermilab) have been selected to receive $3.2 million in funding from the DOE Advanced Research Projects Agency-Energy (ARPA-E). The funding is part of ARPA-E’s Nuclear Energy Waste Transmutation Optimized Now (NEWTON) program, which aims to make the reprocessing of U.S. commercial used nuclear fuel economically viable within 30 years.

Transmutation is a process in which an atomic nucleus is transformed into a different chemical element or isotope. In this case, the long-lived radioactive isotopes in used nuclear fuel are converted into shorter-lived isotopes.

Technologies supported by the ARPA-E NEWTON program, such as transmutation, would speed up the processing cycle of the U.S. used nuclear fuel stockpile, improving safety and decreasing the capital expenditure needed for permanent long-term storage.

Studies have found that particle accelerators offer the greatest potential of any existing technology to address the challenge posed by the 90,000 metric tons of waste at operating U.S. nuclear plants. Superconducting cavities—specialized components stacked together in linear particle accelerators—can efficiently propel charged particles, like protons, to high speeds with energies near 1 billion electron-volts (GeV).

These proton beams can be used to create an intense flux of neutrons from a heavy-element target (typically made of lead or bismuth) through a process called spallation, according to Michael Kelly, Argonne physicist and team leader. When directed at radioactive waste inside a nuclear reactor, these neutrons multiply. Then, they essentially burn the used nuclear fuel, turning it into a material that decays more quickly.

However, most of today’s accelerator cavities, made from pure niobium, are large and cost several hundred thousand dollars each. They must be cooled with costly central cryogenic plants that use a considerable amount of liquid helium at a temperature between 2 and 4 kelvins. When units of six to eight cavities—known as cryomodules—are strung together, they resemble railroad freight cars in size.

Of the $3.2 million allocated for this project, Argonne and Fermilab are receiving about $2.2 million to develop a practical approach to reduce the size and cost of superconducting linear accelerators while simultaneously improving their reliability.

Kelly and his team will leverage smaller, better-performing superconducting cavities based on an emerging technology known as thin-film Nb₃Sn (colloquially called “niobium-three-tin”). This film is only about 2 to 3 micrometers thick—about the size of a spiderweb strand. The team will produce these cavities in a process called vapor diffusion.

The new niobium-three-tin cavities would require less helium for cooling and also replace today’s large, water heater-sized cavities with much smaller cavities, perhaps the size of a coffee can. The physical size reduction of the accelerator cryomodules would be a factor of three to five.

“We think it’s a big deal,” said Kelly. “We won’t know precisely what the size and cost reduction is until we do a lot more research and development. That’s a major part of what this R&D intends to address,” he added.

Critically, niobium-three-tin technology helps eliminate the single point of failure associated with the cryogenic plant. It does so by offering the possibility of replacing large liquid helium refrigerators with a new generation of smaller plug-in cryocoolers. Typically, if the liquid helium refrigerator malfunctions, the accelerator is forced to shut down entirely.

The researchers hope to avoid such forced shutdowns by eliminating the large refrigerator and replacing it with a distributed set of fault-tolerant 10-watt cryocoolers.

The accelerator must be extremely reliable, with an uptime—a period of time in which a machine is continuously functional and available—of 95% or higher to avoid interruptions in the transmutation process, according to Brahim Mustapha, another Argonne physicist working on the project.

If the accelerator stops, the spallation target that produces neutrons inside the reactor cools off. If the process restarts, the spallation target heats up again. When this stop-start sequence happens frequently, the process causes thermal and mechanical stress that can damage the target.

Kelly’s team has already been using the Argonne Tandem Linac Accelerator System (ATLAS), a DOE Office of Science user facility at Argonne, to improve reliability through cryocooler development. As part of that separate project, his team uses artificial intelligence, machine learning and other strategies to minimize accelerator downtime due to malfunctions.

The ultimate goal for the researchers working on the ARPA-E NEWTON-funded project is to demonstrate two high-performance niobium-three-tin-coated cavities optimized for protons moving near 50% the speed of light—a crucial step toward the full high-power accelerator. They also aim to develop an end-to-end linac design and conceptual layout optimized for niobium-three-tin.

The project is not without challenges. For example, relatively complex geometries are required for medium-velocity cavities because of their hard-to-reach surfaces. These irregular shapes may hinder the deposition of smooth, uniform niobium-three-tin films, potentially allowing impurities like dirt or dust to enter the film coating and contaminate it. Small contaminants, and even geometric irregularities, could lower the performance of the superconducting cavity.

While the Argonne team is focused primarily on the niobium-three-tin linac and cavity design and demonstration, Fermilab is providing its expertise and infrastructure to perform the vapor diffusion process that underpins the niobium-three-tin technology. Grigory Eremeev and Sam Posen, both senior scientists and 2016 recipients of the DOE Early Career Award, are leading Fermilab’s efforts.

“Support from DOE made it possible to develop highly capable niobium-three-tin coating facilities at Fermilab and to develop techniques to achieve high performance in cavities with complex geometries,” said Posen. “Now we are building on that foundation, advancing coating techniques and applying them to these exciting applications.”

“Niobium-three-tin films are critical for this type of application. While complex geometries are challenging for deposition, we’ve already seen excellent results in our collaborative work with Argonne,” said Eremeev.

Looking toward the future and the construction of the full accelerator, it is critical to industrialize the technology. To help with this, the project involves collaboration with two companies. RadiaBeam will industrialize most or all of the process of building niobium-tin cavities, and RadiaSoft will conduct reliability studies for the proposed linac design.

This project is one of 11 selected in 2025 to receive $40 million in ARPA-E NEWTON program funding to develop cutting-edge technologies that enable the transmutation of used nuclear fuel.

One of the other projects selected for funding will complement the joint Argonne-Fermilab effort. Led by Taek Kim, a principal nuclear engineer who manages the nuclear systems analysis group within Argonne’s Nuclear Science and Engineering division, a team of researchers is developing a novel transmutation system that uses an innovative separation method to remove waste by-products from the process. The method involves fission, which is the process of splitting an atomic nucleus of, for example, an actinide into two or more smaller nuclei, releasing a large amount of energy. As the actinide fissions, the smaller nuclei that are created can be separated from remaining actinides by centrifugal methods in the recycling system.

Together, these projects will yield a complete accelerator-driven system for nuclear waste transmutation. By significantly reducing the mass, volume, activity and effective half-life of the existing stockpile of commercial used nuclear fuel, these and other ARPA-E NEWTON-funded projects will help shift used nuclear fuel disposal from an intergenerational issue to an intragenerational one.

In addition to Kelly and Mustapha at Argonne and Eremeev and Posen at Fermilab, the project team includes Argonne engineers Troy Petersen and Thomas Reid; Fermilab technician Brad Tennis; RadiaBeam engineer Ronald Agustsson; and RadiaSoft President Jonathan Edelen.

Fermi National Accelerator Laboratory is supported by the Office of Science of the U.S. Department of Energy. The Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, please visit science.energy.gov.

With the approach of National Prairie Day — recognized on the first Saturday in June — volunteers and staff at Fermi National Acceleratory Laboratory will have even more to commemorate, as 2025 marks the 50^th anniversary of prairie restoration on the grounds of Fermilab.

Fermilab’s prairie restoration initiative was built on the idea of responsible land stewardship by transforming the laboratory’s unused open spaces back into native prairie that once dominated the Illinois landscape. The restoration began humbly in a nine-acre patch within the Tevatron particle accelerator ring, guided by Robert Betz, a biology professor at Northeastern Illinois University. Today, it spans over 950 acres.

Central to this ongoing effort are volunteers from Fermilab Natural Areas, an outside not-for-profit organization whose work is coordinated with Fermilab employees. Their contributions include activities such as seed collection and invasive species control.

“Volunteers are truly the backbone of Fermilab’s prairie restoration efforts,” said Wally Levernier, Fermilab’s ecologist. “When employees and visitors see the natural areas, it is largely the way it looks because of the efforts started by Robert Betz and continued by volunteers and staff.”

Dynamic ecosystem

An ecosystem is a dynamic relationship between a group of species — including plants, animals, bacteria and fungi. Their coexistence shapes the landscapes we recognize, such as prairies, forests, woodlands, marshes and wetlands.

“Prairies were historically one of the predominant ecosystems in Illinois,” Levernier said. “Settlers often described the vastness and beauty of prairies. Today, only about 0.01% of Illinois’ original 22 million acres of high-quality prairie remains — just about 2,300 acres.”

Unlike forests or wetlands, prairies have a deep and dense networks of roots, with three-quarters of plant material existing underground. This hidden network plays a critical role in stabilizing soil, which helps prevent erosion, and in storing carbon. Organic carbon improves soil structure, enhances water retention and increases nutrient availability for plants.

“Grasses in prairies can have fibrous roots that reach 10 to 12 feet underground,” said Mitch Adamus, a Fermilab technician and former chair of the Prairie Committee. “That’s where plants and animals go to survive the winters.”

Living laboratory

Fermilab’s prairies have also become a resource for scientific research. Restoring a prairie from scratch gives scientists a rare opportunity to study how ecosystems gradually develop.

Since Fermilab’s prairie restoration was established in stages, this created what ecologists call a chronosequence — sections of land with similar soil and environmental conditions planted at different times that represent various stages of ecosystem development.

In the summer of 1985, soil ecologist and distinguished senior scientist Julie Jastrow from Argonne National Laboratory began studying this chronosequence to see how soil health evolved as farmland was restored to prairie.

“It turned out to be fantastic data,” Jastrow recalled. “We could track how the prairie changed the soil over time.”

As plants grow and the prairie ecosystem develops, ongoing monitoring and research studies have become crucial in finding insights into the health of the restored prairie.

One of the discoveries from studies on Fermilab’s prairies was how soil structure improves during the restoration. Jastrow and her team found that as farmland transitions back to prairie, the soil gradually forms what ecologists refer to as stable crumb structures, which help retain organic matter.

The network of pores that develop within and between these crumb structures, together with organic matter, help sustain the growth of prairie plants by promoting a healthy balance of water, air and nutrients in the soil.

Significantly, the research helped gain new insights into a prairie’s role in storing carbon. As prairie plants grow, their fibrous roots and associated fungal networks bind small soil particles into larger clusters, creating a foundation for long-term carbon storage.

“We found that healthy soil structure, particularly the formation of stable soil aggregates of various sizes, plays a key role in storing carbon,” Jastrow explained.

While these soil structures form relatively quickly — in less than 10 years — the Argonne team found the actual buildup of organic carbon takes much longer, possibly hundreds of years. Most of this stored carbon isn’t in visible plant debris but is associated with soil minerals, protecting it from rapid decomposition.

The path ahead

Even after decades of restoration, Fermilab’s prairies are still evolving. Compared to untouched, native prairie — some of which can be found in small patches on Fermilab’s site — restored sections still contain less organic carbon, but they are steadily improving.

Over the years, land managers and ecologists have gained valuable insights into what works and what doesn’t in prairie restoration. “Originally, we thought prairies would become self-sustaining much sooner,” said Levernier. “But we now know that restoration is a long process that requires active management and patience.”

Part of maintaining the prairie involves conducting periodic prescribed burns. These carefully controlled fires, managed by trained staff, replicate the natural disturbances that historically shaped prairie ecosystems and help stimulate new plant growth.

Despite challenges, the long-term benefits of restoring the prairie are undeniable.

“In the end, restoring native grasslands is one of the most effective ways to improve soil health and store carbon,” said Jastrow. “But it’s a slow process that requires patience and long-term conservation efforts.”

Fermi National Accelerator Laboratory is supported by the Office of Science of the U.S. Department of Energy. The Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, please visit science.energy.gov.