Recently BES at BEPC found evidence for the existence of the $\sigma$ meson in the process of $J/\Psi \to \sigma\omega \to\pi\pi\omega$. In this paper we firstly discuss the relevant coupling $g_{ \sigma\pi\pi}$ and show that the linear $\sigma$ model gives rise to a reasonable description of the $\sigma$ decay into $\pi$'s, then we calculate the coupling constant $g^{ th}_{ J/\Psi\sigma\omega}$ by using the perturbative QCD technique and the light-cone wave functions of the $\sigma$ and $\omega$ mesons. The results show that the theoretical value of $g^{ th}_{ J/\Psi\sigma\omega}$ is within the range of experimental value $g_{ J/\Psi\sigma\omega}$.
Categories: hep-ph