On the Nucleon Stability and Sigma_N Term Puzzles

A stable soliton configuration for a nucleon emerges when the nucleon stability and $\Sigma_N$ term discrepancy problems are studied semi-quantitatively within a local theory developed recently. The approach developed here goes beyond the mean field or Hartree-Fock approximation by taking into account of the non-perturbative wave function renormalization in a way that is consistent with the chiral Ward-Takahashi identities of QCD. The stability condition for a nucleon and the recently extracted nucleon $\Sigma_N$ term are used to estimate the radius of the soliton. It is found that 0.67 fm $\le R \le$ 0.78 fm. A new mechanism for the stability of a nucleon is proposed. The discrepancy between the nucleon $\Sigma_N$ term extracted from pion--nucleon scattering data and the one from baryonic spectra is resolved by assuming the existence of a metastable virtual color superconducting phase for the strong interaction vacuum. Under such a scenario, the difference between the energy density of the chiral symmetry breaking phase and the metastable color superconducting phase is found to be 0.41 GeV/fm$^3$ $\le \Delta\epsilon\le$ 0.85 GeV/fm$^3$.