  The properties of $\sigma$(600) meson are studied using the QCD sum rules
(QSR) for the tetraquark operators. In the SU(3) chiral limit, we investigate
separately SU(3) singlet and octet tetraquark states as constituents of the
$\sigma$ meson, and discuss their roles for the classification of the light
scalar nonets, $\sigma, f_0, a_0$, and $\kappa$, as candidates of tetraquark
states. All our analyses are performed in the the suitable Borel window which
is indispensable to avoid the {\it pseudo peak} artifacts outside of the Borel
window. The acceptably wide Borel window originates after preparing the
favorable set up of a linear combination of operators and the inclusion of the
dimension 12 terms in the OPE. Taking into account for the possible large
width, we estimate masses for singlet and octet states as $700\sim 850$ MeV,
$600\sim 750$ MeV, respectively, although octet states have smaller overlap
with the pole than singlet state and may be strongly affected by low energy
scattering states. This splitting of singlet and octet states emerges from the
number of the $\bar{q}q$ annihilation diagrams, which include both color
singlet annihilation processes, $qq\bar{q}\bar{q}\to (q\bar{q})_1$ and color
octet annihilation processes, $qq\bar{q}\bar{q}\to G (q\bar{q})_8$. The mass
evaluation for the $\sigma$ meson gives the value around $600\sim800$ MeV which
is much smaller than the mass obtained by 2-quark correlators, $1.0\sim1.2$
GeV. This indicates $\sigma$ state has the large overlap with the tetraquark
states.
