At the J-PARC Muon Science Facility (MUSE), the MuSEUM collaboration is now performing new precision measurements of the ground state hyperfine structure (HFS) of both muonium and muonic helium atoms. High-precision measurements of the muonium ground-state HFS are recognized as one of the most sensitive tools for testing bound-state quantum electrodynamics theory to precisely probe the standard model and determine fundamental constants of the positive muon magnetic moment and mass. The same technique can also be employed to measure muonic helium HFS, obtain the negative muon magnetic moment and mass, and test and improve the theory of the three-body atomic system. Measurements at zero magnetic field have already yielded more accurate results than previous experiments for both muonium and muonic helium atoms. High-field measurements are now ready to start collecting data using the world’s most intense pulsed muon beam at the MUSE H-line. We aim to improve the precision of previous measurements ten times for muonium and a hundred times or more for muonic helium. We review all the key developments for these new measurements, focusing on the high-field experiment, and report the latest results and prospects.

Muonic helium atom hyperfine structure (HFS) measurements are a sensitive tool to test the three-body atomic system and bound-state quantum electrodynamics theory, and determine fundamental constants of the negative muon magnetic moment and mass. The world’s most intense pulsed negative muon beam at the Muon Science Facility of the Japan Proton Accelerator Research Complex allows improvement of previous measurements and testing further $CPT$ invariance by comparing the magnetic moments and masses of positive and negative muons (second-generation leptons). We report new ground-state HFS measurements of muonic helium-4 atoms at a near-zero magnetic field, performed for the first time using a small admixture of ${\mathrm{CH}}_4$ as an electron donor to form neutral muonic helium atoms efficiently. Our analysis gives $\mathrm{\Delta }\nu =4464.980(20)\mathrm{MHz}$ (4.5 ppm), which is more precise than both previous measurements at weak and high fields. The muonium ground-state HFS was also measured under the same conditions to investigate the isotopic effect on the frequency shift due to the gas density dependence in He with ${\mathrm{CH}}_4$ admixture and compared with previous studies. Muonium and muonic helium can be regarded as light and heavy hydrogen isotopes with an isotopic mass ratio of 36. No isotopic effect was observed within the current experimental precision.

The mass $m_{{\mu }^{-}}$ of the negative muon is one of the parameters of the elementary particle Standard Model and it allows us to verify the CPT (charge–parity–time) symmetry theorem by comparing $m_{{\mu }^{-}}$ value with the mass $m_{{\mu }^{+}}$ of the positive muon. However, the experimental determination precision of $m_{{\mu }^{-}}$ is $3.1\mathrm{ppm}$, which is an order of magnitude lower than the determination precision of $m_{{\mu }^{+}}$ at $120\mathrm{ppb}$. The authors aim to determine $m_{{\mu }^{-}}$ and the magnetic moment ${\mu }_{{\mu }^{-}}$ with a precision of $\mathcal{O}\left(10\mathrm{ppb}\right)$ through spectroscopy of the hyperfine structure (HFS) of muonic helium-4 atom ${(}^4\mathrm{He}{\mu }^{-}{e}^{-})$ under high magnetic fields. ${}^4\mathrm{He}{\mu }^{-}{e}^{-}$ is an exotic atom where one of the two electrons of the ${}^4\mathrm{He}$ atom is replaced by a negative muon. To achieve the goal, it is necessary to determine the HFS of ${}^4\mathrm{He}{\mu }^{-}{e}^{-}$ with a precision of $\mathcal{O}\left(1\mathrm{ppb}\right)$. This paper describes the determination procedure of the HFS of ${}^4\mathrm{He}{\mu }^{-}{e}^{-}$ in weak magnetic fields reported recently, and the work towards achieving the goal of higher precision measurement.