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

TL;DR

This paper investigates the strong decay modes of the Z(3930) particle, identified as the $ ext{chi}_{c2}(2P)$ state, using two theoretical methods to predict decay widths and ratios.

Contribution

It provides a detailed analysis of Z(3930)'s decay widths and ratios using the Bethe-Salpeter and $^3P_0$ models, offering insights into its structure and decay behavior.

Findings

Total decay widths around 26-27 MeV.

Decay width ratio $rac{ ext{Gamma}_{Dar D}}{ ext{Gamma}_{Dar D^ ext{*}}}$ varies with mass.

Consistent results between the two methods.

Abstract

The new particle Z(3930) found by the Belle and BaBar Collaborations through the $\gamma\gamma\rightarrow D\bar D$ 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 $^3P_0$ model and the former formalism. The total decay widths are 26.3 and 27.3 MeV for the methods with or without the $^3P_0$ 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.