X(3872) is not a true molecule

Understand

A solvable coordinate-space model is employed to study the $c\bar{c}$ component of the X(3872) wave function, by coupling a confined $^3P_1$ $c\bar{c}$ state to the almost unbound $S$-wave $D^0\bar{D}^{*0}$ channel via the $^3P_0$ 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 $D^0\bar{D}^{*0}$ 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.