Inclusive study of bottomonium production in association with an $\eta $ meson in $e^+e^-$ annihilations near $\varUpsilon (5S)$

We study bottomonium production in association with an \(\eta \) meson in \(e^+e^-\) annihilations near the \(\varUpsilon (5S)\), at a centre-of-mass energy of \(\sqrt{s}=10.866\) GeV. The results are based on the 121.4 fb\(^{-1}\) data sample collected by the Belle experiment at the asymmetric-energy KEKB collider. Only the \(\eta \) meson is reconstructed and the missing-mass spectrum of \(\eta \) candidates is investigated. We observe the \(e^+e^-\rightarrow \eta \varUpsilon _J(1D)\) process and find evidence for the \(e^+e^-\rightarrow \eta \varUpsilon (2S)\) process, while no significant signals of \(\varUpsilon (1S)\), \(h_b(1P)\), nor \(h_b(2P)\) are found. Cross sections for the studied processes are reported.