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

The mixing of $S-D$ partial waves for the heavy meson pairs in the decays $\mathrm{{\rm Y}}(5S)\to [B^{\ast }\bar{B}+\mathrm{c}\mathrm{.}\mathrm{c}\mathrm{.}]\pi$ 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$$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.