Hadronic molecules with four charm or beauty quarks

Abstract

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 $J/\ddot{I}ˆ$, $B_c^{\ast }$, and $\hat{I}\yen$. 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 $\hat{I}›>850$ MeV. The other pole in this system corresponds to a sub-threshold bound state when $\hat{I}›>1100$ MeV. In the $cc\bar{c}\bar{b}$ system, the two poles correspond to sub-threshold bound states only when $\hat{I}›>1550$ MeV and $\hat{I}›>2650$ 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 $\hat{I}{¼}^{+}\hat{I}{¼}^{-}{B}_c^{-}$channel at the LHC.

9 pages, 2 figures, 2 tables, revised version