Proton Zemach radius measurement by the hyperfine splitting of muonic hydrogen

A new measurement of the ground-state hyperfine splitting of muonic hydrogen by laser spectroscopy is proposed. The hyperfine splitting energy shift is connected to the proton Zemach radius [1], which is a convolution of the distribution of the charge distribution with the magnetic moment distribution. This can provide new insights on "Proton radius puzzle" [2]. When the laser with the resonance frequency of the hyperfine splitting energy is irradiated, the spin-flip transition is induced from the spin-singlet to the spin-triplet hyperfine sub-levels. Since the muon spin in the spin-triplet state can be polarized by a circularly-polarized laser, we can search for the resonance frequency with the muon decay asymmetry by the decay-electron detection [3,4]. The transition energy is about 0.182 eV, which corresponds to the laser wavelength of 6.7 μm. A narrow-bandwidth tunable mid-infrared laser is being developed in RIKEN [5]. We also started test measurement optimizing the muon beam stopping in the hydrgen gas.

[1] A. Dupays et al., Phys. Rev. A68, 052503 (2003).

[2] R. Pohl et al., Nature 466, 213 (2010).

[3] M. Sato, et al., Proc. 2nd Int. Symp. Science at J-PARC , JPS Conf. Proc. , 025005 (2015)

[4] Y. Ma, et al., Int. J. of Modern Physics: Conf. Series 40 (2016) 1660046

[5] S. Kanda et al., Proceeding of Science, PoS (NuFACT2017) 122 (2018)