X(3872) is not a true molecule

Abstract

A solvable coordinate-space model is employed to study the $c\bar{c}$ component of the X(3872) wave function, by coupling a confined ${}^3{P}_1$ $c\bar{c}$ state to the almost unbound $S$-wave $D^0{\bar{D}}^{\ast 0}$ 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 $c\bar{c}$ component. However, the long tail of the $D^0{\bar{D}}^{\ast 0}$ wave function, in the case of small binding, strongly limits the $c\bar{c}$ 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 $D^0{\bar{D}}^{\ast 0}$ scattering length of 11.6 fm. Finally, the $\mathcal{S}$-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 inevitable mixing with the corresponding quark-antiquark states.

Revtex4, 10 pages, 4 figures, 8 plots, 7 tables; v2: SVJour Document Class, a few extra references, several typos and other minor imprecisions corrected, version accepted for publication in Eur. Phys. J. C

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