Possible Bound States in the Triple-ƞ_c and Triple-J/ψ Systems

The observations of fully-charm tetraquark states in the LHCb, CMS, and ATLAS experiments suggested the existence of hadronic molecules of two-charmonium states, which may also imply bound states in the three-charmonium systems. In this work, we study the possible bound states in the triple-\eta_c and triple-J/\psi systems with J^\rm PC=0^-+ and 1^-, respectively. In quantum chromodynamics sum rules, we calculate the two-point correlation functions and spectral functions up to the dimension-four gluon condensate. We use the iterative dispersion relation approach to deal with the five-loop banana integrals, which significantly improves computational efficiency. Our results show that the masses of triple-\eta_c and triple-J/\psi states lie below the corresponding mass thresholds, supporting the existence of such three-body bound states.