Insights into <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Z</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>10610</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Z</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>10650</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> from dipion transitions from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">ϒ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>10860</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>

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.

Topics & Concepts