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We calculate the masses of $\chi_{\rm c}(3P)$ states with thresholdcorrections in a coupled-channel model. The model was recently applied to thedescription of the properties of $\chi_{\rm c}(2P)$ and $\chi_{\rm b}(3P)$multiplets [Phys.\ Lett.\ B {\bf 789}, 550 (2019)]. We also compute theopen-charm strong decay widths of the $\chi_{\rm c}(3P)$ states and theirradiative transitions. According to our predictions, the $\chi_{\rm c}(3P)$states should be dominated by the charmonium core, but they may also show smallmeson-meson components. The $X(4274)$ is interpreted as a $c \bar c$ $\chi_{\rmc1}(3P)$ state. More informations on the other members of the $\chi_{\rmc}(3P)$ multiplet, as well as a more rigorous analysis of the $X(4274)$'s decaymodes, are needed to provide further indications on the quark structure of theprevious resonance.

Quark structure of the $\chi_{\rm c}(3P)$ and $X(4274)$ resonances and their strong and radiative decays