# Radiative decay of the $X(3872)$ as a mixed molecule-charmonium state in effective field theory

## TL;DR

This paper investigates the radiative decay mechanisms of the $X(3872)$, considering it as a mixture of molecular and charmonium states, and analyzes how interference effects influence decay ratios, aligning with experimental data.

## Contribution

It introduces an effective field theory model for $X(3872)$ as a mixed state, analyzing interference effects on radiative decay ratios and constraining its charmonium content.

## Key findings

- Interference effects significantly alter decay branching ratios.
- Model predictions align with experimental measurements.
- Destructive interference constrains the charmonium admixture.

## Abstract

Assuming that $X(3872)$ is a mixture between $2P$ charmonium and $\bar{D}D^{*}$ molecular states with $J^{PC}=1^{++}$, an analysis of $X(3872)$ radiative decays into $J/\psi \gamma$ and $\psi(2S)\gamma$ is presented. The modification of the radiative branching ratio due to possible constructive or destructive interferences between the meson-loop and the short-distance contact term, which is modeled by a charm quark loop, is shown. The model predictions are shown to be compatible with the experimentally determined ratio of the mentioned branching fractions for a wide range of the $X(3872)$ charmonium content. In the case of the destructive interference, a strong restriction on the charmonium admixture is found.