Partially Muonic Helium

Muonic Helium is an atom made up of a helium atom nucleus with one electron and one muon, rather than two electrons. It isn't stable (since muons have a half-life of about 10^-6 seconds), but they are long lived enough to study rigorously. Their hyperfine splitting has been measured to a precision of about 0.02 M Hz in a recent experiment and the result was about 0.5 M Hz different from the previous state of the art calculation of the Standard Model expectation for its value (which also had an uncertainty much larger than the experimental value which was on the order of 0.5 M Hz).

A new and more precise calculation was made in a new paper:

Using perturbation theory for the fine-structure constant α and the electron-to-muon mass ratio, we calculated new contributions to the hyperfine structure of the ground state of the muon-electron helium atom. Compared to our previous results, we calculated new corrections in second-order perturbation theory. This calculation reduces the discrepancy between the theoretical value and the new experimental hyperfine structure measurement.

F. A. Martynenko, K. A. Seredina, A. P. Martynenko "Improved calculation of the hyperfine structure of muonic helium" arXiv:2609.17454 (September 15, 2026).

The calculation in the new paper which considers a variety of mostly small refinements to the previous state of the art calculation comes up with a result that is consistent with the old calculation (not hard due to its great uncertainties) which is about 0.05 M HZ away from the experimental result and has an uncertainty on the order of 0.07 M Hz which is a huge improvement on the old calculation. 

The uncertainty in the new experimental result, however, is still several times greater than the uncertainty in the experimental measurement, which is unusual in a calculation that is predominantly a quantum electrodynamics (QED) calculation, a part of particle physics which tends to be ultra-precise. The more complicated make up of a muonic hydrogen atom compared to many other ultra-precise QED calculations is the main source of these uncertainties.