Radiative decay of $\ddot{I}{‡}_{c1}$ states in effective Lagrangian approach

Abstract

The $\ddot{I}{‡}_{c1}(3872)$ state, first observed by the Belle collaboration with its quantum numbers identified as $J^{PC}=1^{++}$, has been the subject of extensive research due to its intriguing properties. Several theoretical interpretations have been proposed to explain its unique characteristics, including the $\ddot{I}{‡}_{c1}(2P)$ assignment, a molecular ${\bar{D}}^{\ast }D/\bar{D}{D}^{\ast }$ configuration, a coupled-channel framework incorporating $c\bar{c}$ and di-meson degrees of freedom, and the compact tetraquark hypothesis. However, challenges remain in reconciling its mass coincidence with the threshold and the observed isospin violation within both the pure $c\bar{c}$ and compact tetraquark models. In this study, we examine the radiative decays of the $\ddot{I}{‡}_{c1}(1P)$ and $\ddot{I}{‡}_{c1}(3872)$ states in an effective field theory framework, incorporating triangle loops of $D$ and $D^{\ast }$ mesons. The model parameters are calibrated based on the observed branching fraction of the radiative decay mode $\ddot{I}{‡}_{c1}(1P)\to J/\ddot{I}ˆ{\hat{I}}^3$. Utilizing these fixed parameters, we predict the branching fractions $R_{\ddot{I}{‡}_{c1}(3872)\to J/\ddot{I}ˆ{\hat{I}}^3}\sim 10^{-1}$ and $R_{\ddot{I}{‡}_{c1}(3872)\to \ddot{I}ˆ(2S){\hat{I}}^3}\sim 10^{-2}$, and the relative fraction ${\mathcal{R}}_{\hat{I}¨{\hat{I}}^3}\approx 0.109$. The work supports the argument that the $\ddot{I}{‡}_{c1}(3872)$ is unlikely a $c\bar{c}$ state.

6 pages, 3 figures