The $D^{\ast }{D}^{\ast }\bar{D}$ and $D^{\ast }{D}^{\ast }{\bar{D}}^{\ast }$ Three-Body Systems

Abstract

The hidden charm $X(3872)$ resonance is usually thought to be a $D^{\ast 0}{\bar{D}}^0$ meson-antimeson molecule with quantum numbers $J^{PC}=1^{++}$. If this is the case, there is the possibility that there might be three body bound states with two charmed mesons and a charmed antimeson. Here we argue that the theoretical existence of this type of three body molecules is expected from heavy quark spin symmetry. If applied to the two body sector, this symmetry implies that the interaction of the $D^{\ast 0}{\bar{D}}^{\ast 0}$ meson-antimeson pair in the $J^{PC}=2^{++}$ channel is the same as in the $J^{PC}=1^{++}$ $D^{\ast 0}{\bar{D}}^0$ case. From this we can infer that the $J^P=3^{-}$ $D^{\ast 0}{D}^{\ast 0}{\bar{D}}^{\ast 0}$ molecule will be able to display the Efimov effect if the scattering length of the $2^{++}$ channel is close enough to the unitary limit. Heavy quark spin symmetry also indicates that the $J^P=2^{-}$ $D^{\ast 0}{D}^{\ast 0}{\bar{D}}^0$ molecule is analogous to the $J^P=3^{-}$ $D^{\ast 0}{D}^{\ast 0}{\bar{D}}^{\ast 0}$ one. That is, it can also have a geometric spectrum. If we consider these triply heavy trimers in the isospin symmetric limit, the Efimov effect disappears and we can in principle predict the fundamental state of the $2^{-}$ $D^{\ast }{D}^{\ast }\bar{D}$ and $3^{-}$ $D^{\ast }{D}^{\ast }{\bar{D}}^{\ast }$ systems. The same applies to the $B^{\ast }{B}^{\ast }{\bar{B}}^{\ast }$ system: if the $Z_b(10650)$ is an isovector $B^{\ast }{\bar{B}}^{\ast }$ molecule then the $0^{-}$ isodoublet and the $1^{-}$, $2^{-}$ isoquartet $B^{\ast }{B}^{\ast }{\bar{B}}^{\ast }$ trimers might bind, but do not display Efimov physics. Finally from heavy flavour symmetry it can be argued that scattering in the $BD$ two-body system might be resonant. This would in turn imply the possibility of Efimov physics in the $BBD$ three body system.

12 pages, 2 figures, corresponds to the published version

References in corpus (12)

• Dynamically Generated Open and Hidden Charm Meson Systems
• The Heavy Quark Spin Symmetry Partners of the X(3872)
• Isospin breaking effects in the X(3872) resonance
• What can radiative decays of the X(3872) teach us about its nature?
• Study of $B{\bar{B}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ interactions in $I=1$ and relationship to the $Z_b(10610)$, $Z_b(10650)$ states
• Could the $X(3915)$ and the $X(3930)$ Be the Same Tensor State?
• On the scattering of D and D* mesons off the X(3872)
• $D\Xi$ and $D^{\ast }\Xi$ Molecular States from One Boson Exchange
• A Model Study of Discrete Scale Invariance and Long-Range Interactions
• Production of the spin partner of the X(3872) in e^+e^- collisions
• Three-Body $J^P=0^{+},1^{+},2^{+}$ $B^{\ast }{B}^{\ast }\bar{K}$ Bound States
• Prediction of new states from $D^{(\ast )}{B}^{(\ast )}{\bar{B}}^{(\ast )}$ three-body interactions

Cited by in corpus (12)

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• Heavy-quark spin and flavour symmetry partners of the X(3872) revisited: what can we learn from the one boson exchange model?
• The $\Omega (2012)$ as a hadronic molecule
• Strong decays of the hadronic molecule ${\Omega }^{\ast }(2012)$
• Quadruply charmed baryons as heavy quark symmetry partners of the $D_{s0}^{\ast }(2317)$
• Possible bound states with hidden bottom from ${\bar{K}}^{(\ast )}{B}^{(\ast )}{\bar{B}}^{(\ast )}$ systems
• Analysis of the tetraquark and hexaquark molecular states with the QCD sum rules
• Study on triple-hadron bound states with Gaussian expansion method
• 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
• The ${\bar{D}}^{\ast }{\bar{D}}^{\ast }{\Sigma }_c$ Three-Body System
• Triple-X and beyond: hadronic systems of three and more X(3872)