Hyperfine structure of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math>states in muonic deuterium

On the basis of the quasipotential method in quantum electrodynamics we calculate corrections of orders ${\ensuremath{\alpha}}^{5}$ and ${\ensuremath{\alpha}}^{6}$ to the hyperfine structure of $S\text{-wave}$ energy levels of muonic deuterium. Relativistic corrections, effects of vacuum polarization in first, second and third orders of perturbation theory, nuclear structure, and recoil corrections are taken into account. The obtained numerical values of hyperfine splitting $\ensuremath{\Delta}{E}^{\mathrm{HFS}}(1S)=50.2814$ meV $(1S$ state) and $\ensuremath{\Delta}{E}^{\mathrm{HFS}}(2S)=6.2804$ meV $(2S$ state) represent reliable estimates for a comparison with forthcoming experimental data of the CREMA Collaboration. The hyperfine structure interval ${\ensuremath{\Delta}}_{12}=8\ensuremath{\Delta}{E}^{\mathrm{HFS}}(2S)\ensuremath{-}\ensuremath{\Delta}{E}^{\mathrm{HFS}}(1S)=\ensuremath{-}0.0379$ meV can be used for a precision check of the quantum electrodynamics prediction for muonic deuterium.