UNIVERSITY PARK, Pa., April 22, 2026 -- A tiny discrepancy in particle physics has loomed for decades as an exciting possible crack in one of science’s most successful theories, hinting at unknown forces or quantum objects. Now, an international team led by a Penn State physicist has published the most precise study yet to reveal the discrepancy was a fluke in calculation, not nature.

More than half a century of measurements of a fundamental property of the muon — the more massive, short-lived cousin of the electron — did not line up with theoretical predictions, raising hopes that new physics might be behind the unexplained inconsistency.

In a paper published today (April 22) in the journal Nature, a team led by a Penn State researcher describes one of the most precise calculations ever performed in particle physics, showing that the Standard Model — the theory describing the known building blocks of matter — still holds.

“There were many calculations in the last 60 years or so, and as they got more and more precise they all pointed toward a discrepancy and a new interaction that would upend known laws of physics,” said Zoltan Fodor, distinguished professor of physics at Penn State and lead author of the study. “We applied a new method to calculate this discrepancy quantity, and we showed that it’s not there. This new interaction we hoped for simply is not there. The old interactions can explain the value completely.”

The team’s findings, which took over 10 years to calculate, bring theory and experiment into agreement to within half a standard deviation, with a level of precision that would have been unthinkable just a decade ago, Fodor said. The result strengthens confidence in the Standard Model to 11 decimal places, dramatically narrowing the space where new physics could be hiding.

“People ask me how it feels to make this discovery and, to be honest, I feel somewhat sad,” Fodor said. “When we started to calculate this quantity, we thought we were going to have a good and trustworthy calculation for a new fifth force. Instead, we found there is no fifth force. We did find a very precise proof of not just the Standard Model, but also of quantum field theory, which is the foundation on which the Standard Model was built.”

The new calculations and prior ones hinged on what scientists call the “magnetic moment” of the muon, a measurement for how strongly the particle behaves like a tiny bar magnet. According to quantum theory, that number should be exactly two, representing the ratio of how the particle “wobbles” to the strength of the magnetic field in which it exists. But in experiments, researchers detected deviations from what theory predicted. Other particles popped in and out of existence, tugging on the muon just enough to alter its magnetic strength by a small amount known as the “anomalous magnetic moment,” or g−2.

Because muons are about 200 times heavier than electrons, they are especially sensitive to such tugs and that extreme sensitivity made the muon g−2 one of the most carefully scrutinized quantities in physics.

Experiments at CERN, the European Organization for Nuclear Research, in the 1960s and 1970s and at Brookhaven National Laboratory in New York in the early 2000s and later at Fermi National Accelerator Laboratory in Illinois measured the muon’s magnetic moment with extraordinary precision. The experiments recently received the Breakthrough Prize in Fundamental Physics, one of the most prestigious and lucrative international science awards. For years, the experimental value for the muon g−2 continued to appear in disagreement with the Standard Model prediction, hinting at physics beyond what is currently known.

The theoretical calculation depended on an especially difficult aspect of physics: the strong force, which is the most powerful of the four fundamental forces of nature. The other three are gravity, electromagnetism and the weak force. The strong force, which is about 100 trillion trillion trillion times stronger than gravity, binds subatomic quarks into protons, neutrons and other hadrons.

The strong force is particularly challenging to work with as a theory because it increases with distance, like a rubber band becoming harder to pull the more it is stretched out. It requires so much energy to pull the strong force apart that doing so creates new particles — which, in turn, affect the measurement of the strong force. Due to the enormous strength of the strong force, it is nearly impossible to carry out theoretical calculations to verify if the muon behaves in accordance with the Standard Model or not.

The research team tackled this problem in a new way by employing lattice quantum chromodynamics — a computational approach that simulates the strong force on enormous supercomputers by breaking space and time into a fine grid or lattice.

“The old methodology involved collecting thousands of experimental results and reinterpreting them to get the single number, the magnetic moment of the muon,” Fodor said. “Our approach was completely different. We divided space time into very small cells, a lattice, then we solved the equations of the Standard Model on that. There was an awful lot of theory, mathematics, programming, computational knowledge and computer architecture behind this calculation.”

Over the 10 years that the team has been working together, lattice calculations have improved dramatically, but reaching the precision needed for the muon g−2 still remained a daunting challenge, so they tried something different. The researchers combined lattice calculations at short and intermediate distances between the small cells, with the most reliable experimental data at long distances, where existing measurements are already in strong agreement. This allowed them to reduce uncertainties more effectively than either approach would alone.

At the same time, they simulated the theory on finer lattices than in previous studies, sharply reducing room for error. The result is the most precise calculation yet of the muon’s magnetic moment. When that number is folded into the full Standard Model prediction, the long‑standing mismatch with experimental results essentially disappears.

“The prediction combines electromagnetic, weak and strong forces, that each require vastly different theoretical tools, into a single calculation that’s accurate to parts-per-billion,” Fodor said. “It shows that we really do understand how nature works at an incredibly deep level.”

The result does not mean that new physics has been ruled out, he added, but one of its more promising avenues just got a lot smaller. Future experiments will help clarify the picture, but for now, the Standard Model holds strong.

“We didn't get the fifth force, but we did get a very nice and probably the best proof of quantum theory, which is the underlying theory of all our understanding of the most fundamental questions of nature,” Fodor said.