Hadronic Molecules with Four Charm or Beauty Quarks

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