Image: Ryan Postel, Fermilab
An international science experiment, which includes researchers from the University of Liverpool, has announced the most precise measurement of the magnetic anomaly of the muon.
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 result, based on the last three years of data, is in perfect agreement with the experiment's previous 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.
The Muon g-2 collaboration describes the result in a paper that they submitted today to Physical Review Letters.
The third and final result from the Muon g-2 collaboration, based on the last three years of data, is in perfect agreement with the previous results, further solidifying the experimental world average. Credit: Muon g-2 collaboration.
International collaboration
Hosted by the U.S. Department of Energy's Fermi National Accelerator Laboratory (Fermilab), Muon g-2 is an international collaboration involving nearly 176 scientists from 34 institutions in seven countries including several from the UK.
Researchers at the University of Liverpool provide significant contributions to the experiment's latest findings. Their roles included the precision magnetic field measurement, fitting the muon spin precession frequency and quantifying the corrections to the precession frequency due to beam-dynamics effects, by using the data from the Liverpool-built tracking detectors.
Professor Graziano Venanzoni, Leverhulme International Professor of Physics with the University of Liverpool's Department of Physics, said: "These are truly exciting results that represent a significant test of the Standard Model - the fundamental theory describing matter and forces at the smallest scales. The Liverpool team played a central role in this achievement, particularly through the construction of a tracker detector that was instrumental to the result, as well as through its involvement in detector operation, project leadership, and data analysis.
"I would especially like to acknowledge the outstanding contributions of our junior colleagues: Saskia Charity, who led the field analysis, and Estifa'a Zaid, Elia Bottalico, Cedric Zhang, and Lorenzo Cotrozzi, who carried out one of the analyses of the spin precession that contributed to the final result. I am also deeply grateful to the Leverhulme Trust, STFC, and the University of Liverpool for their continued support throughout this wonderful endeavour."
Dr Joe Price is the Principal Investigator for the Muon g-2 experiment at the University of Liverpool. He said: "The University of Liverpool established itself as a key institute on the experiment due to the performance of the tracking detectors, which were designed and built here. Since then we were able to add to the group and had people in leading roles across every aspect of the measurement. The precision we have reached is beyond the initial expectation, and we now have a result that will be a test of New Physics for many years to come."
Professor Thomas Teubner, from the Department of Mathematical Sciences, is one of only two theory-members of the Fermilab g-2 experiment and also a member of the Steering Committee of the Muon g-2 Theory Initiative.
He said: "It has been a great privilege to be part of this fantastic collaboration. The experiment has delivered beyond expectations. Now it is up to the theory community to further improve the g-2 Standard Model prediction to obtain even better constraints on New Physics."
Muons
The Muon g-2 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, aμ, calculated with (g-2)/2. The Muon g-2 experiment gets its name from this relation.
Previous measurements
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.
A plot showing the accumulated amount of data analyzed (in number of positrons) over the six data-taking periods, or runs, from April 2018 to May 2023. Credit: Muon g-2 collaboration.
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.
Standard Model
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.
Latest measurement
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.
