  In this work, we calculate the amplitudes of the processes $c\bar c({^3P_J})
\rightarrow DD,DD^*, D^*D^* \rightarrow c\bar c({^3P_J})$ in the leading order
of the nonrelativistic expansion. The imaginary parts of the amplitudes are
corresponding to the branch decay widthes of the charmonium $c\bar c({^3P_J})
\rightarrow DD,DD^*, D^*D^*$ and the real parts are corresponding to the mass
shifts of the charmonium $c\bar c({^3P_J})$ due to these decay channels. After
absorbing the polynomial contributions which are pure real and include the UV
divergences, the ratios between the branch decay widthes and the corresponding
mass shifts are only dependent on the center-of-mass energy. We find the decay
widthes and the mass shifts of the $^3P_2$ states are exact zero in the leading
order. The ratios between the branch decay widthes and the mass shifts for the
$^3P_0, {^3P_1}$ states are larger than 5 when the center-of-mass energy is
above the $DD,DD^*, D^*D^*$ threshold. The dependence of the mass shifts on the
center-of-mass energy is nontrivial especially when the center-of-mass energy
is below the threshold. The analytic results can be extended to the $b$ quark
sector directly.
