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Motivated by a recent successful dynamical explanation for the newly observedfully-charm structure $X(6900)$ in the mass spectrum of di-$J/\psi$ by LHCb[J.~Z.~Wang \textit{et al.} arXiv:2008.07430], in this work, we extend the samedynamical rescattering mechanism to predict the line shape of more potentialfully-heavy structures in the invariant mass spectrum of $J/\psi \psi(3686)$,$J/\psi \psi(3770)$, $\psi(3686) \psi(3686)$, and $J/\psi \Upsilon(1S)$ at highenergy proton-proton collisions, whose verification in experiments should behelpful to further clarify the nature of $X(6900)$. The above final states ofvector heavy quarkonia can be experimentally reconstructed more effectively bya $\mu^+\mu^-$ pair in the muon detector compared with $Q\bar{Q}$ meson withother quantum numbers. Furthermore, the corresponding peak mass positions ofeach of predicted fully-heavy structures are also given. Our theoreticalstudies here could provide some valuable information for the future measurementproposals of LHCb and CMS, especially based on the accumulated data aftercompleting Run III of LHC in the near future.

physics letters b

Fully-heavy structures in the invariant mass spectrum of $J/\psi  \psi(3686)$, $J/\psi \psi(3770)$, $\psi(3686) \psi(3686)$, and $J/\psi  \Upsilon(1S)$ at hadron colliders