Fine Splitting in Charmonium Spectrum with Channel Coupling Effect

Abstract

We study the fine splitting in charmonium spectrum in quark model with the channel coupling effect, including $DD$, $D{D}^{\ast }$, $D^{\ast }{D}^{\ast }$ and $D_s{D}_s$, $D_s{D}_s^{\ast }$, $D_s^{\ast }{D}_s^{\ast }$ 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).

Comments: Submitted to Chinese Physics C