Decay of a scalar $\sigma$-meson near the critical end-point in the PNJL model

Properties of a scalar $\sigma$-meson are investigated in the two-flavor Nambu-Jona-Lasinio model with the Polyakov loop. Model analysis of the phase diagram of strong interacting matter is performed. The temperature dependence of the $\sigma \to \pi \pi$ decay width is studied at the zero chemical potential and near the critical end-point. The calculated strong coupling constant $g_{\sigma \pi \pi }$ and the decay width are compared with available experimental data and other model results. Nonthermal enhancement of the total decay width is noted for the $\sigma$ meson near the critical end-point when the condition $m_{\sigma }\ge 2m_{\pi }$ is broken.