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

Abstract

We studied the radiative transitions between the ${\rm Y}(10753)$, the $S$-$D$ mixed state of the ${\rm Y}(4S)$ and ${{\rm Y}}_1(3{}^3{D}_1)$, 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 $B_1^{(\prime )}$ mesons as well as the $S$-wave $B^{(\ast )}$ ones. The consideration of the $B_1^{(\prime )}$ 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 ${\rm Y}(10753)\to \gamma X_b$ is predicted to be order of $10\mathrm{keV}$, 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 $\sqrt{s}=10.754\mathrm{GeV}$, and it is hoped that the calculations here could be tested by the future Belle II experiments.

7 pages, 4 figures, accepted by PRD(20240510)