Pseudoscalar charmonium pair interactions via the Pomeron exchange mechanism

Following the observation of the fully-heavy tetraquark candidates $X(6900)$ and possible $X(6300)$ in the di-$J/\psi$ spectrum by the LHCb Collaboration, we investigate the near-threshold dynamics of the pseudoscalar quarkonium pairs in a coupled-channel approach in the di-$\eta_c$ channel. We show that the Pomeron exchange mechanism should be a general dynamics in the near-threshold heavy quarkonium pair interactions. In the di-$\eta_c$ channel, a coupled-channel system involving the di-$\eta_c$, $\eta_c$-$\eta_c(2S)$ and di-$\eta_c(2S)$ 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-$J/\psi$, $J/\psi$-$\psi(2S)$ and di-$\psi(2S)$ 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-$J/\psi$ 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-$\eta_c$ spectrum should be different from those seen in the di-$J/\psi$ channel. Experimental study of the di-$\eta_c$ channel should be useful for disentangling the nature of the fully-heavy tetraquark systems.