Hadronic molecules with four charm or beauty quarks

We apply the extended local hidden gauge formalism to study the meson-meson interactions with the quark constituents $cc\bar c\bar c$, $cc\bar c\bar b/\bar c\bar c cb$, $cc\bar b\bar b/\bar c\bar c bb$, $bb\bar c\bar b/\bar b\bar b cb$, and $bb\bar b\bar b$, where the exchanged mesons are the fully-heavy vector mesons $J/\psi$, $B_c^*$, and $\Upsilon$. We solve the coupled-channel Bethe-Salpeter equation to derive two poles in the $bb\bar{c}\bar{b}$ system and two poles in the $cc\bar{c}\bar{b}$ system. There are also four charge-conjugated poles in the $\bar{b}\bar{b}cb$ and $\bar{c}\bar{c}cb$ systems. In the $bb\bar{c}\bar{b}$ system, one pole corresponds to a sub-threshold bound state when the cutoff momentum is set to $\Lambda > 850$ MeV. The other pole in this system corresponds to a sub-threshold bound state when $\Lambda > 1100$ MeV. In the $cc\bar{c}\bar{b}$ system, the two poles correspond to sub-threshold bound states only when $\Lambda > 1550$ MeV and $\Lambda > 2650$ MeV. This makes them difficult to identify as deeply-bound hadronic molecules. We propose investigating the two poles of the $bb\bar{c}\bar{b}$ system in the $\mu^+\mu^-B_c^-$channel at the LHC.