Excited K meson, Kc(4180 ), with hidden charm as a D D ¯K bound state

Motivated by the recent discovery of two new states in the B⁺→D⁺D^-K⁺ decay by the LHCb Collaboration, we study the D D ¯K three-body system by solving the Schrödinger equation with the Gaussian Expansion Method. We show that the D D ¯K system can bind with quantum numbers I (J^P)=1/2 (0^-) and a binding energy of B₃(D D ¯ K )=48.9_-2.4^+1.4 MeV . It can decay into J /ψ K and D_sD^¯* via triangle diagrams, yielding a partial decay width of about 1 MeV. As a result, if discovered, it will serve as a highly nontrivial check on the nature of the many exotic hadrons discovered so far and on nonperturbative QCD as well. Assuming heavy quark spin symmetry, the same formalism is applied to study the D D^¯*K system, which is shown to also bind with quantum numbers I (J^P)=1/2 (1^-) and a binding energy of B₃(D D^{¯ *}K )≃77.3_-6.6^+3.1 MeV , consistent with the results of previous works.