Susana Coito, George Rupp, Eef van Beveren
The wave function of the charmonium-like meson X(3872) is expected to have a very significant $D^0\bar{D}^{*0}$ component, as the latter threshold lies only 0.16 MeV above the meson's mass. Some conclude from this mass coincidence that X(3872) is a meson-meson molecule, whatever the dynamics giving rise to the state. This would imply that the $D^0\bar{D}^{*0}$ component of the X(3872) wave function is the only relevant one. In the present paper we study this issue by employing a soluble model for a $^3P_1$ $c\bar{c}$ state coupled to an S-wave $D^0\bar{D}^{*0}$ decay channel, communicating via the $^3P_0$ mechanism. The model is a simplified, coordinate-space version of the resonance-spectrum expansion previously employed in a detailed investigation of X(3872)'s nature. The resulting two-component wave function is calculated for different values of the binding energy (BE) and the transition radius $a$. Thus, a significant $c\bar{c}$ component is found in all situations. However, the long tail of the $D^0\bar{D}^{*0}$ wave function, in the case of small BEs, strongly limits the $c\bar{c}$ probability, which roughly lies in the range 7-11%, for the true BE 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 physical mass, as well as an S-wave $D^0\bar{D}^{*0}$ 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 $c\bar{c}$ 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 the inevitable mixing with the corresponding quark-antiquark states.
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http://arxiv.org/abs/1212.0648
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