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

We investigate the charmless decays of excited $P$-wave charmonia $\chi_{c1}^\prime \to VV$ and $\chi_{c2}^\prime \to VP$ 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 $\chi_{c1}^\prime \to VV$, the partial widths of the $\rho\rho$, $\omega\omega$, and $K^*{\bar K}^*$ channels can reach to the order of MeV, while the partial width of the $\phi\phi$ channel is very small and in the order of keV. For $\chi_{c2}^\prime \to V P$, the partial widths of $\chi_{c2}^{\prime} \to K^\ast \bar{K}+c.c$ turns out to be sizeable, while the partial widths of $\chi_{c2}^{\prime} \to \rho^+\pi^- +c.c$ is found to be much smaller than the $K^\ast \bar{K}+c.c$ channel. Our calculations may be examined by the future BESIII experiments.