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

TL;DR

This paper analyzes the enhanced mixing of partial waves near threshold in heavy meson pairs, focusing on the properties of the $Z_b$ resonances, and predicts significant mixing effects influenced by rescattering and energy proximity to thresholds.

Contribution

It introduces a calculable model for $S-D$ wave mixing in heavy meson pairs near threshold, emphasizing the role of pion exchange and molecular resonances $Z_b(10610)$ and $Z_b(10650)$.

Findings

Mixing effect can reach 10-20% near the threshold energy.

The mixing is maximized at the energy close to the mass gap between thresholds.

Rescattering through pion exchange dominates the mixing process.

Abstract

The mixing of $S-D$ partial waves for the heavy meson pairs in the decays $\Upsilon(5S) \to [B^* \bar B+ {\rm c.c.}] \pi$ and $\Upsilon(5S) \to B^* \bar B^* \pi$ 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 $10 \div 20$% in the rate at the upper end of applicability of the discussed approach, $E \sim 15 $MeV. It is also argued that the mixing is likely to reach maximum at energy approximately equal to the mass gap between the thresholds.