X(3872) is not a true molecule
Abstract
A solvable coordinate-space model is employed to study the cc component of the X(3872) wave function, by coupling a confined 3P1 cc state to the almost unbound S-wave D0D*0 channel via the 3P0 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 cc component. However, the long tail of the D0D*0 wave function, in the case of small binding, strongly limits the cc 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 D0D*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 cc 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.
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