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Fine Splitting in Charmonium Spectrum with Channel Coupling Effect

We study the fine splitting in charmonium spectrum in quark model with the channel coupling effect, including $DD$, $DD^*$, $D^*D^*$ and $D_sD_s$, $D_sD_s^*$, $D_s^*D_s^*$ channels. The interaction for channel coupling is constructed from the current-current Lagrangian related to the color confinement and the one-gluon exchange potentials. By adopting the massive gluon propagator from the lattice calculation in the nonperturbative region, the coupling interaction is further simplified to the four-fermion interaction. The numerical calculation still prefers the assignment $1^{++}$ of X(3872).