X (3872) Diagnostics with decays to D D̄γ

It is pointed out that in the decays X (3872) → D D̄γ the possible "molecular" component of the X (3872) should give rise essentially only to a, D⁰ D̄⁰γ final state with a predictable spectrum, and should yield virtually no contribution to decays into D⁺ D^-γ. The latter final state with charged D mesons should however arise from the radiative decays of the short-distance core of the X (3872) through the transition X (3872) → ψ(3770)γ. Thus an observation of the radiative decays of X (3872) to pairs of neutral and charged D mesons would provide an insight into the internal dynamics of the X (3872) resonance.