Production of $X_b$ via radiative transition of $\mathrm{{\rm Y}}(10753)$

We studied the radiative transitions between the $\mathrm{{\rm Y}}(10753)$, the $S$-$D$ mixed state of the $\mathrm{{\rm Y}}(4S)$ and ${\mathrm{{\rm Y}}}_1(3{}^3{D}_1)$, and the $X_b$, the heavy quark flavor symmetry counterpart of the $X(3782)$ in the bottomonium sector. The radiative transition was assumed to occur through the intermediate bottom mesons, including $P$-wave $B_1^{(\mathrm{\prime })}$ mesons as well as the $S$-wave $B^{(\ast )}$ ones. The consideration of the $B_1^{(\mathrm{\prime })}$ mesons leads to the couplings to be in $S$-wave, and hence enhances the contributions of the intermediate meson loops. The radiative decay width for the $\mathrm{{\rm Y}}(10753)\to \gamma X_b$ is predicted to be order of $10\mathrm{k}\mathrm{e}\mathrm{V}$, corresponding to a branching fraction of ${10}^{-4}$. Based on the theoretical results, we strongly suggest to search for the $X_b$ in the $e^{+}{e}^{-}\to \gamma X_b$ with $X_b\to \pi \pi {\chi }_{b1}$ near $\sqrt{s}=10.754\mathrm{G}\mathrm{e}\mathrm{V}$, and it is hoped that the calculations here could be tested by the future Belle II experiments.