Is the X(3872) a molecule?

Abstract

Because of the controversial X(3872) meson's very close proximity to the $D^0{\bar{D}}^{\ast 0}$ threshold, this charmonium-like resonance is often considered a meson-meson molecule. However, a molecular wave function must be essentially of a meson-meson type, viz. $D^0{\bar{D}}^{\ast 0}$ in this case, with no other significant components. We address this issue by employing a simple two-channel Schrödinger model, in which the $J^{PC}=1^{++}$ $c\bar{c}$ and $D^0{\bar{D}}^{\ast 0}$ channels can communicate via the ${}^3{P}_0$ mechanism, mimicked by string breaking at a sharp distance $a$. Thus, wave functions and their probabilities are computed, for different bound-state pole positions approaching the $D^0{\bar{D}}^{\ast 0}$ threshold from below. We conclude that at the PDG X(3872) mass and for reasonable values of $a$, viz. 2.0 to 3.0 GeV${}^{-1}$, the $c\bar{c}$ component remains quite substantial and certainly not negligible, despite accounting for only about 6 to 10% of the total wave-function probability, owing to the naturally long tail of the $D^0{\bar{D}}^{\ast 0}$ component.

Comments: Contribution to the International Meeting "Excited QCD", Peniche, Portugal, 06 - 12 May 2012; 6 pages, 2 figures (4 plots), 2 tables, Acta Physica Polonica style