Search for $e^{+}{e}^{-}\to \gamma {\chi }_{bJ}$ ($J$ = 0, 1, 2) near $\sqrt{s}=10.746$ GeV at Belle II

We search for the $e^{+}{e}^{-}\to \gamma {\chi }_{bJ}$ ($J$ = 0, 1, 2) processes at center-of-mass energies $\sqrt{s}$ = 10.653, 10.701, 10.746, and 10.804 GeV. These data were collected with the Belle II detector at the SuperKEKB collider and correspond to 3.5, 1.6, 9.8, and 4.7 fb${}^{-1}$ of integrated luminosity, respectively. We set upper limits at the 90% confidence level on the Born cross sections for $e^{+}{e}^{-}\to \gamma {\chi }_{bJ}$ at each center-of-mass energy $\sqrt{s}$ near 10.746 GeV. The upper limits at 90% confidence level on the Born cross sections for $e^{+}{e}^{-}\to \gamma {\chi }_{b1}$ are significantly smaller than the corresponding measured values for $e^{+}{e}^{-}\to \omega {\chi }_{b1}$ and $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\mathrm{{\rm Y}}(2S)$ at $\sqrt{s}$ = 10.746 GeV.