Where are <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mi>P</mml:mi></mml:math> and higher <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>P</mml:mi></mml:math>-wave states in the charmonium family?
Ming-Xiao Duan, Xiang Liu
Abstract
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 $3P$, $4P$, and $5P$ states in charmonium family. 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 $\ensuremath{\gamma}\ensuremath{\gamma}$ 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.