What can radiative decays of the X(3872) teach us about its nature?
  Starting from the hypothesis that the X(3872) is a $D\bar D^*$ molecule, we discuss the radiative decays of the X(3872) into $\gamma J/\psi$ and $\gamma\psi'$ from an effective field theory point of view. We show that radiative decays are very weakly sensitive to the long-range structure of the X(3872). In particular, contrary to earlier claims, we argue that the experimentally determined ratio of the mentioned branching fractions is not in conflict with a wave function of the X(3872) that is dominated by the $D\bar D^*$ hadronic molecular component. 
Feng-Kun Guo, C. Hanhart, Yu.S. Kalashnikova, Ulf.-G. Mei{\ss}ner,   A.V. Nefediev
hep-ph hep-ex nucl-th