Systematic $1/N_c$ counting of correlators is performed to directly relate quark-gluon dynamics to qualitatively different hadronic states order by order. Both 2q and 4q correlators of $\sigma$ quanta are analyzed with $1/N_c$ separation of the instanton, glueball, and in particular, two meson scattering states. The { \it bare} resonance pole with no mixing effects are studied with the QCD sum rules (QSR). The bare mass relation for large $N_c$ mesons, $m_{ \rho}<m_{ 4q}^{ I=J=0}<m_{ 2q}^{ I=J=0}$, is derived. The firm theoretical ground of the QSR at the leading $1/N_{ c}$ analyses is also emphasized.
Categories: hep-ph