Where are $3P$ and higher $P-$wave states in charmonium family?

2021 
How to hunt for higher $P$-wave states of charmonium is still an open topic when $2P$ charmonia were identified. In this work, we present an unquenched quark model calculation to illustrate the spectroscopy behavior of these discussed higher $P$-wave charmonia. For the $3P$ charmonia, the predicted masses are around 4.2 GeV and their two-body open-charm decay behaviors were given, by which we propose that searching for these $3P$ states via their open-charm decay channels from $\gamma\gamma$ fusion and $B$ decay can be accessible at future experiment like LHCb and Belle II. We continue to calculate the masses of these $4P$ and $5P$ charmonia. Combing with these calculated results of higher $P$-wave states of charmonium, we find that the coupled-channel effect becomes more obvious with increasing the radial quantum number, which can be understood well by the modified Godfrey-Isgur model with screened potential.
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