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 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 * B * 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.

One pion exchange and the quantum numbers of the Pc(4440) and PValderrama1 2019Phys. Rev. D782390View full textAdd to dashboardCite

“…[4], i.e., Λ ¼ 0.5-1.0 GeV. The choice of a harder cutoff is driven by the experience from pionful EFT as applied to heavy meson-antimeson molecules [37,38], in which larger cutoffs than in a purely contact theory seemed to make a difference. For the coordinate space calculation we choose…”

“…[42] with the ideas of Ref. [38] (properly adapted from the heavy mesonantimeson to the heavy baryon-antimeson case) to better pinpoint the quantum numbers of the pentaquark trio. Table V), the contribution of which can be checked to be negligible (less than 0.1 MeV).…”

Spin partners WbJ from the line shapes of the Zb(10610) and Baru1, Epelbaum2, Filin3 et al. 2019Phys. Rev. DSelf Cite

“…where S P qq denotes the wave function of the light qq pair with the total spin S and parity P, and S P bb means the same for the bb pair. Based on this structure four additional isovector sibling states W bJ are predicted to exist [7,8,[12][13][14] with the quantum numbers J PC ¼ J þþ (J ¼ 0, 1,2) and with the wave functions…”

D*D*D¯ and D*D*Valderrama1 2018Phys. Rev. D164110View full textAdd to dashboardCite

“…We do not have any experimental information about them and their treatment will require a phenomenological model of their interactions. However we will mention that bound states have been theorized in a few of these channels [37,52,53].…”