Muonium hyperfine and 1S-2S intervals at improved precision
In plain words
Muonium, an antimuon holding an electron, contains no proton, so its energy levels test the theory of light and charges without nuclear-structure uncertainty and give the muon mass and magnetism. Its best measurements date from about 25 years ago.
Precise statement
The muonium ground-state hyperfine interval (about $4.463\,\mathrm{GHz}$) was last measured at LAMPF in 1999 and the $1\mathrm{S}-2\mathrm{S}$ two-photon interval at RAL in 2000. Improve both by at least a factor of 10 (MuSEUM at J-PARC for the hyperfine interval, Mu-MASS at PSI for $1\mathrm{S}-2\mathrm{S}$) and determine $m_\mu/m_e$ and $\mu_\mu/\mu_p$ from them, testing whether the two routes and QED theory agree.
What would settle it
New muonium hyperfine and 1S-2S measurements, each with an uncertainty at least ten times below the 1999-2000 values, combined with bound-state QED theory to yield consistent $m_{\mu}/m_e$ values.
Status in the literature
Unverified note
MuSEUM reported ongoing hyperfine measurements at J-PARC aiming at a tenfold improvement in 2025 (arXiv 2501.02736).