The anomalous magnetic moment of the muon was measured by the E821 Muon g-2 experiment at Brookhaven National Laboratory. Data was taken between 1997 and 2001. An uncertainty of 540 parts per billion (ppb) was achieved. But the result left the scientific community with a long-standing, larger-than-3σ deviation from the prediction obtained within the Standard Model of Particle Physics (SM).
The comparison of the experimental result with the high precision SM prediction provides as stringent test of the fundamental assumptions of the model. This discrepancy between the BNL result and the theoretical expectation at the time was taken as a strong hint of new physics.
Over the years, the SM prediction was continuously refined and verified. In 2017 the Muon g-2 Theory Initiative was founded to provide a comprehensive SM prediction in light of the upcoming new Muon g-2 experiment at Fermi National Accelerator Laboratory (FNAL), Batavia, IL, USA. Their 2020-recent result is summarized in the White Paper and has an uncertainty of 350 ppb. Their latest result from 2025 has an uncertainty of 540 ppb. This increased uncertainty reflects the yet unresolved tensions between different methods to predict an expectation value for the anomalous magnetic moment of the muon.
The Muon g-2 experiment E989 at Fermi National Accelerator Laboratory, Batavia, IL, USA has decreased the global experimental uncertainty from 350 ppb in 2021, to 190 ppb in 2023 to its final result with 127 ppb in 2025.
The development of the experiment and the theoretical prediction have to be seen in interaction within their temporal sequence. While the 2020-White Paper prediction and the 2021-experimental result showed a tantalizing 4.2 standard deviation large tension, seemingly confirming the long-standing hints towards new physics. The subsequent improved experimental results are all self-consistent. But the hard work of the theory community revealed tensions among the two prevalent methods to predict the theoretical expectation value. In 2021, the approach using so-called lattice Quantum Chromo Dynamics (lattice QCD) just reached the accuracy level needed to weigh in to the comparison with the traditional method to derive the theoretical prediction from extremely difficult-to-perform measurements of electron-positron scattering cross-sections.
The tensions between the theoretical approaches are currently under investigation. The resolution of the tension is poised to allow deep insights into these two different approaches and will extend the scientific reach of our unprecedentedly precise measurement of muon g-2 even further.
As a postdoctoral researcher at the University of Washington's Center for Experimental Nuclear Physics and Astrophysics Martin Fertl was heavily involved in the construction of the precision magnetic field measurement instrumentation that is required to ultimately measure the magnetic field in the muon storage volume.
After relocating to JGU Mainz and the PRISMA+ Cluster of Excellence in 2019, Martin Fertl's group has provided groundbreaking contributions to the continued improvement of the magnetic field and the analysis of the acquired data. In particular, postdoctoral fellow Dr. René Reimann and graduate student Hassan Qureshi have revealed a plethora of subtle effects, that alter the precision magnetic field and need to be taken into account for an accurate determination of the experimental value of muon g-2. Details about the determination of the precision magnetic field environment can be found here and here.
More details about the Muon g-2 experiment at Fermilab in general can be found on the collaboration's webpage. A one-page description of the experiment in German is available here.
NEWS (April 7th, 2021): The newest measurement of the anomalous magnetic moment from the FNAL E989 experiment can be found here (after the embargo has dropped).
A PDF-version of the poster summarizing the results of the Muon g-2 experiment at Fermilab can be found here.
A description of the experiment in one page can be found here in German and in English.
