Evasion of HSR in the charmless decays of excited $P$-wave charmonia

We investigate the charmless decays of excited $P$-wave charmonia ${\chi }_{c1}^{\mathrm{\prime }}\to VV$ and ${\chi }_{c2}^{\mathrm{\prime }}\to VP$ via intermediate charmed meson loops, where $V$ and $P$ denote the light vector and pseudoscalar mesons, respectively. Within the model parameters, the charmed meson loop contributions are evaluated by using the effective Lagrangian approach. For ${\chi }_{c1}^{\mathrm{\prime }}\to VV$, the partial widths of the $\rho \rho$, $\omega \omega$, and $K^{\ast }{\bar{K}}^{\ast }$ channels can reach to the order of MeV, while the partial width of the $\varphi \varphi$ channel is very small and in the order of keV. For ${\chi }_{c2}^{\mathrm{\prime }}\to VP$, the partial widths of ${\chi }_{c2}^{\mathrm{\prime }}\to K^{\ast }\bar{K}+c\mathrm{.}c$ turns out to be sizeable, while the partial widths of ${\chi }_{c2}^{\mathrm{\prime }}\to {\rho }^{+}{\pi }^{-}+c\mathrm{.}c$ is found to be much smaller than the $K^{\ast }\bar{K}+c\mathrm{.}c$ channel. Our calculations may be examined by the future BESIII experiments.