Double heavy tri-hadron bound state via delocalized $\pi$ bond

Abstract

The number of exotic candidates which are beyond the conventional quark model has grown dramatically during the last decades. Some of them could be viewed as analogues of the deuteron. Similarly, the existence of the triton indicates that bound states formed by three hadrons could also exist. To illustrate this possibility, we study the $D{D}^{\ast }K$ and $B{B}^{\ast }\bar{K}$ systems by using the Born-Oppenheimer Approximation. To leading order, only one-pion exchange potentials are considered, which means that the three constitutes share one virtual pion. That is similar to the role of the delocalized $\pi$ bond for the formation of Benzene in chemistry. After solving the Schrödinger equation, we find two three-body $D{D}^{\ast }K$ and $B{B}^{\ast }\bar{K}$ bound states with masses $4317.92_{-4.32}^{+3.66}\mathrm{MeV}$ and $11013.65_{-8.84}^{+8.49}\mathrm{MeV}$, respectively. The masses of their $D{\bar{D}}^{\ast }K$ and $B{\bar{B}}^{\ast }\bar{K}$ analogues are $4317.92_{-6.55}^{+6.13}\mathrm{MeV}$ and $11013.65_{-9.02}^{+8.68}\mathrm{MeV}$. From the experimental side, the $D{\bar{D}}^{\ast }K$ bound state could be found by analyzing the current world data of the $B\to J/\psi \pi \pi K$ process by focusing on the $J/\psi \pi K$ channel. Its confirmation could also help to understand the formation of kaonic nuclei in nuclear physics.

5 pages, 7 figures

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Cited by in corpus (17)

• $DK$, $DDK$, and $DDDK$ molecules--understanding the nature of the $D_{s0}^{\ast }(2317)$
• Few-body systems consisting of mesons
• Bound state formation in the $DDK$ system
• Excited $K$ meson, $K_c(4180)$, with hidden charm as a $D\bar{D}K$ bound state
• Strong decays of the explicitly exotic doubly charmed $DDK$ bound state
• Faddeev fixed-center approximation to the $D\bar{D}K$ system and the hidden charm $K_{c\bar{c}}(4180)$ state
• Remarks on non-perturbative three--body dynamics and its application to the $KK\bar{K}$ system
• Molecular states of $D^{\ast }{D}^{\ast }{\bar{K}}^{\ast }$ nature
• One way to verify the molecular picture of exotic hadrons --from $DK$ to $DDK/D{\bar{D}}^{(\ast )}K$
• Possible bound states with hidden bottom from ${\bar{K}}^{(\ast )}{B}^{(\ast )}{\bar{B}}^{(\ast )}$ systems
• Tri-meson bound state $BB{B}^{\ast }$ via delocalized $\pi$~Bond
• Binding of the three-hadron $D{D}^{\ast }K$ system from the lattice effective field theory
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• Production of the (predicted) $K^{\ast }(4307)$ in $B$ decays
• Electromagnetic properties of the $D{\bar{D}}^{\ast }K$ molecular hexaquark state
• Finding Interaction Mechanism between Exotic Molecule and Conventional Hadron
• Tri-meson state $\bar{\mathbf{B}}{\bar{\mathbf{B}}}^{\ast }{\bar{\mathbf{B}}}^{\ast }$