Insights into $Z_b(10610)$ and $Z_b(10650)$ from dipion transitions from ${\rm Y}(10860)$

Abstract

The dipion transitions ${\rm Y}(10860)\to {\pi }^{+}{\pi }^{-}{\rm Y}(nS)$ ($n=1,2,3$) are studied in the framework of a unitary and analytic coupled-channel formalism previously developed for analysing experimental data on the bottomoniumlike states $Z_b(10610)$ and $Z_b(10650)$ [Phys. Rev. D 98, 074023 (2018)] and predicting the properties of their spin partners [Phys. Rev. D 99, 094013 (2019)]. In this work we use a relatively simple but realistic version of this approach, where the scattering and production amplitudes are constructed employing only short-ranged interactions between the open- and hidden-flavour channels consistent with the constraints from heavy quark spin symmetry, for an extended analysis of the experimental line shapes. In particular, the transitions from the ${\rm Y}(10860)$ to the final states $\pi \pi h_b(mP)$ ($m=1,2$) and $\pi B^{(\ast )}{\bar{B}}^{\ast }$ already studied before, are now augmented by the ${\rm Y}(10860)\to {\pi }^{+}{\pi }^{-}{\rm Y}(nS)$ final states ($n=1,2,3$). This is achieved by employing dispersion theory to account for the final state interaction of the $\pi \pi$ subsystem including its coupling to the $K\bar{K}$ channel. Fits to the two-dimensional Dalitz plots for the ${\pi }^{+}{\pi }^{-}{\rm Y}$ final states were performed. Two real subtraction constants are adjusted to achieve the best description of the Dalitz plot for each ${\rm Y}(nS)$ $(n=1,2,3)$ while all the parameters related to the properties of the $Z_b$'s are kept fixed from the previous study. A good overall description of the data for all ${\rm Y}(10860)\to {\pi }^{+}{\pi }^{-}{\rm Y}(nS)$ channels achieved in this work provides additional strong support for the molecular interpretation of the $Z_b$ states.

16 pages, 7 figures

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