Lightest scalar in the SU_L(2)*SU_R(2) linear \sigma model

Understand

We consider the lightest scalar meson in the frame of the $SU_L(2)\times SU_R(2)$ linear $\sigma$ model, keeping in mind that this model could be the low energy realization of the two-flavour QCD.

• We show that the $\sigma$ field is described by its four-quark component at least in the $\sigma$ resonance energy (virtuality) region and the $\sigma\to\gamma\gamma$ decay is the four quark transition.
• We emphasize that residues of the $\sigma$ pole in the $\pi\pi\to\pi\pi$ and $\gamma\gamma\to\pi\pi$ amplitudes do not give an idea about the $\sigma$ meson nature, and the progress in studying the $\sigma$ meson production mechanisms in different processes could essentially further us in understanding its nature.