QCD Sum-Rule Interpretation of X(3872) with $J^{PC}=1^{++}$ Mixtures of Hybrid Charmonium and $bar D D^*$ Molecular Currents

QCD sum-rules are employed to determine whether the X(3872) can be described as a mixed state that couples to $J^{PC}=1^{++}$ charmonium hybrid and $bar D D^*$ molecular currents. After calculating the mixed correlator of hybrid and molecular currents, we formulate the sum-rule in terms of a mixing parameter that interpolates between the pure molecular and hybrid scenarios. As the mixing parameter is increased from the pure molecular case, the predicted mass increases until it reaches a maximum value in good agreement with the X(3872) and the resulting sum-rule analysis appears more robust than the pure molecular case.