Observation of $\it{e^+e^- \to \pi^+ \pi^- \pi^0 \chi_{bJ}}$ and search for $\it{X_b \to \omega \Upsilon(1S)}$ at $\sqrt{s}\sim 10.867$ GeV

The ${e}^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{0}{\chi }_{bJ}$ ($J=0,1,2$) processes are studied using a $118\text{}\text{}{\mathrm{fb}}^{-1}$ data sample acquired with the Belle detector at a center-of-mass energy of 10.867 GeV. Unambiguous ${\pi }^{+}{\pi }^{-}{\pi }^{0}{\chi }_{bJ}$ ($J=1,2$), $\omega {\chi }_{b1}$ signals are observed, and indication for $\omega {\chi }_{b2}$ is seen, both for the first time, and the corresponding cross section measurements are presented. No significant ${\pi }^{+}{\pi }^{-}{\pi }^{0}{\chi }_{b0}$ or $\omega {\chi }_{b0}$ signals are observed, and 90% confidence level upper limits on the cross sections for these two processes are obtained. In the ${\pi }^{+}{\pi }^{-}{\pi }^{0}$ invariant mass spectrum, significant non-$\omega $ signals are also observed. We search for the $X\left(3872\right)$-like state (named ${X}_{b}$) decaying into $\omega \mathrm{\Upsilon }\left(1S\right)$; no significant signal is observed with a mass between 10.55 and $10.65\text{}\text{}\mathrm{GeV}/{c}^{2}$