Observation of $e^+e^- \to π^+ π^- π^0 χ_{bJ}$ and search for $X_b \to ωΥ(1S)$ at $\sqrt{s}\sim 10.867$ GeV
The $e^+e^- \to π^+ π^- π^0 χ_{bJ}$ ($J=0,~1,~2$) processes are studied using a 118~fb$^{-1}$ data sample collected at a center-of-mass energy of 10.867 GeV, in the $Υ(10860)$ energy range, with the Belle detector. The $π^+ π^- π^0 χ_{b1}$, $π^+π^-π^0χ_{b2}$, $ωχ_{b1}$ signals and the evidence of $ωχ_{b2}$ are observed for the first time and the cross sections are measured. No significant $π^+π^-π^0χ_{b0}$ or $ωχ_{b0}$ signal is observed and 90\% confidence level upper limits on the cross sections for these two processes are obtained. In the $π^+π^-π^0$ invariant mass spectrum, significant non-$ω$ signals are also observed. We search for the $X(3872)$-like state with a hidden $b\bar{b}$ component (named $X_b$) decaying into $ωΥ(1S)$; no significant signal is observed with a mass between $10.55$ and $10.65$ GeV/$c^2$.