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→X(3872)K, assumed to be a mixture between charmonium and exotic molecular [cq¯][qc¯] states with JPC=1++. We find that in a small range for the values of the mixing angle, 5°⩽θ⩽13°, we get the branching ratio B(B→XK)=(1.00±0.68)×10−5, 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/ψ(nπ) and the radiative decay mode J/ψγ performed in the same approach.