Isospin breaking, coupled-channel effects, and X(3872)

TL;DR

This paper investigates the X(3872) as a Dar{D}^* molecule considering isospin breaking and coupled-channel effects, successfully explaining its large isospin violation and decay ratios within meson-exchange models.

Contribution

It provides a detailed meson-exchange model analysis showing X(3872) as a loosely bound state with significant isospin violation and consistent decay ratios, incorporating S-D wave mixing and meson mass differences.

Findings

X(3872) can be described as a loosely bound Dar{D}^* molecule.

Large isospin violation is naturally explained by tiny binding energy.

Predicted decay ratio matches experimental data.

Abstract

We re-investigate the possibility of X(3872) as a $D\bar{D}^*$ molecule with $J^{PC}=1^{++}$ within the framework of both the one-pion-exchange (OPE) model and the one-boson-exchange (OBE) model. After careful treatment of the S-D wave mixing, the mass difference between the neutral and charged $D(D^*)$ mesons and the coupling of the $D(D^*)$ pair to $D^*\bar{D}^*$, a loosely bound molecular state X(3872) emerges quite naturally with large isospin violation in its flavor wave function. For example, the isovector component is 26.24% if the binding energy is 0.30 MeV, where the isospin breaking effect is amplified by the tiny binding energy. After taking into account the phase space difference and assuming the $3\pi$ and $2\pi$ come from a virtual omega and rho meson respectively, we obtain the ratio of these two hidden-charm decay modes: $\mathcal{B}(X(3872)\rightarrow \pi^+\pi^-\pi^0 J/\psi)/\mathcal{B}(X(3872)\rightarrow \pi^+\pi^- J/\psi)=0.42$ for the binding energy being 0.3 MeV, which is consistent with the experimental value.