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The third and final result is in perfect agreement with the with the first two results of the experiment
Today the Muon g-2 collaboration has published its third and final result of the measurement of the anomalous magnetic moment of the muon. The final result is in perfect agreement with the two previously published results from 2021 and 2023 but is characterized by a much better precision of 127 parts in a billion (127 ppb). This even exceeds the original goal of the experiment, which was to achieve a precision of 140 parts in a billion. This most precise measurement of the anomalous magnetic moment of the muon to date was presented at a seminar at the Fermi National Accelerator Laboratory (Fermilab, FNAL) and submitted to the renowned journal Physical Review Letters for publication.
The research group led by Professor Martin Fertl, who has been conducting research in the field of low-energy particle physics at the PRISMA⁺ Cluster of Excellence at Johannes Gutenberg University Mainz (JGU) since 2019, is the only one in Germany to make experimental contributions to the muon g-2 collaboration. Martin Fertl himself started working on the muon g-2 experiment in 2014 as a postdoctoral researcher at the University of Washington, Seattle. “This long-awaited value will be the world's most precise measurement of the anomalous magnetic moment of the muon for many years to come - and will set the experimental benchmark,” says Martin Fertl. “We can be very proud of this enormous achievement. It can only be achieved together in a large team like the Muon g-2 Collaboration. Internationality and the pooling of many different areas of expertise from high-energy, nuclear, laser, atomic and accelerator physicists are the key to success here.” Despite the recent convergence of the theoretical prediction to the now measured experimental value - which makes the detection of new physics using the muon less likely - this is a milestone in the search for extensions to the Standard Model.
Final result exceeds expected precision
The experimental value now determined for the anomalous magnetic moment of the muon a(μ) (see explanation below) 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.)
+- 0.000 000 000 026(ext.)
The quadrature combination of the statistical and systematic uncertainties with the uncertainties on other natural constants results in 0.001 165 920 705 +- 0.000 000 000 148, which corresponds to a relative uncertainty of 127 ppb. This final result is based on data collected over six years since 2018. It therefore includes the newly evaluated data from the fourth, fifth and sixth measurement rounds, which were recorded from 2020 to 2023, as well as the data from the first three measurement campaigns already published in 2021 and 2023. The data set of the fourth, fifth and sixth measurement rounds comprises more than 72% of the total of 308 billion muons measured.
The final result of g-2 could be determined with a total precision of 127 parts in a billion - compared to 200 parts in a billion, which was achieved with the evaluation of the first three years of data and announced in August 2023. Overall, the precision target of 140 parts in a billion formulated in 2012 was ultimately exceeded by far.
“This is a great experimental achievement,” says Dr. René Reimann, a postdoc in Martin Fertl's research group, who has made crucial contributions to the calibration of the magnetic field in the experimental setup, together with doctoral student Mohammad Ubaidullah Hassan Qureshi. “We have checked many systematic effects in an independent way, so that at least two teams come to the same conclusion. This has greatly increased our confidence in the quoted uncertainties.”
Muons as test objects for new physics – What does g-2 mean?
Physicists describe the workings of the universe at its most fundamental level using a theory known as the Standard Model. By making theoretical predictions based on the Standard Model and comparing them with experimental results, they can determine whether the theory is complete or, alternatively, whether there must be physics beyond the Standard Model in case that experiment, and theory do not match. In this context, the anomalous magnetic moment of the muon is a very important precision quantity that provides one of the most stringent tests of the Standard Model.
Muons are fundamental particles in the Standard Model that are similar to electrons but are about 200 times heavier and only live for a millionth of a second. Like the electron, the muon has a magnetic moment, a kind of miniature internal bar magnet which, in the presence of a magnetic field, precesses or wobbles like the axis of a spinning top. The precession frequency in a given magnetic field depends on the magnetic moment of the muon, whose characteristic strength is determined by the factor g.
The muon g-2 experiment receives its name from the fact that the “g” of the muon always deviates slightly - by around 0.1 percent - from the simple expectation of g=2. This anomaly is commonly referred to as the anomalous magnetic moment of the muon (a(μ) = (g-2)/2). The difference from g to 2 - or “g minus two” - is due to the muon's interactions with virtual particles in a kind of quantum foam that surrounds it. Figuratively speaking, these particles, which are constantly created and decay again in fractions of a second, reach for the muon's “hand” like subatomic “dance partners”, thereby changing the way the muon interacts with the magnetic field. The Standard Model includes all known “dance partners” and predicts how the quantum foam changes the value of g. But there could be more. The physics world is excited about the possible existence of previously undiscovered particles that would also contribute to the value of g-2 – and open the window to the exploration of new physics.
Race track 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 uses this to determine the anomalous magnetic moment. The muon beam was generated at the FNAL muon campus especially for the experiment - and exhibited a previously unattained purity.
To carry out the measurement, the muon g-2 collaboration repeatedly sent this beam of muons into a superconducting magnetic storage ring with a diameter of 14 meters, where they circulated on average around 1000 times at almost the speed of light. Using detectors lining the ring, the researchers were able to determine how fast the muons' compass needles moved relative to their trajectories. The physicists also have to precisely measure the strength of the magnetic field in order to determine the value of g-2. And this is precisely where the expertise of Martin Fertl and his working group lies: the extremely precise measurement of the magnetic field in the muon storage ring over the entire measurement period of several years. At his previous place of work, Martin Fertl already led the development of an array of highly sensitive magnetometers based on the principle of pulsed nuclear magnetic resonance. Several hundred of these measuring heads are installed in the walls of the vacuum chambers surrounding the muons. A further 17 remotely controlled measuring heads orbit the storage ring in order to precisely measure the applied magnetic field. “To do this, we had to investigate and understand countless effects. For example, in dedicated measurement campaigns we discovered that the magnet changes its magnetic field minimally even days after being switched on,” reports René Reimann.
For the Fermilab experiment, a storage ring was reused that was originally built for the previous experiment at Brookhaven National Laboratory, which was completed in 2001. In 2013, the muon g-2 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 been continuously improved ever since. Finally, on July 9, 2023, the collaboration switched off the muon beam and ended data collection with muons after six years. This was followed by a one-year measurement campaign to finally characterize the magnetic field. As a result, the goal of collecting a data set for statistical analysis that is more than 21 times larger than the data set from the previous experiment in Brookhaven was achieved.
Is there a discrepancy between theory and experiment?
Physicists can calculate the effects of the known “dance partners” of the Standard Model on the anomalous magnetic moment of the muon with incredible precision. The calculations take into account the electromagnetic, weak and strong interactions. If the Standard Model is correct, this ultra-precise prediction should agree with the experimental measurements.
Calculating the prediction of the Standard Model for the muon g-2 is a major challenge. The contributions of the strong interaction caused by the quarks have been a particular focus for many years. In 2017, well over 100 physicists worldwide joined forces in the “Muon g-2 Theory Initiative” to tackle this challenge together, including Prof. Dr. Hartmut Wittig, theoretical physicist and spokesperson of the PRISMA⁺ Cluster of Excellence, 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 prediction of the Standard Model for the muon g-2 that was available at the time: it uses the so-called “data-driven” method, in which measurement data from experiments are incorporated into the theoretical prediction, as the usual calculation methods generally fail when naively applied to the strong interaction. The value calculated in this way deviated significantly from the first experimental result of the muon g-2 experiment - a strong indication of new physics beyond the Standard Model, which caused quite a stir. “Since 2021, however, there has been mounting evidence that the theoretical value needs to be adjusted again,” says Hartmut Wittig, looking back. “In the meantime, calculations based on the fundamental theory of Quantum Chromodynamics (QCD) had become possible, which do not rely on experimental data but require large-scale numerical calculations on supercomputers. This method - called lattice QCD - provided a significantly higher value for the anomalous magnetic moment of the muon, which was closer to the experimental result.”
Recently, the “Muon g-2 Theory Initiative” published a new official prediction: it is based on lattice QCD calculations, which have been significantly refined since 2020. At the same time, the data-driven method is no longer taken into account because strong inconsistencies in the experimental input quantities have been observed since then. The new value is
a(μ) = (g-2)/2 (muon, theory) = 0.001 165 920 33 +- 0.000 000 000 62
“We have therefore switched to lattice-QCD calculations and have accordingly shifted the value of the Standard Model prediction upwards as a result. Our new reference value is thus in good agreement with the now published measurement results, so that the Standard Model may have pulled its neck out of the noose once again,” comments Hartmut Wittig, before continuing: ”And yet the muon anomaly is far from solved: Above all, we need to understand why the data-driven method and lattice-QCD calculations give such different results. And we must also bear in mind that the uncertainty of the Standard Model prediction is about four times larger than that of the experimental value. To achieve true comparability, we need to further refine our computational methods to ultimately achieve a precision similar to that of the experiment. No matter how you look at it: The different results of the theoretical predictions remain a puzzle. Once this has been resolved, we can expect that the precision of the theoretical prediction will be comparable to that of the experiment, which is when the question of the validity of the Standard Model will be raised again. The muon anomalous magnetic moment remains an exciting topic.”
Numerous contributions from Mainz – in experiment and theory
The mystery surrounding the anomalous magnetic moment of the muon is one of the key initiatives of the PRISMA⁺ Cluster of Excellence. Martin Fertl's working group was responsible for operating the magnet from Mainz, especially during the Covid19-related travel restrictions, to relieve the colleagues on site at Fermilab. “Suddenly, many collaboration members were no longer able to travel to the experiment, and the experiment had to be fully automated within a very short time,” Martin Fertl recalls. “This allowed us European collaboration members in particular to work the night shifts at Fermilab and keep the experiment running day and night,” says Hassan Qureshi. Hartmut Wittig and his colleagues Achim Denig, Marc Vanderhaeghen and Harvey Meyer are making numerous important contributions to theoretical prediction as part of PRISMA⁺. Achim Denig's working group, for example, is focused on clarifying the discrepancies in the experimental input variables for data-driven prediction. Marc Vanderhaeghen and Harvey Meyer address other significant contributions of the strong interaction. “It is this close interaction that defines our cluster,” emphasize Martin Fertl and Hartmut Wittig in unison.
The muon g-2 collaboration
The muon g-2 collaboration involves almost 180 scientists from 37 institutions in seven countries, including almost 40 students who have completed their doctorates based on their work on the experiment. Unusually, the scientists come from different areas of physics and normally work on different experiments. For example, not only high-energy physicists are involved in the muon g-2 experiment, but also accelerator physicists, nuclear physicists and atomic physicists.
More images:
1) The Muon g-2 storage ring with a diameter of 14 meters at the Fermi National Accelerator Laboratory
https://download.uni-mainz.de/presse/08_prisma+_muon_g-2_run_4_5_6_Speicherring_...
Photo/©: Ryan Postel, Fermilab
2) Dr. René Reimann working on the Muon g-2 storage ring
https://download.uni-mainz.de/presse/08_prisma+_muon_g-2_run_4_5_6_Speicherring_...
Photo/©: Private
3) Final result of the Muon g-2 experiment (light background)
https://download.uni-mainz.de/presse/08_prisma+_muon_g-2_run_4_5_6_Ergebnis_hell...
Ill./©: Muon g-2 collaboration, Fermilab
4) Final result of the Muon g-2 experiment (dark background)
https://download.uni-mainz.de/presse/08_prisma+_muon_g-2_run_4_5_6_Ergebnis_dunk...
Ill./©: Muon g-2 collaboration, Fermilab
5) Collected statistics over the course of the experiment (light background)
https://download.uni-mainz.de/presse/08_prisma+_muon_g-2_run_4_5_6_Statistik_hel...
Ill./©: Muon g-2 collaboration, Fermilab
6) Collected statistics over the course of the experiment (dark background)
https://download.uni-mainz.de/presse/08_prisma+_muon_g-2_run_4_5_6_Statistik_dun...
Ill./©: Muon g-2 collaboration, Fermilab
7) Prof. Dr. Martin Fertl in the Muon g-2 storage ring
https://download.uni-mainz.de/presse/08_prisma+_muon_g-2_run_4_5_6_Speicherring_...
Photo/©: Private
Prof. Dr. Martin Fertl
Institute for Physics and PRISMA⁺ Cluster of Excellence
Johannes Gutenberg University Mainz, 55099 Mainz
phone: +49 (0)6131 39-37687
Email: mfertl@uni-mainz.de
https://ag-fertl.physik.uni-mainz.de/
Prof. Dr. Hartmut Wittig
Institute for Nuclear Physics and PRISMA⁺ Cluster of Excellence
Johannes Gutenberg University Mainz, 55099 Mainz
Email: hartmut.wittig@uni-mainz.de
https://wwwth.kph.uni-mainz.de/
Link to the pre-publication version of the article that will be available on the arXiv on June 3, 2025 https://seafile.rlp.net/f/8ebc4dca95c2403da73b/
Muon g-2 Theory Initiative, The anomalous magnetic moment of the muon in the Standard Model: an update
https://inspirehep.net/literature/2925594 , https://arxiv.org/abs/2505.21476 [hep-ph]
https://muon-g-2.fnal.gov/ – homepage muon g-2 experiment
https://www.prisma.uni-mainz.de – PRISMA⁺ Cluster of Excellence
Prof. Dr. Martin Fertl working on the Muon g-2 storage ring
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Prof. Dr. Martin Fertl working on the Muon g-2 storage ring
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