Excited $K$ meson, $K_c(4180)$, with hidden charm as a $D\bar{D}K$ bound state

Abstract

Motivated by the recent discovery of two new states in the $B^{+}\to D^{+}{D}^{-}{K}^{+}$ decay by the LHCb Collaboration, we study the $D\bar{D}K$ three-body system by solving the Schrödinger equation with the Gaussian Expansion Method. We show that the $D\bar{D}K$ system can bind with quantum numbers $I(J^P)=\frac{1}{2}(0^{-})$ and a binding energy of $B_3(D\bar{D}K)=48.9_{-2.4}^{+1.4}$ MeV. It can decay into $J/\psi K$ and $D_s{\bar{D}}^{\ast }$ 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 non-perturbative QCD as well. Assuming heavy quark spin symmetry, the same formalism is applied to study the $D{\bar{D}}^{\ast }K$ system, which is shown to also bind with quantum numbers $I(J^P)=\frac{1}{2}(1^{-})$ and a binding energy of $B_3(D{\bar{D}}^{\ast }K)\simeq 77.3_{-6.6}^{+3.1}$ MeV, consistent with the results of previous works.

arXiv comment6 pages, 3 figures

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• Can we understand the decay width of the $T_{cc}^{+}$ state?
• Production of $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ in $B$ decays as $D^{(\ast )}K$ and $D_s^{(\ast )}\eta$ molecules
• On the structures of new scalar resonances $T_{cs0}^a(2900{)}^{++}$ and $T_{cs0}^a(2900{)}^0$
• Triple-charm molecular states composed of $D^{\ast }{D}^{\ast }D$ and $D^{\ast }{D}^{\ast }{D}^{\ast }$
• Production rates of $D_s^{+}{D}_s^{-}$ and $D\bar{D}$ molecules in $B$ decays
• Double-charm heptaquark states composed of two charmed mesons and one nucleon
• Faddeev fixed-center approximation to the $D\bar{D}K$ system and the hidden charm $K_{c\bar{c}}(4180)$ state
• Molecular states of $D^{\ast }{D}^{\ast }{\bar{K}}^{\ast }$ nature
• One way to verify the molecular picture of exotic hadrons --from $DK$ to $DDK/D{\bar{D}}^{(\ast )}K$
• Is the resonance $X_0(2900)$ a ground-state or radially excited scalar tetraquark $[ud][\overline{c}\overline{s}]$?
• Theoretical investigation of the molecular nature of $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ and the possibility of observing the $D\bar{D}K$ bound state $K_{c\bar{c}}(4180)$ in inclusive $e^{+}{e}^{-}\to c\bar{c}$ collisions
• Binding of the three-hadron $D{D}^{\ast }K$ system from the lattice effective field theory
• Study on triple-hadron bound states with Gaussian expansion method
• Predictions of super-exotic heavy mesons from $K^{\ast }{B}^{\ast }{B}^{\ast }$ interactions
• Faddeev fixed-center approximation to the $\eta K^{\ast }{\bar{K}}^{\ast }$, $\pi K^{\ast }{\bar{K}}^{\ast }$ and $K{K}^{\ast }{\bar{K}}^{\ast }$ systems
• Electromagnetic properties of the $D{\bar{D}}^{\ast }K$ molecular hexaquark state
• Dynamically generated states from the $\eta K^{\ast }{\bar{K}}^{\ast }$, $\pi K^{\ast }{\bar{K}}^{\ast }$, and $K{K}^{\ast }{\bar{K}}^{\ast }$ systems within the fixed-center approximation
• Tri-meson state $\bar{\mathbf{B}}{\bar{\mathbf{B}}}^{\ast }{\bar{\mathbf{B}}}^{\ast }$
• Exotic hadrons associated with $b$-quark
• Prospects for compact hexaquarks under the limitation imposed by quark confinement