Charmonium mass shifts in an unquenched quark model

In this paper, we performed a coupled-channel calculation and evaluated the mass shifts for all 1S, 2S, 1P, 2P and 1D charmonium valence states below 4 GeV, by incorporating the four-quark components (D, D*, Dsand D-s* meson pairs) into the quark model. The valence-continuum coupling is provided by the P-3(0) quark-pair creation model. The induced mass shifts appear to be large and negative with the original transition operator in P-3(0) model, which raised up challenges for the valence quark model. More QCD-motivated models should be employed for the quark-pair creation Hamiltonian. So herein, we recalculated the mass shifts with the improved P-3(0) transition operator introduced in our previous work and the mass shifts are reduced by 75% averagely. Besides, as a exercise, we adjust the confinement parameter A and recalculate the spectrum of the charmonium states. The masses of some charmonium states are reproduced well.