Likely existence of bound states and the Efimov effect in the triple- J/ψ system

The ground-breaking discovery of the first fully charmed tetraquark state X(6900) in the J/ψJ/ψ invariant mass distribution by the LHCb collaboration has inspired intensive theoretical studies. Various interpretations, such as molecular states, compact tetraquark states, and coupled-channel effects, have been proposed for these states. Of particular interest is the ongoing search for the triple-J/ψ state-a fully-charmed hexaquark state. To deepen our understanding of the triple-J/ψ state and to guide future experimental searches, we study the triple-J/ψ system in this work employing the Gaussian expansion method and the J/ψJ/ψ potential parametrized to yield a shallow bound state, as suggested in several theoretical works. Our results support a triple-J/ψ bound state, even in cases where the attractive interaction between the two J/ψ mesons is very weak. Moreover, our analysis implies the Efimov effect in the triple-J/ψ system. In addition, we extend our investigation to the triple-ϒ(1S) system and obtain results similar to those for the triple-J/ψ system.