Excited K meson, Kc (4180), with hidden charm as a D D ¯ K bound state EXCITED K MESON, Kc (4180), with HIDDEN CHARM ¯ WU TIAN-WEI, LIU MING-ZHU, and GENG LI-SHENG

Motivated by the recent discovery of two new states in the B+→D+D-K+ decay by the LHCb Collaboration, we study the DD¯K three-body system by solving the Schrödinger equation with the Gaussian Expansion Method. We show that the DD¯K system can bind with quantum numbers I(JP)=12(0-) and a binding energy of B3(DD¯K)=48.9-2.4+1.4 MeV. It can decay into J/ψK and DsD¯∗ 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 DD¯∗K system, which is shown to also bind with quantum numbers I(JP)=12(1-) and a binding energy of B3(DD¯∗K)≃77.3-6.6+3.1 MeV, consistent with the results of previous works.