What can radiative decays of the X(3872) teach us about its nature?

Starting from the hypothesis that the X(3872)X(3872) is a DD¯⁎ molecule, we discuss the radiative decays of the X(3872)X(3872) into γJ/ψγJ/ψ and γψ′γψ′ 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)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)X(3872) that is dominated by the DD¯⁎ hadronic molecular component.