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We study some of the main properties (masses and open-flavor strong decaywidths) of $4P$ and $5P$ charmonia. While there are two candidates for the$\chi_{\rm c0}(4P,5P)$ states, the $X(4500)$ and $X(4700)$, the properties ofthe other members of the $\chi_{\rm c}(4P,5P)$ multiplets are still completelyunknown. With this in mind, we start to explore the charmonium interpretationfor these mesons. Our second goal is to investigate if the apparent mismatchbetween the Quark Model (QM) predictions for $\chi_{\rm c0}(4P,5P)$ states andthe properties of the $X(4500)$ and $X(4700)$ mesons can be overcome byintroducing threshold corrections in the QM formalism. According to ourcoupled-channel model results for the threshold mass shifts, the $\chi_{\rmc0}(5P) \rightarrow X(4700)$ assignment is unacceptable, while the $\chi_{\rmc0}(4P) \rightarrow X(4500)$ or $X(4700)$ assignments cannot be completelyruled out.

Quark structure of the $X(4500)$, $X(4700)$ and $\chi_{\rm c}(4P,5P)$ states