Deriving the existence of $B{\bar{B}}^{\ast }$ bound states from the X(3872) and Heavy Quark Symmetry

Abstract

We discuss the possibility and the description of bound states between $B$ and ${\bar{B}}^{\ast }$ mesons. We argue that the existence of such a bound state can be deduced from (i) the weakly bound X(3872) state, (ii) certain assumptions about the short range dynamics of the $D{\bar{D}}^{\ast }$ system and (iii) heavy quark symmetry. From these assumptions the binding energy of the possible $B{\bar{B}}^{\ast }$ bound states is determined, first in a theory containing only contact interactions which serves as a straightforward illustration of the method, and then the effects of including the one pion exchange potential are discussed. In this latter case three isoscalar states are predicted: a positive and negative C-parity ${}^3{S}_1-{}^3{D}_1$ state with a binding energy of $20\mathrm{MeV}$ and $6\mathrm{MeV}$ below threshold respectively, and a positive C-parity ${}^3{P}_0$ shallow state located almost at the $B{\bar{B}}^{\ast }$ threshold. However, large uncertainties are generated as a consequence of the $1/m_Q$ corrections from heavy quark symmetry. Finally, the newly discovered isovector $Z_b(10610)$ state can be easily accommodated within the present framework by a minor modification of the short range dynamics.

21 pages, 3 figures; a sign error in the potential has been corrected and new predictions have been computed

References in corpus (14)

• Dynamically Generated Open and Hidden Charm Meson Systems
• X(3872) and Other Possible Heavy Molecular States
• Pion Interactions in the X(3872)
• Is X(3872) {\sl Really} a Molecular State?
• Is X(3872) a molecule?
• $Z_b(10610{)}^{\pm }$ and $Z_b(10650{)}^{\pm }$ as the $B^{\ast }\bar{B}$ and $B^{\ast }{\bar{B}}^{\ast }$ molecular states
• Axial Resonances in the Open and Hidden Charm Sectors
• Isospin breaking effects in the X(3872) resonance
• Radiative transitions from Upsilon(5S) to molecular bottomonium
• Dynamics of Hadronic Molecule in One-Boson Exchange Approach and Possible Heavy Flavor Molecules
• BB Potentials in Quenched Lattice QCD
• Strong D* -> D+pi and B* -> B+pi couplings
• Precision study of B^* Bπcoupling for the static heavy-light meson
• Determination of the strong coupling $g_{B^{\ast }B\pi }$ from semi-leptonic $B\to \pi \ell \nu$ decay

Cited by in corpus (65)

• Hadronic molecules
• The hidden-charm pentaquark and tetraquark states
• The $XYZ$ states: experimental and theoretical status and perspectives
• Nuclear effective field theory: status and perspectives
• Exotic Hadrons with Heavy Flavors -X, Y, Z and Related States-
• Consequences of Heavy Quark Symmetries for Hadronic Molecules
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• The Heavy Quark Spin Symmetry Partners of the X(3872)
• An overview of $XYZ$ new particles
• Light Flavour and Heavy Quark Spin Symmetry in Heavy Meson Molecules
• Possible assignments of the $X(3872)$, $Z_c(3900)$ and $Z_b(10610)$ as axial-vector molecular states
• Heavy-quark spin and flavour symmetry partners of the X(3872) revisited: what can we learn from the one boson exchange model?
• Reanalysis of the $Y(3940)$, $Y(4140)$, $Z_c(4020)$, $Z_c(4025)$ and $Z_b(10650)$ as molecular states with QCD sum rules
• Could the near-threshold $XYZ$ states be simply kinematic effects?
• Heavy Quark Symmetry Predictions for Weakly Bound B-Meson Molecules
• The $Z_b(10610)$ and $Z_b(10650)$ as axial-vector tetraquark states in the QCD sum rules
• Power Counting and Perturbative One Pion Exchange in Heavy Meson Molecules
• Tetraquark Interpretation of the Charged Bottomonium-like states Z_b^+-(10610) and Z_b^+-(10650) and Implications
• Confirming the molecular nature of the $Z_b(10610)$ and the $Z_b(10650)$
• $Z_b(10610)$ and $Z_b(10650)$ structures produced by the initial single pion emission in the ${\rm Y}(5S)$ decays
• Three-body $D\bar{D}\pi$ dynamics for the X(3872)
• Employing spin symmetry to disentangle different models for the XYZ states
• Hidden beauty molecules within the local hidden gauge approach and heavy quark spin symmetry
• Baryon states with open beauty in the extended local hidden gauge approach
• Interplay of quark and meson degrees of freedom in near-threshold states: A practical parametrisation for line shapes
• Exotic mesons with hidden bottom near thresholds
• X(3872) in the molecular model
• The line shapes of the $Z_b(10610)$ and $Z_b(10650)$ in the elastic and inelastic channels revisited
• 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
• Hidden beauty baryon states in the local hidden gauge approach with heavy quark spin symmetry
• General considerations on the nature of $Z_b(10610)$ and $Z_b(10650)$ from their pole positions
• Detecting the long-distance structure of the X(3872)
• Investigating different structures of the Z_{b}(10610) and Z_{b}(10650)
• Hadronic molecular assignment for the newly observed ${\Omega }^{\ast }$ state
• Spin partners $W_{bJ}$ from the line shapes of the $Z_b(10610)$ and $Z_b(10650)$
• Establishing the heavy quark spin and light flavor molecular multiplets of the $X(3872)$, $Z_c(3900)$ and $X(3960)$
• Heavy Baryons and their Exotics from Instantons in Holographic QCD
• Line shapes in Υ(5S) \to B^{(*)} \bar{B}^{(*)}πwith Z(10610) and Z(10650) using effective field theory
• Decay behavior of the strange and beauty partners of $P_c$ hadronic molecules
• Holographic Heavy-Light Chiral Effective Action
• Could $Z_c(4025)$ be a $J^P=1^{+}$ $D^{\ast }\overline{D^{\ast }}$ molecular state?
• Heavy Exotic Molecules with Charm and Bottom
• $Z_b(10650)$ and $Z_b(10610)$ states in a chiral quark model
• Hadron physics potential of future high-luminosity B-factories at the Upsilon(5S) and above
• Heavy-Light Mesons in Chiral AdS/QCD
• On the binding of the $BD\bar{D}$ and $BDD$ systems
• Heavy Holographic Exotics: Tetraquarks as Efimov States
• Heavy and Strange Holographic Baryons
• Insights into $Z_b(10610)$ and $Z_b(10650)$ from dipion transitions from ${\rm Y}(10860)$
• Remarks on the Heavy-Quark Flavour Symmetry for doubly heavy hadronic molecules
• The $Z_b$ structures in a constituent quark model coupled-channels calculation
• Possible bound states with hidden bottom from ${\bar{K}}^{(\ast )}{B}^{(\ast )}{\bar{B}}^{(\ast )}$ systems
• Prediction of new states from $D^{(\ast )}{B}^{(\ast )}{\bar{B}}^{(\ast )}$ three-body interactions
• Bottomonium-like tetraquarks in a chiral quark model
• Production and absorption of exotic bottomonium-like states in high energy heavy ion collisions
• Composite nature of $Z_b$ states from data analysis
• Predictions of super-exotic heavy mesons from $K^{\ast }{B}^{\ast }{B}^{\ast }$ interactions
• $Z_b(10610)$ in a hadronic medium
• Modification by pion exchange of near threshold resonance line shape in open heavy flavor channel
• Charged bottomonium-like structures $Z_b(10610)$ and $Z_b(10650)$
• Hidden and open heavy-flavor hadronic states
• Spin Partners of the $B^{(\ast )}{\bar{B}}^{(\ast )}$ resonances with a different approach than the Breit-Wigner parameterization
• Hidden charm and bottom molecular states
• The nature of near-threshold XYZ states
• Exotic hadrons associated with $b$-quark