Strong decays of χcJ(2P) and χcJ(3P)

In the framework of the chiral quark model, the mass spectrum of χcJ (J = 0, 1, 2, n = 1, 2, 3) is studied with the Gaussian expansion method. Using the wave functions obtained in the study of mass spectrum, the open charm two-body strong decay widths of these states are calculated by using the 3P0 model. The results show that the masses of χcJ(1P) and χc2(2P) are consistent with the experimental data. But the strong decay width of χc2(2P) is three times that of the experimental value. The decay width of χc1(2P) is sensitive to its mass. In the quark-antiquark picture, the width is about 385 MeV. However, if the channel coupling effects shift its mass to 3872 MeV, its decay width will be around 1 MeV. The possibility of assigning the state X(3872) as χc1(2P) cannot be excluded. To assign X(3915) as χc0(2P) is disfavored, due to the unmatching of decay channel. For the χcJ(3P) states, no states have been assigned. The possible candidates of χc0(3P) are X(4160) and X(4140). Their masses are close to the theoretical ones. The experimental branching ratio of X(4160), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma (X(4160) \to D\bar D)/\Gamma (X(4160) \to D*\bar D*) < 0.09$$\end{document} is compatible with that of χc0(3P), 0.07. However the broad decay width of X(4160) cannot be explained by the open charm two-body decay. To assign X(4140) as χc0(3P) is also possible, due to the compatibility of the total decay width, the further measurement of decay modes of X(4140) are expected to justify the assignment.