New calculation narrows muon g-2 anomaly and refocuses debate on hadronic inputs

For years, the muon g-2 anomaly was framed as a possible crack in the Standard Model, the reigning theory of particle physics. Now the center of the dispute has moved. A peer-reviewed calculation published in Nature on April 22, 2026, brings the Standard Model into agreement with the best muon g-2 measurements, shifting the argument away from experiment versus theory and toward a narrower but still consequential question: Which theory inputs, and which older electron-positron collider datasets, are correct?

That matters because muon g-2 — a measure of how a muon wobbles in a magnetic field — had long been treated as one of the strongest possible hints of unknown particles or forces. The new result weakens that case. But it does not mean the issue is settled, or that physicists have closed the book on new physics. Instead, the debate has focused on the messy part of the Standard Model prediction: the contribution from hadronic vacuum polarization, or HVP, which reflects the effect of quark-antiquark activity on the muon’s magnetism.

In the new paper, “Hybrid calculation of hadronic vacuum polarization in muon g−2 to 0.48%,” researchers Boccaletti, Borsányi, Cotellucci and co-authors report a Standard Model value of aμ = 11,659,205.2(3.6) × 10−10. “Adding our determination of aμ(LO-HVP) to the other standard-model contributions compiled in ref. [3] yields aμ = 11,659,205.2(3.6) × 10−10. ... Our prediction differs from that measurement by −0.5σ,” the paper says.

The experimental benchmark comes from the Muon g−2 Collaboration at Fermilab, which published its final result on June 2, 2025, using data collected from 2020 through 2023. Fermilab reported aμ = 116 592 0710(162) × 10−12 for the new datasets and a combined Fermilab result of 116 592 0705(148) × 10−12. The world average is 116 592 0715(145) × 10−12, with 124 parts-per-billion precision. In the collaboration’s words: “The new experimental world average, dominated by the measurements at FNAL, is aμ(exp) = 116 592 0715(145) × 10−12.”

So the measurement has not moved much. What changed is the theory estimate.

The biggest source of disagreement has been HVP, the part of the calculation tied to the strong interaction, which is harder to pin down than the rest of the Standard Model. Physicists have used two main approaches. One is data-driven: take measurements from electron-positron collisions that produce hadrons and use those data to infer the HVP contribution. The other is lattice QCD, a first-principles method that calculates the effect numerically on a spacetime lattice.

Those methods have not agreed. In 2021, the BMW Collaboration published a lattice QCD result in Nature that was larger than the then-standard data-driven estimates and narrowed the apparent gap between theory and experiment. The new 2026 Nature paper pushes further in that direction. It gives the key HVP input as aμ(LO-HVP) = 715.1(2.5)(2.3)[3.4] × 10−10 and says some data-driven determinations remain in “serious tension” with lattice-based results, including a 4.3-standard-deviation difference in one comparison.

A major flashpoint is a 2024 result from the CMD-3 Collaboration at the VEPP-2000 collider in Novosibirsk, Russia, measuring the process e+e− → π+π−, or electron-positron collisions producing a pion pair. That channel is especially important in the HVP estimate. CMD-3 reported a 0.7% systematic uncertainty in the crucial rho-resonance region and found a higher pion-production rate than several earlier electron-positron experiments.

That matters because when the CMD-3 result is folded into the data-driven HVP calculation, it pushes the theory prediction upward, complicating the older picture built from previous collider data. As Quanta Magazine reported, physicist Fedor Ignatov said of the CMD-3 result, “It was a surprise. No one expected it to be like that.”

The broader lesson is that muon g-2 is no longer mainly a story about whether Fermilab found a deviation from the Standard Model. Fermilab’s measurement is precise and stable. The live question is which ingredients belong in the Standard Model prediction, especially for the hadronic contribution.

That leaves physicists with a more specific mystery than before, but not a trivial one. If the lattice-based calculations and newer collider inputs are right, the long-advertised gap between theory and experiment largely fades. If the older electron-positron datasets are right, the tension returns. The 2026 Nature paper says additional e+e− → π+π− measurements are needed and points to MUonE, a proposed complementary experiment, as another route to probe HVP. For now, the wobble of the muon looks less like a clean signal of new physics than a test of which data and calculations should be trusted.