Radiative decays of the neutral $Z_c(3900)$ and $Z_c(4020)$

Abstract

We study the radiative decays $Z_c(3900)/Z_c(4020)\to \gamma {\chi }_{cJ}(\gamma {\chi }_{cJ}^{\prime })$ ($J=0,1,2$), with the assumption that the $Z_c(3900)$ and $Z_c(4020)$ couple strongly to $D{\bar{D}}^{\ast }+c.c$ and $D^{\ast }{\bar{D}}^{\ast }$ channel, respectively. By considering the contributions of intermediate charmed mesons triangle loops within an effective Lagrangian approach, it is shown that the calculated partial widths of $Z_c(3900)\to \gamma {\chi }_{cJ}$ are about a few hundreds keVs, while the obtained partial widths $Z_c(4020)\to \gamma {\chi }_{cJ}$ are about tens of keVs. The predicted partial widths of $Z_c(3900)\to \gamma {\chi }_{c0,1}^{\prime }$ are less than 1 keV, which mainly due to the very small phase space. For $Z_c(4020)\to \gamma {\chi }_{c0,2}^{\prime }$, the calculated partial widths are usually smaller than 1 keV. For the $Z_c(4020)\to \gamma {\chi }_{c1}^{\prime }$ process, the obtained partial widths can reach up to the order of 10 keV. Furthermore, the dependence of these ratios between different decay modes on the masses of $Z_c(3900)$ or $Z_c(4020)$ are also investigated, which may be a good quantity for the experiments. It is hoped that these calculations here could be tested by future experiments.

arXiv comment9 pages, 6 figures. Accepted by Physical Review D

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