Production of $ B \bar{B}$ bound state via $\Upsilon (4S)$ radiative decays

Motivated by recent theoretical predictions about the existence of a $B \bar{B}$ bound state (also denoted as $X(10550)$), in this work we estimate the production of the $S$-wave $B^+ B^-$ molecule via $\Upsilon (4S)$ radiative decays. In particular, we make use of effective Lagrangian approach and the compositeness condition to calculate the $X(10550)$ production rate via $\Upsilon(4S)\rightarrow \gamma X(10550)$ decays employing triangle diagrams. Our results show that the partial decay width of this reaction is of the order of $0.5 - 192 \ \keV$ for a respective binding energy of $1 - 100$ MeV, corresponding to a branching fraction of $10^{-5} - 10^{-3}$. These findings suggest that the existence of the $X(10550)$ might be checked via the analysis of the mentioned decay in present and future experiments.