QCD Phenomenology based on a Chiral Effective Lagrangian

TL;DR

This paper presents an NJL-type low-energy effective theory for QCD that captures dynamical chiral symmetry breaking, vacuum structure, and hadron phenomenology through a four-fermion interaction complemented by the $U_A(1)$-breaking Kobayashi–Maskawa–’t Hooft term. It explains how constituent quark masses, meson spectra, and flavor mixing emerge from the interplay of dynamical mass generation, current-quark masses, and axial anomalies, with particular attention to the $\eta$–$\eta'$ system and the scalar $\sigma$ meson. Part I focuses on vacuum structure, spectra, and mixing; Part II extends the framework to finite temperature and density, examining quark condensates, in-medium hadron properties, and soft modes near the chiral transition. The work provides a coherent bridge between fundamental QCD and chiral effective theories, yielding testable predictions for in-medium phenomena and guiding lattice QCD and heavy-ion experiments, while clarifying the connections to other approaches in hadron phenomenology.

Abstract

We review the Nambu-Jona-Lasinio (NJL) approach to the dynamical breaking of chiral symmetry in Quantum Chromodynamics (QCD). The subjects treated in Part I include the vacuum structure of QCD, mass spectra and coupling constants of hadrons, flavor mixing in mesons, the violation of the OZI rule in baryons, and the validity of the chiral perturbation in QCD. A subtle interplay between the axial anomaly and the current-quark masses is shown to play important roles, and a realistic evaluation of the strangeness and heavy quark contents of hadrons is given. In Part II, the NJL model is applied to the system at finite temperature ($T$) and density ($ρ$) relevant to the early universe, interior of the neutron stars and the ultra-relativistic heavy ion collisions. The subjects treated here include the quark condensates in the medium, meson properties at finite $T$ ($ρ$) and their experimental implications. A special attention is paid to fluctuation phenomena near the critical temperature. (to be published in Physics Reports)