Soft Modes Associated with Chiral Symmetry Breaking: The Use of a QCD-Motivated Effective Interaction

Abstract

Possible critical phenomena associated with chiral symmetry breaking and restoration are studied in the mean field approximation with the use of a QCD-motivated effective Lagrangian. Collective excitations in a system with zero temperature and zero chemical potential are examined extensively: It is shown that (i) there exists a precursory mode in the Wigner phase, which softens as the system approaches the critical point for chiral symmetry breaking, and (ii) the σ-meson mode in the Nambu-Goldstone (NG) phase softens being associated with symmetry restoration. The observabilities of these critical phenomena in experiment such as ultra-relativistic heavy ion collisions are discussed. We also calculate the critical temperature T_χ and critical chemical potential µ_χ where chiral symmetry gets restored and we obtain T_χ=164 MeV for (N_c=3, N_f=2)-case without free parameters.