https://doi.org/10.1140/epjc/s10052-020-08552-0
Regular Article - Theoretical Physics
Decay widths of 
charmonium to 
and corresponding mass shifts of charmonium
School of Physics, Southeast University, 211189, Nanjing, China
Received:
29
August
2020
Accepted:
13
October
2020
Published online:
21
October
2020
In this work, we calculate the amplitudes of the processes 
in the leading order of the nonrelativistic expansion. The imaginary parts of the amplitudes are corresponding to the branch decay widths of the charmonium 
and the real parts are corresponding to the mass shifts of the charmonium 
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-of-mass energy. We find the decay widths and the mass shifts of the 
states are exact zero in the leading order. The ratios between the branch decay widths and the mass shifts for the 
states are larger than 5 when the center-of-mass energy is above the 
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.
© The Author(s) 2020
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