Spin partners of the $Z_b(10610)$ and $Z_b(10650)$ revisited

Abstract

We study the implications of the heavy-quark spin symmetry for the possible spin partners of the exotic states $Z_b(10610)$ and $Z_b(10650)$ in the spectrum of bottomonium. We formulate and solve numerically the coupled-channel equations for the $Z_b$ states that allow for a dynamical generation of these states as hadronic molecules. The force includes short-range contact terms and the one-pion exchange potential, both treated fully nonperturbatively. The strength of the potential at leading order is fixed completely by the pole positions of the $Z_b$ states such that the mass and the most prominent contributions to the width of the isovector heavy-quark spin partner states $W_{bJ}$ with the quantum numbers $J^{++}$ ($J=0,1,2$) come out as predictions. Since the accuracy of the present experimental data does not allow one to fix the pole positions of the $Z_b$'s reliably enough, we also study the pole trajectories of their spin partner states as functions of the $Z_b$ binding energies. It is shown that, once the heavy-quark spin symmetry is broken by means of the physical $B$ and $B^{\ast }$ masses, especially the pion tensor force has a significant impact on the location of the partner states clearly demonstrating the need of a coupled-channel treatment of pion dynamics to understand the spin multiplet pattern of hadronic molecules.

21 pages, 5 figures, 1 table

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• Interpretation of the LHCb $P_c$ States as Hadronic Molecules and Hints of a Narrow $P_c(4380)$
• Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners
• Revisiting the nature of the $P_c$ pentaquarks
• One pion exchange and the quantum numbers of the Pc(4440) and Pc(4457) pentaquarks
• 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
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• Spin partners $W_{bJ}$ from the line shapes of the $Z_b(10610)$ and $Z_b(10650)$
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• The $D^{\ast }{D}^{\ast }\bar{D}$ and $D^{\ast }{D}^{\ast }{\bar{D}}^{\ast }$ Three-Body Systems
• Heavy hadron molecules in effective field theory: the emergence of exotic nuclear landscapes
• The $Z_b$ structures in a constituent quark model coupled-channels calculation
• Hidden-bottom hadronic transitions of ${\rm Y}(10753)$
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• Two-pion exchange for coupled-channel scattering of two heavy mesons
• Superfactory of bottomed hadrons Belle II
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• Spin Partners of the $B^{(\ast )}{\bar{B}}^{(\ast )}$ resonances with a different approach than the Breit-Wigner parameterization
• Theory Concepts for Heavy Exotic Mesons
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