Ground-state hyperfine splitting of muonic hydrogen at the ppm level
In plain words
In muonic hydrogen the muon orbits very close to the proton, so the small magnetic splitting of its lowest level depends on how charge and magnetism are spread inside the proton. This splitting has never been measured directly, and several experiments are now trying.
Precise statement
Measure the $1\mathrm{S}$ hyperfine transition of muonic hydrogen (about 0.18 eV, mid-infrared wavelength near 6.8 micron) with relative uncertainty of order 1e-5 (FAMU goal) to 1e-6 (CREMA goal), and extract the proton Zemach radius $r_Z$ and the polarizability part of the two-photon-exchange correction. The answer is $r_Z$ with uncertainty below 1% and a statement of whether it agrees with values from electron scattering and from the hydrogen 21 cm hyperfine splitting.
What would settle it
A laser-spectroscopy measurement of the muonic hydrogen 1S hyperfine transition at ppm or 10 ppm uncertainty, combined with a two-photon-exchange calculation of matching precision.
Status in the literature
Unverified note
FAMU reported first operation at the RIKEN-RAL muon facility at ISIS in 2025 (arXiv 2509.10350) and CREMA is preparing a pulsed-laser measurement at PSI (arXiv 2211.08297); no measured value has been published as of mid-2026.