Where are $χ_{cJ}(3P)$?

Abstract

In the present work, we propose $Y(4140)$ as the $χ_{c1}(3P)$ state by studying the $χ_{c1} π^+ π^-$ invariant mass spectrum of the $B\to K χ_{c1} π^+ π^-$ process. In the $D\bar{D}$ invariant mass spectrum of the $B\to K D\bar{D}$ process, we find a new resonance with the mass and width to be $ (4083.0 \pm 5.0) $ and $ (24.1 \pm 15.4) $ MeV, respectively, which could be a good candidate of the $χ_{c0}(3P)$ state. The theoretical investigations on the decay behaviors of the $χ_{cJ}(3P)$ in the present work support the assignments of the $Y(4140)$ and $Y(4080)$ as the $χ_{c1}(3P)$ and $χ_{c0}(3P)$ states, respectively. In addition, the $χ_{c2}(3P)$ state is predicted to be a very narrow state. The results in the present work could be tested by further experiments in the LHCb and forthcoming Belle II.