Observation of $e^+e^-\toηΥ(2S)$ and search for $e^+e^-\toηΥ(1S),~γX_b$ at $\sqrt{s}$ near 10.75 GeV

Abstract: We present an analysis of the processes $e<sup>{+}e<sup>{-}\to\eta\Upsilon(1S)$, $\eta\Upsilon(2S)$, and $\gamma X_b$ with $$X_b\to\pi<sup>+\pi<sup>-\chi_{bJ},~\chi_{bJ}\to\gamma\Upsilon(1S)$$ $(J=1,~2)$ reconstructed from $$\gamma\gamma\pi<sup>+\pi<sup>-\ell<sup>+\ell<sup>-~(\ell=e,~\mu)$$ final states in $19.6~{\rm fb<sup>{-1}}$ of Belle II data collected at four energy points near the peak of the $\Upsilon(10753)$ resonance. Here, $X_b$ is a hypothetical bottomonium-sector partner of the $X(3872)$. A signal of $e<sup>{+}e<sup>{-}\to\eta\Upsilon(2S)$ is observed with a significance greater than $6.0\sigma$. The central value of the Born cross section at 10.653 GeV is measured to be higher than that at 10.745 GeV, and we find evidence for a possible new state near $B^{*}\bar B<sup>{*}$ threshold, with a significance of $3.2\sigma$. No significant signal is observed for $e<sup>{+}e<sup>{-}\to\eta\Upsilon(1S)$ or $\gamma X_b$. Upper limits on the Born cross sections for the processes $e<sup>{+}e<sup>{-}\to\eta\Upsilon(1S)$ and $e^{{+}e^{-}\to\gamma} X_b$ with $X_b\to\pi<sup>+\pi<sup>-\chi_{bJ}$ are determined.