Hyperfine structure of excited state of muonic helium atom

The recoil, vacuum polarization and electron vertex corrections of first and second orders in the fine structure constant $\alpha$ and the ratio of electron to muon and electron to \alpha-particle masses are calculated in the hyperfine splitting of the $1s_{1\mathrm{/}2}^{(e)}2s_{1\mathrm{/}2}^{(\mu )}$ state of muonic helium atom (\mu e ^4_2He) on the basis of a perturbation theory. We obtain total result for the muonically excited state hyperfine splitting $\mathrm{\Delta }{\nu }^{hfs}=4295.66$ MHz which improves previous calculations due to the account of new corrections and more accurate treatment of the electron vertex contribution.