Fine Splitting in Charmonium Spectrum with Channel Coupling Effect

TL;DR

This paper investigates the fine splitting in the charmonium spectrum considering channel coupling effects, using a quark model with lattice-inspired interactions, and supports the $1^{++}$ assignment for X(3872).

Contribution

It introduces a quark model incorporating channel coupling effects with a lattice-inspired gluon propagator to study charmonium fine splitting.

Findings

Numerical results favor the $1^{++}$ assignment for X(3872).

Channel coupling significantly influences the charmonium spectrum.

The model simplifies the interaction to a four-fermion form based on lattice data.

Abstract

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).