Probing the $XYZ$ states through radiative decays

In this work, we adopt the spin rearrangement scheme in the heavy quark limit and extensively investigate three classes of the radiative decays: $\mathfrak{M}\to (b\overline{b})+\gamma$, $(b\overline{b})\to \mathfrak{M}+\gamma$, $\mathfrak{M}\to {\mathfrak{M}}^{\prime }+\gamma$ corresponding to the electromagnetic transitions between one molecular (resonant) state and bottomonium, one bottomonium and molecular (resonant) state, and two molecular (resonant) states, respectively. We also extend the same formalism to study the radiative decays of the molecular (resonant) states with hidden charm. We derive some model-independent ratios when the initial or final states belong to the same spin-flavor multiplet. Future experimental measurement of these ratios will test the molecular picture and explore the underlying structures of the $XYZ$ states.