Non-$D\bar{D}$ Decays into Light Meson Pairs of the $D$-Wave Charmonium ${\psi }_3(3842)$

As a $D$-wave partner of $\psi (3770)$ identified by the LHCb Collaboration, ${\psi }_3(3842)$ lies between the $D\bar{D}$ and $D\overline{D^{\ast }}$ thresholds. Its non-$D\bar{D}$ decay channels have attracted considerable interest. In this study, we investigate these allowed non-$D\bar{D}$ decays of ${\psi }_3(3842)$ into $PP$, $PV$, and $VV$ final states using the hadronic loop mechanism, where $P$ and $V$ represent light pseudoscalar and vector mesons, respectively. Our results suggest that these non-$D\bar{D}$ decays of ${\psi }_3(3842)$ can be significant, with contributions primarily driven by hadronic loops. Notably, the $\rho \pi$ channel stands out as the main non-$D\bar{D}$ decay mode, while non-$D\bar{D}$ decay channels involving strange mesons are also sizable. These predictions could be tested in future experiments such as those at LHCb and BESIII.