QCD Sum Rules for the production of the X(3872) as a mixed molecule-charmonium state in B meson decay

We use QCD sum rules to calculate the branching ratio for the production of the meson X(3872) in the decay $B\to X(3872)K$, 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, $5^\circ\leq\theta\leq13^\circ$, we get the branching ratio ${\mathcal{B}}(B\to XK)=(1.00\pm0.68)\times10^{-5}$, which is in agreement with the experimental upper limit. This result is compatible with the analysis of the mass and decay width of the mode $J/\psi(n\pi)$ and the radiative decay mode $J/\psi\gamma$ performed in the same approach.