Fine Splitting in Charmonium Spectrum with Channel Coupling Effect

Understand

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).