Muons may not behave as expected. But scientists can’t agree on what to expect.
By analyzing how subatomic particles oscillate in a magnetic field, physicists have determined a property of the muon’s internal magnet with greater precision than ever before, researchers from the Muon g−2 experiment reported Aug. 10 at a workshop hosted by Fermilab in Batavia, Illinois.
Previous measurements of muon magnetism did not agree with theoretical predictions. These predictions come from one of the most important and thoroughly tested scientific theories ever developed, the Standard Model of particle physics, which describes subatomic particles and the forces that bind them.
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Many physicists hoped that the muon discrepancy might point to a flaw in an unshakable theory that could lead to a better understanding of the universe. But several recent scientific surprises have confounded the theoretical prediction of the muon’s tiny magnet force, making it difficult to tell whether the measurement points to new physics or an unresolved problem with the prediction.
Measurements of muon magnetism have long hinted at unknown particles
Muons belong to the same family of particles as electrons, but they are about 200 times more massive. These short-lived particles behave like miniature magnets, each with its own magnetic field. The strength of this magnet is regulated by a strange effect of quantum physics. Empty space is filled with a constant barrage of particles that appear temporarily before disappearing. Known as “virtual” particles, they have very real effects. These temporary particles change the strength of the muon magnet by an amount that can be calculated according to the standard model.
The exact value of this setting—known as the anomalous magnetic moment, or “g−2” in physics equations—is what has puzzled physicists.
Surprisingly, particles unknown to science can change the value of g−2 that scientists measure. So previous hints of disagreement with the predictions of the standard model caused an uproar among physicists.
“The muon behavior we measure is affected by all the forces and particles in the universe,” says g−2 muon researcher Brynn McCoy, a physicist at the University of Washington in Seattle. “Essentially, it gives us a direct window into how the universe works.”
The first indication of a discrepancy between the prediction and measurements of g−2 comes from an experiment at Brookhaven National Laboratory in Upton, New York, completed more than two decades ago. Then in 2021, the Fermilab-based Muon g−2 experiment reported its first results, confirming the discrepancy.
Muon g−2 has now doubled its accuracy in an updated measurement of magnetism, the researchers reported at a Fermilab workshop and in a paper published Aug. 10 on the Muon g−2 collaboration website.
“Achieving this level of precision is truly unprecedented and truly impressive,” says University of Chicago physicist Carlos Wagner, who was not involved in the experiment. “I’m just thrilled.” The new measurement contains four times more data than the previous one, among other improvements that increased accuracy.
Scientists aim to compare this measured value with the prediction of a standard model. But it is difficult to determine exactly what the standard model implies.
There is a complicated step to calculate the value of g−2
In 2020, after careful consideration, a group of theoretical physicists called the g−2 Muon Theory Initiative arrived at a consensus prediction, which can be compared to measurements. But since then, new, conflicting information from other experiments and theoretical calculations has emerged, detailed in a statement published Aug. 9 on the g−2 Muon Theory Initiative website. This information left the prognosis uncertain.
“At this point, it’s impossible to compare and say whether the Standard Model agrees with experiment,” says theoretical physicist Tom Blum of the University of Connecticut in Storrs.
The confusion is related to a particularly difficult part of calculating g−2. Known as hadronic vacuum polarization, it refers to the rectification resulting from a virtual photon emitted by a muon that decays into a quark and its antimatter partner, the antiquark. Quarks are a class of particles that make up larger particles known as hadrons, including protons and neutrons. The quark and antiquark interact before annihilating back into a virtual photon.
Scientists have invented two main methods of calculating the polarization of the hadronic vacuum. The traditional method involves the use of certain experimental data as input data for the calculation. This data comes from experiments that measure how electrons and their antimatter particles, positrons, collide to form hadrons. It is believed that the results of such experiments are well studied.
But a recent experiment, CMD-3, at the VEPP-2000 particle collider in Novosibirsk, Russia, is inconsistent with these other experiments, the researchers reported in February on arXiv.org. If this one outlier is correct, it means that the hint of a discrepancy between the muon measurements and the prediction may be weaker than previously thought.
A second way to estimate spiny hadronic vacuum polarization uses a method called lattice quantum chromodynamics. This technique involves mathematically dividing space-time into a grid to make calculations more understandable. Scientists have only recently been able to make such calculations precise enough for useful comparisons.
In 2021, a group called “BMW” published own calculation of the contribution of the polarization of the hadronic vacuum in Nature . This estimate indicated a closer harmony between the prediction and g−2 measurement and disagreed with the data-driven approach. But the technique required confirmation. Other scientists have since performed their own calculations to verify part of BMW’s result. These teams achieved similar results to BMW, increasing confidence in the grid method.
Attention has now shifted away from the careful study of experimental measurements and is instead directed towards analyzing the discrepancies between various theoretical methods.
“The experiment was a success,” says theoretical physicist Thomas Teubner of the University of Liverpool in England, a member of the Muon g−2 collaboration. Now, he says, it’s up to theoretical physicists to figure out whether muons conform to the standard model or break it. “We have to get our house in order.”
