Unquenched quark-model calculation of X(3872) electromagnetic decays

TL;DR

This paper extends a quark-model for X(3872) by including meson-meson configurations to better predict its electromagnetic decay widths, showing significant improvements over previous quenched models and aligning more closely with experimental data.

Contribution

It introduces an unquenched quark-model calculation including all relevant meson-meson channels to accurately predict X(3872) electromagnetic decay widths.

Findings

Unquenching increases the c̄c probability in the wave function.

Decay rate for X(3872) to γψ(2S) is reduced, while to γJ/ψ is enhanced.

Results show improved agreement with experimental decay ratios.

Abstract

A recent quark-model description of X(3872) as an unquenched $2\,{}^{3\!}P_1$ $c\bar{c}$ state is generalised by now including all relevant meson-meson configurations, in order to calculate the widths of the experimentally observed electromagnetic decays $X(3872) \to \gamma J/\psi$ and $X(3872) \to \gamma\psi(2S)$. Interestingly, the inclusion of additional two-meson channels, most importantly $D^\pm D^{\star\mp}$, leads to a sizeable increase of the $c\bar{c}$ probability in the total wave function, although the $D^0\bar{D}^{\star0}$ component remains the dominant one. As for the electromagnetic decays, unquenching strongly reduces the $\gamma\psi(2S)$ decay rate yet even more sharply enhances the $\gamma J/\psi$ rate, resulting in a decay ratio compatible with one experimental observation but in slight disagreement with two others. Nevertheless, the results show a dramatic improvement as compared to a quenched calculation with the same confinement force and parameters. Concretely, we obtain $\Gamma ( X(3872) \to \gamma \psi(2S) )=28.9$ keV and $\Gamma ( X(3872) \to \gamma J/\psi)=24.7$ keV, with branching ratio $\mathcal{R}_{\gamma\psi}=1.17$.