What is a sigma meson? I have seen some articles talking about the role of sigma meson in nuclear force, but more articles omit it and only mention pion, rho and omega (e.g., Wikipedia). What is this sigma meson?
 A: For example:

The existence and properties of the sigma meson have been controversial for almost six decades, despite playing a central role in the spontaneous chiral symmetry of QCD or in the nucleon-nucleon attraction. This controversy has also been fed by the strong indications that it is not an ordinary quark-antiquark meson. Here we review both the recent and old experimental data and the model independent dispersive formalisms which have provided precise determinations of its mass and width, finally settling the controversy and leading to its new name: f0(500).

Here it is as f_0 (500).
The dominant decay mode is pi-pi. I expect it is used in nuclear physics as one of the particle exchanges in the models.
A: Abstract from   arXiv:1205.6606
On the size of the sigma meson and its nature

In this work the nature of the $\sigma$ or $f_0(600)$ resonance is discussed by evaluating its quadratic scalar radius, $r^2$. This allows one to have a quantitative estimate for the size of this resonance. We obtain that the $\sigma$ resonance is a compact object with $ r^2=(0.19\pm0.02)-i(0.06\pm 0.02)$ $fm^2$. Within our approach, employing unitary chiral perturbation theory, the $\sigma$ is a dynamically generated resonance that stems from the pion-pion interactions. Given its small size we conclude that the two pions inside the resonance are merged. A four-quark picture is then more appropriate. However, when the pion mass increases, for pion masses somewhat above 400 MeV, the picture of a two-pion molecule is the appropriate one. The $\sigma$ is then a spread $\pi\pi$ bound state. 

