2SHyperfine splitting of muonic hydrogen

Abstract

Corrections of orders ${\ensuremath{\alpha}}^{5}$ and ${\ensuremath{\alpha}}^{6}$ are calculated in the hyperfine splitting of the $2S$ state in the muonic hydrogen. The nuclear structure effects are taken into account in the one- and two-loop Feynman amplitudes by means of the proton electromagnetic form factors. The total numerical value of the $2S$ state hyperfine splitting in the muonic hydrogen is $22.8148\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. This value can be considered as a reliable estimate in conducting a corresponding experiment with an accuracy ${10}^{\ensuremath{-}5}$. The value of the Sternheim hyperfine splitting interval $[8\ensuremath{\Delta}{E}^{\mathit{HFS}}(2S)\ensuremath{-}\ensuremath{\Delta}{E}^{\mathit{HFS}}(1S)]$ is obtained with an accuracy ${10}^{\ensuremath{-}6}$.