X(3872) is not a true molecule

A solvable coordinate-space model is employed to study the cc̄ component of the X(3872) wave function, by coupling a confined 3 P 1 cc̄ state to the almost unbound S-wave D⁰D̄*0 channel via the 3 P 0 mechanism. The two-component wave function is calculated for different values of the binding energy and the transition radius a, always resulting in a significant cc̄ component. However, the long tail of the D⁰D̄*0 wave function, in the case of small binding, strongly limits the cc̄ probability, which roughly lies in the range 7–11 %, for the average experimental binding energy of 0.16 MeV and a between 2 and 3 GeV−1. Furthermore, a reasonable value of 7.8 fm is obtained for the X(3872) r.m.s. radius at the latter binding energy, as well as an S-wave D⁰D̄*0 scattering length of 11.6 fm. Finally, the S -matrix pole trajectories as a function of coupling constant show that X(3872) can be generated either as a dynamical pole or as one connected to the bare cc̄ confinement spectrum, depending on details of the model. From these results we conclude that X(3872) is not a genuine meson–meson molecule, nor actually any other mesonic system with non-exotic quantum numbers, due to inevitable mixing with the corresponding quark–antiquark states.