Possibility of charmoniumlike state $X(3915)$ as $\chi_{c0}(2P)$ state

In this work, we seriously discuss whether $X(3915)$ can be treated as a $\chi_{c0}(2P)$ state. Based on an unquenched quark model, we give the mass spectrum of the $\chi_{cJ}(2P)$ states, where there are no free input parameters in our calculation. Our result shows that the mass gap between $\chi_{c0}(2P)$ and $\chi_{c2}(2P)$ can reach 13 MeV, which can reproduce the mass difference between $Z(3930)$ and $X(3915)$. Additionally, the calculated masses of $\chi_{c0}(2P)$ and $\chi_{c2}(2P)$ are consistent with experimental values of $X(3915)$ and $Z(3930)$, respectively. Besides, giving the mass spectrum analysis to support $X(3915)$ as $\chi_{c0}(2P)$, we also calculate the width of $\chi_{c0}(2P)$ with the same framework, which is also consistent with the experimental data of $X(3915)$. Thus, the possibility of charmoniumlike state $X(3915)$ as $\chi_{c0}(2P)$ state is further enforced.