QCD Sum Rules for the X(3872) as a mixed molecule-charmoniun state

Abstract

We use QCD sum rules to test the nature 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 there is only a small range for the values of the mixing angle, \theta, that can provide simultaneously good agreement with the experimental value of the mass and the decay width, and this range is \theta between 5 and 13 degrees. In this range we get m_X=(3.77 \pm 0.18) GeV and \Gamma(X to J/\psi \pi^+ \pi^-)=(9.3 \pm 6.9) MeV, which are compatible, within the errors, with the experimental values. We, therefore, conclude that the X(3872) is approximately 97% a charmonium state with 3% admixture of \sim 88% D^0D^{*0} molecule and \sim 12% D^+D^{*-} molecule.