Inspired by the newly observed state $X^{ *}(3860)$, we analyze the strong decay behaviors of some charmonium-like states $X^{ *}(3860)$,$X(3872)$, $X(3915)$, $X(3930)$ and $X(3940)$ by the $^{ 3}P_{ 0}$ model. We carry out our work based on the hypothesis that these states are all being the charmonium systems. Our analysis indicates that $0^{ ++}$ charmonium state can be a good candidate for $X^{ *}(3860)$ and $1^{ ++}$ state is the possible assignment for $X(3872)$. Considering as the $3^{ 1}S_{ 0}$ state, the decay behavior of $X(3940)$ is inconsistent with the experimental data. So, we can not assign $X(3940)$ as the $3^{ 1}S_{ 0}$ charmonium state by present work. Besides, our analysis imply that it is reasonable to assign $X(3915)$ and $X(3930)$ to be the same state, $2^{ ++}$. However, combining our analysis with that of Zhou~\cite{ ZhouZY}, we speculate that $X(3915)$/$X(3930)$ might not be a pure $c\overline{ c}$ systems.
Categories: hep-ph