Decays of $\Upsilon(10860)$ and $\Upsilon(10753)$ into $\omega\chi_{bJ}$

In this paper, we model $\Upsilon(10753)$ as a $4S$-$3D$ bottomonium mixture and $\Upsilon(10860)$ as a $5S$-$4D$ mixture, and predict the properties of a new bottomonium state, $\Upsilon(10950)$, as the mixing partner of $\Upsilon(10860)$. The mixing angles are derived from dielectron decay widths and mass shifts of these bottomonia. We consider open-bottom meson loops in the decays of the $D$-wave bottomonium components, based on a nonrelativistic effective field theory power counting. We show that the $S$-$D$ mixing scheme is consistent with the experimental data of the decays of $\Upsilon(10860)$ into $\omega\chi_{bJ}$ ($J=0,1,2$) and $\Upsilon(10753)$ into $\omega\chi_{bJ}$ ($J=1,2$). Predictions for the dielectron widths and partial decay widths into $\chi_{bJ}\omega$ for $\Upsilon(10753)$ and $\Upsilon(10950)$ are presented.