Pseudoscalar charmonium pair interactions via the Pomeron exchange mechanism

Abstract

Following the observation of the fully-heavy tetraquark candidates $X(6900)$ and possible $X(6300)$ in the di-$J/ψ$ spectrum by the LHCb Collaboration, we investigate the near-threshold dynamics of the pseudoscalar quarkonium pairs in a coupled-channel approach in the di-$η_c$ channel. We show that the Pomeron exchange mechanism should be a general dynamics in the near-threshold heavy quarkonium pair interactions. In the di-$η_c$ channel, a coupled-channel system involving the di-$η_c$, $η_c$-$η_c(2S)$ and di-$η_c(2S)$ interactions can be established. Their $S$-wave interactions near threshold via the Pomeron exchange potential can produce near-threshold resonance poles similar to the di-$J/ψ$, $J/ψ$-$ψ(2S)$ and di-$ψ(2S)$ coupled channels. Interestingly, we find here that the pole positions are more shifted to the corresponding thresholds and turn out to be different from those seen in the di-$J/ψ$ spectrum. Taking into account the suppression of the heavy quark spin flips in the transitions between two vector and two pseudoscalar heavy quarkonium systems, the enhancements in the di-$η_c$ spectrum should be different from those seen in the di-$J/ψ$ channel. Experimental study of the di-$η_c$ channel should be useful for disentangling the nature of the fully-heavy tetraquark systems.