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A lot of exotic hadrons were reported in the past twenty years, which bringus the renaissance of the hadron spectroscopy. Most of them can be understoodas hadronic molecules, whose interactions are mainly due to the exchange oflight mesons, and specifically, light vector mesons through the coupled-channelunitary approach within the local hidden-gauge formalism. It is stillcontroversial whether the interaction arising from the exchange of heavy mesonsis capable of forming hadronic molecules. We apply the coupled-channel unitaryapproach to study the fully-heavy $b \bar b c \bar c$ system, where theexchanged mesons can only be the fully-heavy vector mesons $J/\psi$, $B_c^*$,and $\Upsilon$. Especially, the $J/\psi$ meson is much lighter than the$B_c^{(*)}$ mesons, so the present study can be taken as a generalinvestigation on the question whether a lower-mass fully-heavy meson is able tobind two higher-mass fully-heavy hadrons. Our results suggest the existence ofthe fully-heavy hadronic molecules $|B_c^{+} B_c^{-}; J^{PC}=0^{++} \rangle$,$|B_c^{*+} B_c^{-} - c.c.; J^{PC}=1^{+-} \rangle$, and $|B_c^{*+} B_c^{*-};J^{PC}=2^{++} \rangle$ as well as the possible existence of $|B_c^{*+} B_c^{-}+ c.c.; J^{PC}=1^{++} \rangle$. These states are potentially to be observed inthe $\mu^+ \mu^- J/\psi$ and $\mu^+ \mu^- \Upsilon$ channels in future ATLAS,CMS, and LHCb experiments.

Fully-heavy hadronic molecules $B_c^{(*)+} B_c^{(*)-}$ bound by fully-heavy mesons

Fully-heavy hadronic molecules $B_c^{()+} B_c^{()-}$ bound by fully-heavy mesons