Observation of $e^+e^-\to\pi^+\pi^-\pi^0\chi_{b1,2}(1P)$ and search for $e^+e^-\to\phi\chi_{b1,2}(1P)$ at $\sqrt{s}=$10.96---11.05 GeV

We report searches for the processes $e^+e^-toπ^+π^-π^0χ_{bJ}$ and $e^+e^-toφχ_{bJ}$ (J=1,2) in the vicinity of the $Υ(11020)$ resonance using energy scan data collected by the Belle experiment at the KEKB collider. We observe $e^+e^-to π^+π^-π^0χ_{b1}$ and find evidence for $e^+e^-to ωχ_{b2}$ processes for data with center-of-mass energies from 10.96 to 11.05~GeV for the first time. The statistical significance for $π^+π^-π^0χ_{b1}$ and $ωχ_{b2}$ are $6.1σ$ and $4.0σ$, respectively. We investigate energy dependence of the $e^+e^-toπ^+π^-π^0χ_{bJ}$ cross section and find that it is consistent with production of $Υ(10860)$ and $Υ(11020)$ resonances without significant non-resonant contribution. Assuming $e^+e^-to π^+π^-π^0χ_{bJ}$ proceeds via $Υ(10860)$ and $Υ(11020)$, the branching fraction $mathcal{B}(Υ(11020)toπ^+π^-π^0χ_{bJ})=(8.6pm4.1pm6.1^{+4.5}_{-2.5})times10^{-3}$ is measured for the first time, where the first error is statistical, the second is systematic, and the third from the branching fraction of $Υ(11020)to e^+e^-$. The signals for $e^+e^-to φχ_{bJ}$ are not significant, and the upper limits of the Born cross sections at the 90% confidence level are $0.6$ and $1.0$~pb for $e^+e^-to φχ_{b1}$ and $φχ_{b2}$, respectively, for center-of-mass energies from 10.96 to 11.05~GeV.