The mysteries of the muon continue to fascinate physicists. Last year, an experiment suggested that the elementary particle had an inexplicably strong magnetism, potentially breaking a decades-long series of victories for the leading theory of particle physics known as the Standard Model. Now, revised calculations by several groups suggest that the theory of muon magnetism’s prediction may not be too far removed from the experimental measurements after all.
The new predictions are preliminary and do not fully justify the Standard Model. But by narrowing the gap between theory and experiment, they can make it easier to resolve the discrepancy — while potentially creating another.
The muon is nearly identical to the electron, except it is 200 times heavier and short-lived, decaying in a millionth of a second after forming in particle collisions. Like the electron, the muon has a magnetic field that makes it act like a small bar magnet. As muons travel, they generate various particles that briefly jump in and out of existence. These ephemeral particles slightly increase the muon’s magnetism, known as its magnetic moment. The big question is: by how much?
If the Standard Model already includes all the elementary particles of the universe, it should be able to precisely quantify this additional magnetic contribution. But if experiments prove that nature deviates from that prediction, it would indicate the existence of hitherto unknown particles, whose fleeting appearances could skew the muon’s magnetic moment more than expected. Researchers have already seen evidence of such a discrepancy and have spent decades improving the accuracy of both theory and experiments to confirm whether they yield different results.
In 2020, the theoretical-physical community produced a consensus paper with the most accurate prediction yet for the magnetic moment of the muon1† This was largely based on calculations based on the fundamental principles of the Standard Model, but the researchers had to input some experimental data to represent the magnetic influence of particles such as quarks and gluons, which could not be adequately calculated with theory alone.
This calculation was soon accompanied by the most accurate experimental measurement of the muon’s magnetic moment. In April 2021, the Muon g – 2 experiments at the Fermi National Accelerator Laboratory (Fermilab), outside Chicago, Illinois, reported that the magnetic moment of the muon was significantly higher than the theoretical prediction2†
But on the same day, physicists in a collaboration called BMW revealed separate magnetic moment calculations that didn’t require the help of experimental data. They used a technique called lattice quantum chromodynamics (lattice QCD) to simulate the behavior of quarks, gluons and other particles. This linked the magnetic moment of the muon higher than the calculation in the 2020 consensus paper, and closer to the muon g – 2 experimental value3†
Lattice QCD had not played a prominent role in the consensus paper because the technique’s predictions were not accurate enough at the time. State-of-the-art mathematical techniques and sheer supercomputing power then helped the BMW team boost their grid QCD simulations to hit the mark. Since then, at least eight teams of physicists around the world have raced to validate or improve the BMW prediction. They started by focusing on a narrow range of the particle energies that BMW has simulated.
Two preliminary results from this “energy window” were posted to arXiv’s preprint repository in April 2022: one by Christopher Aubin of Fordham University in New York City and his collaborators.4and the other by General Wang at the University of Aix-Marseille in France5† Earlier this month, two more groups — one led by Hartmut Wittig at Johannes Gutenberg University in Mainz, Germany, the other by Silvano Simula of the National Institute for Nuclear Physics in Rome — announced their own framework results at a muon conference in Los Angeles, California. Simula’s group is writing a preprint and Wittig’s group has submitted its preprint on June 14th6† All four calculations validated BMW’s own window results, although their grid techniques vary. “Very different ways of tackling the problem get a very similar result,” Aubin says.
“As time goes on, the different groups come together to a result consistent with BMW’s, at least in the intervening window,” said Davide Giusti, a physicist at the University of Regensburg, Germany, who is a former member of Simula’s collaboration. , and who is now working with another roster QCD group led by his Regensburg colleague Christoph Lehner.
However, the calculations are still preliminary and may deviate once applied outside the current window. “We don’t yet know if the roster results from other collaborations match the BMW result for the other pieces” of the calculation, said Aida El-Khadra, a theorist at the University of Illinois at Urbana-Champaign who is part of another grid-QCD effort.
In addition, the Muon g – 2 experimental result is still higher than the value calculated by lattice QCD, so it is too early to conclude that the standard model was always correct. The Fermilab experiment expects to publish an updated value for the magnetic moment next year, but “even if the gap between theoretical prediction and experiment turns out to be smaller — even if it’s only half that — it would still be a big discrepancy.” , says Wittig.
And if lattice QCD and experiments eventually come to the same value, physicists would still have to explain why the 2020 consensus paper was so erroneous, says Sven Heinemeyer, a theoretical physicist at CERN, the European laboratory for particle physics outside Geneva, Switzerland.
For now, physicists continue to scratch their heads. “It would be hard to believe that all of our lattice simulations were wrong,” Aubin says. But it’s also hard to imagine how the data-driven calculations from 2020 could go wrong, he says.
Still, it’s already clear that lattice QCD will have a significant impact on the issue of muon magnetism, Giusti says. “This calculation is really exciting, and whatever the answer is, it will be decisive.”