Decay widths of 3PJ charmonium to DD, DD*, D*D* and corresponding mass shifts of 3PJ charmonium

In this work, we calculate the amplitudes of the processes c (c) over bar(P-3(J)) -> DD, DD*, D*D* -> c (c) over bar(P-3(J)) in the leading order of the nonrelativistic expansion. The imaginary parts of the amplitudes are corresponding to the branch decay widths of the charmonium c (c) over bar(P-3(J)). DD, DD*, D*D* and the real parts are corresponding to the mass shifts of the charmonium c (c) over bar(P-3(J)) due to these decay channels. After absorbing the polynomial contributions which are pure real, the ratios between the branch decay widths and the corresponding mass shifts are only dependent on the center-ofmass energy. We find the decay widths and the mass shifts of the P-3(2) states are exact zero in the leading order. The ratios between the branch decay widths and the mass shifts for the P-3(0), P-3(1) states are larger than 5 when the center-ofmass 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.