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 full nonperturbatively. The strength of the potential at leading order is fixed completely by the pole positions of the Z b states so 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. In particular, we predict the existence of an isovector 2++ tensor state lying a few MeV below the \( {B}^{\ast }{\overline{B}}^{\ast } \) threshold which should be detectable in the experiment. 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 the physical B and B ∗ mass difference, 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.
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Baru, V., Epelbaum, E., Filin, A. et al. Spin partners of the Z b (10610) and Z b (10650) revisited. J. High Energ. Phys. 2017, 158 (2017). https://doi.org/10.1007/JHEP06(2017)158
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DOI: https://doi.org/10.1007/JHEP06(2017)158