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Physicists leverage a concept known as the Standard Model to articulate how the cosmos operates at its most foundational tier. Scholars globally have examined this model to ascertain if there exist additional forces or particles that remain undiscovered.

One assessment involves striving to accurately gauge the magnetic moment of a subatomic particle referred to as a muon (articulated as “mew-on”). Muons share similarities with electrons but are approximately 200 times heavier. Exact measurement of the muon’s magnetic moment, or magnetic anomaly, will assist scientists in discerning whether it interacts solely with recognized particles and forces or if there are unknown particles or forces present.

The researchers involved in the Muon g-2 experiment (pronounced “mew-on gee-minus-two”) previously published two datasets aimed at accurately determining the muon’s magnetic moment. These datasets exhibited some inconsistencies between the observed values and calculated outcomes.

On June 3, the group unveiled the third and concluding measurement of the muon magnetic anomaly. This outcome aligns with the published findings from 2021 and 2023, but with a significantly enhanced precision of 127 parts per billion, exceeding the initial experimental design aim of 140 parts per billion. This fresh measurement is also in closer agreement with the most-recent average computed value of the magnetic anomaly. These results have been submitted to the journal Physical Review Letters.

“Now we’ve released the final dataset and once more achieved a consistent result, yet with even smaller uncertainties,” remarked David Hertzog, a physics professor at the University of Washington and director of the UW Center for Experimental Nuclear Physics and Astrophysics. “This is a legacy experiment with exceptional precision on a highly fundamental quantity. It scrutinizes the Standard Model in an extensive and significant manner. If these latest findings are accurate, it would imply no new physics; however, it’s ‘stay tuned’ for now as it will take additional time for theorists to derive their precise predictions.”

The Muon g-2 experiment investigates the phenomenon known as “the wobble” of the muon. Like electrons, muons possess a quantum mechanical characteristic referred to as “spin” that can be likened to a minuscule internal magnet. In the presence of an external magnetic field, the internal magnet will wobble — or precess — similar to the axis of a twirling top.

The rate of precession is contingent upon the muon’s magnetic moment, commonly denoted by the letter g. In the most basic terms, theory forecasts that g should equal 2. Any deviation of g from 2 — or “g minus 2” — could be attributed to the muon’s interactions with other particles that influence the muon’s precession.

The Standard Model predicts how g should fluctuate based on the electromagnetic, weak nuclear, and strong nuclear forces, as well as particles such as photons, electrons, quarks, gluons, neutrinos, W and Z bosons, and the Higgs boson. However, if the measured g value diverges from the Standard Model’s prediction, it could indicate the potential existence of as-yet-undetected particles or forces contributing to the g-2 value — opening avenues to probe into new physics.

When measurements from Brookhaven National Laboratory in the late 1990s and early 2000s indicated a potential inconsistency with the theoretical calculations at that time, physicists opted to enhance the Muon g-2 experiment to achieve a more precise measurement.

For this experiment, the Muon g-2 collaboration continuously directed a beam of muons into a superconducting magnetic storage ring with a diameter of 50 feet, where muons revolved approximately 1,000 times at nearly light-speed. Detectors lining the interior of the ring — including UW-designed and constructed NMR probes to gauge the magnetic field and calorimeters to reconstruct the decay positrons — facilitated their ability to determine how swiftly the muons were precessing.

This experiment, characterized by refined techniques, instrumentation, and simulations, gathered data for six years before ceasing the muon beam on July 9, 2023, culminating in a dataset more than 21 times the size of Brookhaven’s original dataset.

This ultimate measurement is derived from the analysis of the last three years of data, collected between 2021 and 2023, in conjunction with previously published datasets. This effort more than tripled the dataset utilized for their second result in 2023, allowing the collaboration to finally reach the precision target set forth in 2012.

The latest experimental measurement of the muon’s magnetic moment from the Fermilab experiment is:

g-2 = 0.001165920705 +/- 0.000000000114(stat.) +/- 0.000000000091(syst.)

The first figure represents the calculation, while the second and third denote statistical and systematic uncertainties, respectively.

This dataset also signifies an analysis of the experiment’s highest-quality data. Towards the conclusion of their second data collection run, the Muon g-2 collaboration implemented adjustments and enhancements to the experiment that improved the quality of the muon beam and reduced uncertainties.

The Muon g-2 experiment is situated at the Fermi National Accelerator Laboratory, a Department of Energy site near Chicago. Currently, the team includes 179 scientists from 37 institutions across seven nations.

Researchers affiliated with the UW Precision Muon Physics Group have been integral to the Muon g-2 team from its inception, involved in designing and fabricating detectors as well as spearheading efforts

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to examine the vast quantities of data gathered. Alongside Hertzog, other scientists from UW participating in the team’s recent initiatives include Peter Kammel, research professor of physics; Erik Swanson, a research engineer associated with CENPA; as well as current and former postdoctoral researchers Jarek Kaspar, Zach Hodge, Svende Braun, Christine Claessens, Brynn MacCoy, and Joshua LaBounty. Hertzog pointed out that seven previous UW doctoral students — Rachel Osofsky, Matthias Smith, Nathan Froemming, Aaron Fienberg, Hannah Binney, Brynn MacCoy, and Joshua LaBounty — grounded their dissertations on this experiment.

“Our UW team even ignited three new g-2 teams as postdocs who moved on to become professors and established their own teams,” Hertzog remarked.

This outcome will maintain its status as the world’s most exact measurement of the muon magnetic anomaly for many years ahead. Although recent obstacles with theoretical predictions have decreased indications of new physics from Muon g-2, this finding sets a rigorous benchmark for proposed extensions to the Standard Model of particle physics.

“This is an incredibly thrilling moment because we not only reached our objectives but went beyond them, which is quite challenging for these types of precision measurements,” commented Peter Winter, who was a postdoctoral researcher in Hertzog’s group and currently works as a physicist at Argonne National Laboratory, also serving as the co-spokesperson for the Muon g-2 collaboration. “With the backing of funding agencies and our host institution, Fermilab, the overall success has been remarkable, as we achieved or exceeded nearly all the goals we set.”

Though the primary analysis of the experiment has concluded, further insights can still be extracted from the six years’ worth of Muon g-2 data. In upcoming phases, the collaboration plans to measure a characteristic of the muon known as the electric dipole moment and conduct examinations of a fundamental aspect of physical laws referred to as charge, parity, and time-reversal symmetry.

“Naturally, it’s disheartening to conclude such a significant effort as it has been a major aspect of many collaborators’ journeys,” stated Winter, a member of the collaboration since 2011. “However, we also aim to shift towards other physics avenues, striving to advance the domain further. I believe this will stand as a classic experiment serving as a lasting reference for many decades to follow.

For additional information, reach out to Hertzog at [email protected].

Derived from a press release by Fermilab.

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