Vacuum polarization and quadrupole corrections to the hyperfine splitting of P-states in muonic deuterium

On the basis of quasipotential approach in quantum electrodynamics we calculate vacuum polarization and quadrupole corrections in first and second orders of perturbation theory in hyperfine structure of P-states in muonic deuterium. All corrections are presented in integral form and evaluated analytically and numerically. The obtained results can be used for the improvement of the transition frequencies between levels 2P and 2S.