Hidden-charm decays of $X(3915)$ and $Z(3930)$ as the P-wave charmonia

In this work, we investigate the $X(3915)$ and $Z(3930)$ decays into $J\mathrm{/}\psi \omega$ with the ${\chi }_{c0}^{\mathrm{\prime }}(2P)$ and ${\chi }_{c2}^{\mathrm{\prime }}(2P)$ assignments to $X(3915)$ and $Z(3930)$, respectively. The results show that the decay width of $Z(3930)\to J\mathrm{/}\psi \omega$ is at least one order smaller than that of $X(3915)\to J\mathrm{/}\psi \omega$. This observation explains why only one structure $X(3915)$ has been observed in the $J\mathrm{/}\psi \omega$ invariant mass spectrum for the process $\gamma \gamma \to J\mathrm{/}\psi \omega$.