Radiative decays of X(3872) discriminate between the molecular and compact interpretations

Radiative decays X→ψ(1S)γ and X→ψ^'(2S)γ might be expected to have a ratio of branching fractions following the phase space volumes ratio. However data suggest the opposite, indicating a value for R=B(ψ^'γ)/B(ψγ) consistently larger than one. In this paper we present a calculation of R for both a compact diquark-antidiquark (cq)(c̄q̄) state and a DD̄* molecule. In the former case R~1 or larger is found. In contrast, in the molecular picture, with D and D̄* mesons described by the universal wave function used by Voloshin, Braaten and Kusunoki, we find R to be of order 10^-2. These starkly different predictions are to be confronted with forthcoming high-statistics data analyses; a more precise experimental measure would be extremely helpful in clarifying the true nature of the $X(3872)$.