Excited <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>K</mml:mi></mml:math> meson, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>K</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4180</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, with hidden charm as a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>K</mml:mi></mml:math> bound state
Tian-Wei Wu, Ming-Zhu Liu, Li‐Sheng Geng
Abstract
Motivated by the recent discovery of two new states in the ${B}^{+}\ensuremath{\rightarrow}{D}^{+}{D}^{\ensuremath{-}}{K}^{+}$ decay by the LHCb Collaboration, we study the $D\overline{D}K$ three-body system by solving the Schr\"odinger equation with the Gaussian Expansion Method. We show that the $D\overline{D}K$ system can bind with quantum numbers $I({J}^{P})=\frac{1}{2}({0}^{\ensuremath{-}})$ and a binding energy of ${B}_{3}(D\overline{D}K)={48.9}_{\ensuremath{-}2.4}^{+1.4}\text{ }\text{ }\mathrm{MeV}$. It can decay into $J/\ensuremath{\psi}K$ and ${D}_{s}{\overline{D}}^{*}$ 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 $D{\overline{D}}^{*}K$ system, which is shown to also bind with quantum numbers $I({J}^{P})=\frac{1}{2}({1}^{\ensuremath{-}})$ and a binding energy of ${B}_{3}(D{\overline{D}}^{*}K)\ensuremath{\simeq}{77.3}_{\ensuremath{-}6.6}^{+3.1}\text{ }\text{ }\mathrm{MeV}$, consistent with the results of previous works.