Two-Body Strong Decay of Z(3930) as the ${\chi }_{c2}(2P)$ State

Abstract

The new particle Z(3930) found by the Belle and BaBar Collaborations through the $\gamma \gamma \to D\bar{D}$ process is identified to be the ${\chi }_{c2}(2P)$ state. Since the mass of this particle is above the $D{\bar{D}}^{(\ast )}$ threshold, the OZI-allowed two-body strong decays are the main decay modes. In this paper, these strong decay modes are studied with two methods. One is the instantaneous Bethe-Salpeter method within Mandelstam formalism. The other is the combination of the ${}^3{P}_0$ model and the former formalism. The total decay widths are 26.3 and 27.3 MeV for the methods with or without the ${}^3{P}_0$ vertex, respectively. The ratio of ${\Gamma }_{D\bar{D}}$ over ${\Gamma }_{D{\bar{D}}^{\ast }}$ which changes along with the mass of the initial meson is also presented.

Comments: 11 pages, 3 figures