Hunting for $B\bar B$ molecular state $X_{b0}$ via radiative transition of $\Upsilon(10753)$

Abstract

We investigate the radiative decay $\Upsilon(10753) \to \gamma X_{b0}$ within the framework of nonrelativistic effective field theory (NREFT). The $\Upsilon(10753)$ is treated as an $S$-$D$ mixed state of the $\Upsilon(4S)$ and $\YD$, while the $X_{b0}$ is interpreted as a weakly bound $B\bar{B}$ molecule with $J^{PC}=0^{++}$. The decay process was assumed to occur via the intermediate meson loops involving the $S$-wave $B^{(*)}$ and $P$-wave $B_1^{(\prime)}$ mesons. Our calculated results indicate that the decay $\Upsilon(10753) \to \gamma X_{b0}$ is dominated by the $B_1^{(\prime)}$ meson loops. The partial decay width is predicted to be $0.2-1.5~\mathrm{keV}$ for a binding energy range of $\epsilon_X=0-10~\mathrm{MeV}$, corresponding to a branching fraction of $10^{-6}-10^{-5}$. The decay width is found to be insensitive to the full width of the $B_1^{\prime}$ meson. Our study suggests that the radiative decay of the $\Upsilon(10753)$ is a promising channel to search for the $X_{b0}$ state, which is crucial for testing heavy-quark symmetries and understanding the exotic hadron spectrum in the bottom sector.