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

TL;DR

This paper investigates the properties of higher charmonium states, specifically the $4P$ and $5P$ multiplets, and explores whether threshold corrections can reconcile quark model predictions with observed exotic mesons $X(4500)$ and $X(4700)$.

Contribution

The study introduces a coupled-channel model to analyze mass shifts and decay widths of $4P$ and $5P$ charmonia, assessing their potential as explanations for the $X(4500)$ and $X(4700)$ states.

Findings

Threshold mass shifts challenge the assignment of $X(4700)$ to $ ext{chi}_{c0}(5P)$.

The $X(4500)$ could be consistent with $ ext{chi}_{c0}(4P)$.

Assignments of these states depend on detailed coupled-channel effects.

Abstract

We study some of the main properties (masses and open-flavor strong decay widths) 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 of the other members of the $\chi_{\rm c}(4P,5P)$ multiplets are still completely unknown. With this in mind, we start to explore the charmonium interpretation for these mesons. Our second goal is to investigate if the apparent mismatch between the Quark Model (QM) predictions for $\chi_{\rm c0}(4P,5P)$ states and the properties of the $X(4500)$ and $X(4700)$ mesons can be overcome by introducing threshold corrections in the QM formalism. According to our coupled-channel model results for the threshold mass shifts, the $\chi_{\rm c0}(5P) \rightarrow X(4700)$ assignment is unacceptable, while the $\chi_{\rm c0}(4P) \rightarrow X(4500)$ or $X(4700)$ assignments cannot be completely ruled out.