Insights into \nZb(10610)\n and \nZb(10650)\n from dipion transitions from \nϒ(10860)

Abstract

The dipion transitions $\\mathrm{\\ensuremath{\\Upsilon}}(10860)\\ensuremath{\\rightarrow}{\\ensuremath{\\pi}}^{+}{\\ensuremath{\\pi}}^{\\ensuremath{-}}\\mathrm{\\ensuremath{\\Upsilon}}(nS)$ ($n=1$, 2, 3) are studied in the framework of a unitary and analytic coupled-channel formalism previously developed for analyzing 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-flavor 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 $\\mathrm{\\ensuremath{\\Upsilon}}(10860)$ to the final states $\\ensuremath{\\pi}\\ensuremath{\\pi}{h}_{b}(mP)$ ($m=1$, 2) and $\\ensuremath{\\pi}{B}^{(*)}{\\overline{B}}^{*}$ already studied before, are now augmented by the $\\mathrm{\\ensuremath{\\Upsilon}}(10860)\\ensuremath{\\rightarrow}{\\ensuremath{\\pi}}^{+}{\\ensuremath{\\pi}}^{\\ensuremath{-}}\\mathrm{\\ensuremath{\\Upsilon}}(nS)$ final states ($n=1$, 2, 3). This is achieved by employing dispersion theory to account for the final state interaction of the $\\ensuremath{\\pi}\\ensuremath{\\pi}$ subsystem including its coupling to the $K\\overline{K}$ channel. Fits to the two-dimensional Dalitz plots for the ${\\ensuremath{\\pi}}^{+}{\\ensuremath{\\pi}}^{\\ensuremath{-}}\\mathrm{\\ensuremath{\\Upsilon}}$ final states were performed. Two real subtraction constants are adjusted to achieve the best description of the Dalitz plot for each $\\mathrm{\\ensuremath{\\Upsilon}}(nS)$ ($n=1$, 2, 3) while all the parameters related to the properties of the ${Z}_{b}\\mathrm{s}$ are kept fixed from the previous study. A good overall description of the data for all $\\mathrm{\\ensuremath{\\Upsilon}}(10860)\\ensuremath{\\rightarrow}{\\ensuremath{\\pi}}^{+}{\\ensuremath{\\pi}}^{\\ensuremath{-}}\\mathrm{\\ensuremath{\\Upsilon}}(nS)$ channels achieved in this work provides additional strong support for the molecular interpretation of the ${Z}_{b}$ states.