Radiative decays of $X(3872)$ in $D{\bar D}^*$ molecule scenario

TL;DR

This paper studies the radiative decay processes of the $X(3872)$ assuming it is a $Dar{D}^*$ molecular state, highlighting the model dependence of decay widths and the influence of molecular composition.

Contribution

It provides a detailed calculation of the radiative decay widths of $X(3872)$ within the molecular scenario using an effective Lagrangian approach, emphasizing the relative decay ratios.

Findings

Decay widths are model-dependent.

Relative decay width ratios are model-independent.

Decay processes are sensitive to the charged and neutral molecular components.

Abstract

We investigate the radiative decays of the $X(3872)$ to $\gamma V~(V=\rho^0,\, \omega)$ in the molecule scenario, where the $X(3872)$ is regarded as a pure hadronic molecule of the $D\bar{D}^*+c.c$ in an $S$-wave with the quantum numbers $J^{PC}=1^{++}$. The radiative processes were assumed to occur via the triangle hadronic loops, and the relevant calculations were conducted using an effective Lagrangian approach. It is found that the absolute decay widths are model-dependent, but the relative width ratio is rather independent of the model parameter. Moreover, the calculated results indicate that the radiative decays of the $X(3872)$ are strongly influenced by the molecular configuration characterized by the proportion of the charged and neutral constituents. We hope that the present calculations could be tested by the experimental measurements.