Hunting for the $X_b$ via hidden bottomonium decays

In this work, we study the isospin conserved hidden bottomonium decay of $X_b\to \Upsilon(1S)\omega$, where $X_b$ is taken to be the counterpart of the famous $X(3872)$ in the bottomonium sector as a candidate for the meson-meson molecule. Since it is likely that the $X_b$ is below the $B\bar B^*$ threshold and the mass difference between the neutral and charged bottom meson is small compared to the binding energy of the $X_b$, the isospin violating decay mode $X_b\to \Upsilon (nS)\pi^+\pi^-$ would be greatly suppressed. We use the effective Lagrangian based on the heavy quark symmetry to explore the rescattering mechanism of $X_b\to \Upsilon(1S)\omega$ and calculate the partial widths. Our results show that the partial width for the $X_b\to \Upsilon(1S)\omega$ is about tens of keVs. Taking into account the fact that the total width of $X_b$ may be smaller than a few MeV like $X(3872)$, the calculated branching ratios may reach to orders of $10^{-2}$. These hidden bottomonium decay modes are of great importance in the experimental search for the $X_b$ particularly at the hadron collider. Also, the associated studies of hidden bottomonium decays $X_b \to \Upsilon(nS) \gamma$, $\Upsilon(nS)\omega$, and $B\bar B \gamma$ may help us investigate the structure of $X_b$ deeply. The experimental observation of $X_b$ will provide us with further insight into the spectroscopy of exotic states and is helpful to probe the structure of the states connected by the heavy quark symmetry.