Radiative decay of the X(3872) as a mixed molecule-charmonium state in QCD Sum Rules

We use QCD sum rules to calculate the width of the radiative decay of the meson X(3872), assumed to be a mixture between charmonium and exotic molecular $[c\bar{q}][q\bar{c}]$ states with $J^{PC}=1^{++}$. We find that in a small range for the values of the mixing angle, $5^0\leq\theta\leq13^0$, we get the branching ratio $\Gamma(X\to J/\psi\gamma)/\Gamma(X\to J/\psi\pi^+\pi^-)=0.19\pm0.13$, which is in agreement, with the experimental value. This result is compatible with the analysis of the mass and decay width of the mode $J/\psi(n\pi)$ performed in the same approach.