Improved Measurements of Muonic Helium Ground-State Hyperfine Structure at a Near-Zero Magnetic Field

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.

Figure 1

Schematic view of the experimental setup to measure ground-state muonic helium atom HFS at zero magnetic field.

Figure 2

Muonic helium HFS resonance curve measured at zero field with $\mathrm{He}+{\mathrm{CH}}_4$ (2%) at (a) 3.0, (b) 4.0, and (c) 10.4 atm, respectively. Delayed events from $1.6\mathrm{\mu }\mathrm{s}$ after the second muon pulse were selected. The solid lines represent the fitting results.

Figure 3

Muonic helium atom hyperfine frequency $\mathrm{\Delta }\nu$ as a function of the $\mathrm{He}+{\mathrm{CH}}_4$ (2%) gas pressure (closed circle). The solid line shows the linear fit to the data to determine $\mathrm{\Delta }\nu (0)$. Previous results from [18] (open circle) and [19] (open square) with the linear extrapolation (dashed line) measured with $\mathrm{He}+\mathrm{Xe}$ (1.5%) are also shown for comparison.

Figure 4

Muonium HFS resonance curve measured under the same experimental conditions of $\mathrm{He}+{\mathrm{CH}}_4$ (2%) at 10.4 atm. The same time selection as in Fig. 2 was applied.