A deviation between measured values and the standard model for the muon – the “heavy brother” of the electron – has been a mystery for decades. The anomalous magnetic moment of this elementary particle measured in experiments did not match the theoretical value. Now it becomes clear that it is not the experiments that are the problem, but the theoretical value. Using a new approach, physicists have recalculated an important parameter of this value. Their result provides the most precise value to date for the muon’s anomalous magnetic moment – and it agrees with the experimental measurements. The result confirms the standard model to the eleventh decimal place, as the team reports in Nature.
The Standard Model of particle physics has so far withstood all tests. Nevertheless, it has crucial gaps: it cannot explain the nature of dark matter or dark energy, nor the asymmetry of matter and antimatter. In recent years, physicists have repeatedly observed deviations from the model’s theoretical predictions in experiments. One of them concerns the muon’s magnetic moment. This “brother” of the electron, which is around 200 times heavier, has a magnetic moment like it and reacts to external magnetic fields. The extent of this “tumbling” is described by the muon’s magnetic moment. This so-called g-factor can be precisely calculated based on the charge, mass and spin of the particle and would have to correspond to the value 2 – if there were no quantum fluctuations. Through them, the muon constantly encounters pairs of particles that appear out of nowhere and then disappear again. These interactions change the g-factor by a small value – the so-called anomalous magnetic moment.
Puzzle about the discrepancy
The problem: For decades, measurements of the anomalous magnetic moment (aµ) in the muon have repeatedly shown significant deviations from the theoretical values based on the Standard Model. According to these, the magnetic moment would have to deviate from 2 by around 0.1 percent – if the theories are correct and complete. However, even the most precise measurements to date from the muon g-2 experiment at the Fermi National Accelerator Laboratory (Fermilab) in the USA have continued to provide different values in recent years. Physicists therefore suspect that so-called “new physics” could be hidden behind these discrepancies: previously unrecognized forces or particles that act on the muon.
However, it has so far remained unclear whether the error might not be on the theoretical side. The anomalous magnetic moment depends crucially on the strong interaction – the fundamental force that connects quarks and other subatomic elementary particles to form atomic nuclear building blocks such as protons and neutrons. “When calculating aµ, the uncertainties arise almost exclusively from the strong interaction that is described in the Standard Model by quantum chromodynamics,” explain Zoltan Fodor from the University of Wuppertal and his colleagues.
They therefore recalculated an important parameter for the theoretical value of the muon’s magnetic moment using a new approach. “We use a hybrid approach: It combines the strengths of experimental data with those of lattice gauge theory in different energy ranges,” explain the physicists. Lattice gauge theory divides space-time into cells with minimal distances and then solves the equations of the Standard Model in them. For the recalculation, the team used a finer grid than previously possible and also specified some other influencing factors.
Standard model confirmed
After more than ten years of data analysis and calculations using supercomputers, the result is now available. It represents the most precise value to date for this so-called vacuum polarization of the muon. If this parameter is included in the calculation of the magnetic moment, it also results in the most precise calculation of this important quantity to date, as the team reports. “By reducing the uncertainties, we can now compare theory and experiment with unprecedented precision – and thus test the standard model down to eleven decimal places,” says co-author Finn Stokes from Adelaide University in Australia.
The crucial thing is that with the new theoretical value for the anomalous magnetic moment of the muon, the discrepancies between measurement results and theory also disappear. “We were able to show that they are no longer there,” said Stokes. “The interactions known so far can fully explain the measured values.” The deviation between theory and the most recent experiment is only 0.5 standard deviations. In doing so, physicists could have solved a puzzle that has existed for decades.
At the same time, the new value reveals that, at least when it comes to the muon’s interactions with the quantum world, there is apparently no new physics in the form of unknown particles or forces. “I’ve been asked how it feels to make this discovery, and to be honest, I’m almost a little sad,” says Fodor. “When we started calculating this value, we thought that we would find strong evidence for a fifth fundamental force. Instead, we found that there is no such fifth fundamental force. We now have very precise evidence for the Standard Model and its basis, quantum field theory.”
Source: Zoltan Fodor (University of Wuppertal) et al., Nature, doi: 10.1038/s41586-026-10449-z