Where are $\chi_{cJ}(3P)$?

Abstract

In the present work, we propose $Y(4140)$ as the $\chi_{c1}(3P)$ state by studying the $\chi_{c1} \pi^+ \pi^-$ invariant mass spectrum of the $B\to K \chi_{c1} \pi^+ \pi^-$ 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 $\chi_{c0}(3P)$ state. The theoretical investigations on the decay behaviors of the $\chi_{cJ}(3P)$ in the present work support the assignments of the $Y(4140)$ and $Y(4080)$ as the $\chi_{c1}(3P)$ and $\chi_{c0}(3P)$ states, respectively. In addition, the $\chi_{c2}(3P)$ 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.