  In this paper, we study radiative decays of X_b, the counterpart of the
famous X(3872) in the bottomonium-sector as a candidate for meson-meson
molecule, into the \gamma \Upsilon(nS) (n=1, 2, 3). 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. This will promote the importance of the radiative decays.
We use the effective Lagrangian based on the heavy quark symmetry to explore
the rescattering mechanism and calculate the partial widths. Our results show
that the partial widths into \gamma \Upsilon(nS) are about 1 keV, and thus the
branching fractions may be sizeable, considering the fact the total width may
also be smaller than a few MeV like the X(3872). These radiative decay modes
are of great importance in the experimental search for the X_b particularly at
hadron collider. An observation of the X_b will provide a deeper insight into
the exotic hadron spectroscopy and is helpful to unravel the nature of the
states connected by the heavy quark symmetry.
