Dynamical study of bare $\sigma$ pole with $1/N_c$ classifications

TL;DR

This paper uses $1/N_c$ expansion and QCD sum rules to analyze the nature of the $\sigma$ resonance, distinguishing between 2-quark and 4-quark states and deriving mass relations for large $N_c$ mesons.

Contribution

It provides a systematic $1/N_c$ analysis of correlators to relate quark-gluon dynamics to hadronic states, and derives a mass hierarchy for mesons in the large $N_c$ limit.

Findings

Bare resonance pole studied with no mixing effects.

Derived mass relation: $m_{ ho}<m_{4q}^{I=J=0}<m_{2q}^{I=J=0}$ for large $N_c$.

Emphasized the theoretical robustness of QCD sum rules at leading $1/N_c$ order.

Abstract

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.