For decades, a puzzling contradiction about tiny subatomic particles called muons fueled speculation that physicists were on the verge of discovering an entirely new force of nature. Now, an international research team led by physicists at Penn State University says the mystery appears to be solved, and the answer supports rather than overturns existing physics.
The researchers published their findings in the journal naturedescribes one of the most accurate particle physics calculations ever completed. Their study shows that the long-debated discrepancy between theory and experiment is likely caused by limitations in early calculations rather than evidence of unknown physics.
Decades of expectations for “new physics”
The mystery focuses on muons, short-lived particles that are similar to electrons but about 200 times heavier. For more than 60 years, measurements of muons’ magnetic behavior have appeared inconsistent with predictions by the Standard Model, the framework scientists use to describe the fundamental particles and forces in the universe.
This discrepancy excited physicists because it suggested an undiscovered particle or even the possibility of a new “fifth force” beyond the four known fundamental forces.
“Over the past 60 years or so, many calculations have been made, and as the precision of the calculations has increased, they have all pointed to contradictions and new interactions that overturn the known laws of physics,” said Zoltan Fodor, Distinguished Professor of Physics at Pennsylvania State University and lead author of the study. “We applied a new method to calculate this amount of mismatch and showed that it does not exist. This new interaction that we wanted simply does not exist. The old interaction can fully explain its value.”
The team spent more than a decade refining their calculations. Their final results matched theoretical predictions and experimental measurements to within less than half a standard deviation. According to Fodor, the new study confirms the Standard Model to 11 decimal places, significantly narrowing the possibility that unknown physics is hidden in this particular measurement.
“People ask me how I feel about this discovery, and to be honest, I’m a little sad,” Fodor said. “When we started calculating this quantity, we thought we had a good, reliable calculation for a new fifth force. Instead, we found that the fifth force does not exist. We found a very precise proof not only of the Standard Model, but also of quantum field theory, the basis on which the Standard Model was built.”
Muon’s strange magnetic behavior
The study focused on a property known as the muon’s magnetic moment, which describes how strongly the particle acts like a tiny magnet. Quantum theory predicts that the relationship between a particle’s wobble and its surrounding magnetic field should be exactly equal to 2.
However, in real experiments, the values shift slightly because other particles briefly appear and disappear in empty space, subtly influencing the muon’s behavior. This small deviation is known as the “anomalous magnetic moment” or g−2.
Muons are especially sensitive to these transient quantum effects because they are much heavier than electrons. Its sensitivity has made muon g−2 one of the most closely studied measurements in modern physics.
Experiments conducted at CERN in the 1960s and 1970s, then at Brookhaven National Laboratory, and more recently at Fermi National Accelerator Laboratory, all measured the muon’s magnetic moment with remarkable precision. These experiments recently won the Breakthrough Prize in Fundamental Physics, one of the world’s most prestigious scientific awards.
For years, experimental measurements continued to appear to contradict the Standard Model’s predictions, raising hopes that something entirely new might be influencing muons.
Why did strong forces make problems difficult?
The challenge in calculating muon behavior was primarily posed by the strong force, the strongest of the four known fundamental forces. This strong force binds quarks together inside protons, neutrons, and other particles.
Unlike gravity or electromagnetism, strong forces become stronger the further apart particles are. It’s like a rubber band that gets tighter the more you pull it. Trying to separate particles held together by strong forces requires so much energy that entirely new particles can form in the process. These additional particles further complicate the calculations.
Because of this extreme complexity, accurately predicting muon behavior within the Standard Model remains one of the most difficult problems in particle physics.
Supercomputers and lattice quantum chromodynamics
To tackle this problem, the researchers turned to lattice quantum chromodynamics, a computational technique that uses huge supercomputers to simulate strong forces. This method divides space and time into very fine grids that allow scientists to numerically solve the equations that govern particle interactions.
“The old methodology required collecting thousands of experimental results and reinterpreting them to arrive at a single number: the muon’s magnetic moment,” Fodor said. “Our approach was completely different. We divided spacetime into very small cells, or lattices, and then solved the Standard Model equations. There was a great deal of theory, mathematics, programming, computational knowledge, and computer architecture behind this calculation.”
Although lattice calculations have become increasingly powerful over the past decade, it has remained very difficult to achieve the accuracy required for muon g−2 calculations. So the team combined several approaches.
They used lattice calculations for short and intermediate distances between cells and incorporated reliable experimental measurements for long distances, where existing data were already in strong agreement. This hybrid strategy reduced uncertainty more effectively than relying on either method alone.
The researchers also simulated the equations using a finer grid than previous studies, further improving accuracy and reducing possible errors.
The final calculations represent the most accurate determination of the muon’s magnetic moment to date. Once incorporated into the predictions of the full standard model, longstanding experimental disagreements essentially disappear.
“This prediction combines the electromagnetic, weak, and strong forces, each of which requires very different theoretical tools, into a single calculation that is accurate to parts in a billion,” Fodor said. “This shows that we really understand how nature works at an incredibly deep level.”
What the results mean for physics
The researchers say the discovery does not completely rule out the possibility of undiscovered physics. But one of the strongest potential clues to something beyond the standard model is now much less convincing.
Future experiments may discover evidence of new particles and forces elsewhere, but for now, the Standard Model will continue to withstand intense scrutiny.
“Although we didn’t have the fifth force, we did have a very nice and perhaps the best proof of quantum theory, a theory that is fundamental to our understanding of nature’s most fundamental problems,” Fodor said.
The Pennsylvania portion of the study was supported by the U.S. Department of Energy and the European Research Council.
