Laser spectroscopy of ground-state hyperfine splitting energy of muonic hydrogen

We propose a new measurement of the ground-state hyperfine splitting of muonic hydrogen by laser spectroscopy with the accuracy of $\sim$2 ppm. The hyperfine splitting energy is connected to the Zemach radius [1], which is a convolution of the spatial distribution of the charge and the magnetic moment within the proton. 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. The transition energy is about 0.182 eV, which corresponds to the laser wavelength of 6.7 $\mu$m. The experiment becomes feasible by a narrow-bandwidth tunable mid-infrared laser recently developed in RIKEN. In this contribution, we present the physics motivation, the experimental principle and its feasibility.\\[4pt] [1] A. Dupays et al., Phys. Rev. A68, 052503 (2003).\\[0pt] [2] R. Pohl et al., Nature 466, 213 (2010).