Is the X(3872) a molecule?

TL;DR

This study uses a two-channel Schrödinger model to analyze the X(3872) meson, revealing that it has a significant charmonium component despite its proximity to the meson-meson threshold, challenging the pure molecular interpretation.

Contribution

The paper introduces a simple two-channel Schrödinger model with string breaking to evaluate the wave function composition of X(3872), showing the substantial presence of a charmonium component.

Findings

The c̄c component remains significant at the X(3872) mass.

The D0 D*0 component is dominant but not exclusive.

The c̄c component accounts for about 6-10% of the wave function.

Abstract

Because of the controversial X(3872) meson's very close proximity to the $D^0\bar{D}^{*0}$ 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. $D^0\bar{D}^{*0}$ in this case, with no other significant components. We address this issue by employing a simple two-channel Schr\"odinger model, in which the $J^{PC}=1^{++}$ $c\bar{c}$ and $D^0\bar{D}^{*0}$ channels can communicate via the $^3P_0$ 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 $D^0\bar{D}^{*0}$ 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 $D^0\bar{D}^{*0}$ component.