Spin partners of the Zb(10610) and Zb(10650) revisited

Abstract

We study the implications of the heavy-quark spin symmetry for the possible spin partners of the exotic states Zb(10610) and Zb(10650) in the spectrum of bottomonium. We formulate and solve numerically the coupled-channel equations for the Zb 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 Zb states so that the mass and the most prominent contributions to the width of the isovector heavy-quark spin partner states WbJ 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 Zb’s reliably enough, we also study the pole trajectories of their spin partner states as functions of the Zb 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.