Possible bound states in the triple-η_c and triple-J/ψ systems

The observations of fully-charm tetraquark states in the LHCb, CMS and ATLAS experiments suggested the existence of the 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-η_c and triple-J/ψ systems with J^PC = 0^-+ and 1^--, respectively. In QCD 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 the computational efficiency. Our results show that the masses of triple-η_c and triple-J/ψ states lie below the corresponding mass thresholds, supporting the existence of such three-body bound states.