Enhanced mixing of partial waves near threshold for heavy meson pairs and properties ofZb(10610)andZb(10650)resonances

Abstract

The mixing of $S\mathrm{\text{\ensuremath{-}}}D$ partial waves for the heavy meson pairs in the decays $\ensuremath{\Upsilon}(5S)\ensuremath{\rightarrow}[{B}^{*}\overline{B}+\mathrm{c}.\mathrm{c}.]\ensuremath{\pi}$ and $\ensuremath{\Upsilon}(5S)\ensuremath{\rightarrow}{B}^{*}{\overline{B}}^{*}\ensuremath{\pi}$ is considered. It is argued that this mixing, enhanced by the heavy meson mass, is calculable as dominated by a rescattering through pion exchange if the production of the heavy mesons is dominated by $S$-wave ``molecular'' resonances ${Z}_{b}(10610)$ and ${Z}_{b}(10650)$. The effect of the mixing grows with the c.m. energy $E$ in each channel over the threshold, and may reach $10\textdiv{}20%$ in the rate at the upper end of applicability of the discussed approach, $E\ensuremath{\sim}15\text{ }\text{ }\mathrm{MeV}$. It is also argued that the mixing is likely to reach maximum at an energy approximately equal to the mass gap between the thresholds.