Ground-state hyperfine structure of the muonic helium atom

Abstract

On the basis of perturbation theory using the fine structure constant $\ensuremath{\alpha}$ and the ratio of the electron to muon masses, we calculate the one-loop vacuum polarization, electron vertex corrections, and nuclear structure corrections to the hyperfine splitting of the ground state of the muonic helium atom $(\ensuremath{\mu}\phantom{\rule{0.2em}{0ex}}e\phantom{\rule{0.2em}{0ex}}_{2}^{4}\mathrm{He})$. We obtain the total result for the ground-state hyperfine splitting $\ensuremath{\Delta}{\ensuremath{\nu}}^{\mathrm{HFS}}=4465.526\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, which improves the previous calculation of Lakdawala and Mohr due to the additional corrections taken into account. The remaining difference between the theoretical result and experimental value of the hyperfine splitting, equal to $0.522\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, lies in the range of theoretical error and requires subsequent investigation of higher-order corrections.