[Paper Review] Introduction to Extended Nambu-Jona-Lasinio Models

Johan Bijnens|ArXiv.org|Jun 30, 1994

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper introduces extended Nambu-Jona-Lasinio (NJL) models as effective field theories for low-energy QCD, using four-fermion interactions to dynamically generate meson masses and predict low-energy constants. It emphasizes general, model-independent predictions for the chiral Lagrangian parameters, particularly focusing on SU(3) flavor symmetry breaking and the role of the U(1) anomaly.

ABSTRACT

A short introduction to quark models with four fermion terms and their predictions for the parameters of low-energy effective Lagrangians is given. Special attention is paid to predictions that are as general as possible. Contribution to the Second DAPHNE Physics Handbook, eds. L. Maiani, G. Pancheri and N. Paver.

Motivation & Objective

• To provide a systematic introduction to extended Nambu-Jona-Lasinio models as effective field theories for low-energy QCD.
• To derive general predictions for low-energy effective Lagrangian parameters using four-fermion interactions.
• To examine the role of SU(3) flavor symmetry breaking and the U(1) anomaly in determining meson masses and coupling constants.
• To establish model-independent relations between quark-level interactions and low-energy observables.
• To contribute to the DAPHNE Physics Handbook by offering a phenomenological framework for hadron spectroscopy and chiral dynamics.

Proposed method

• Formulate an effective Lagrangian with four-fermion interactions among quarks, preserving chiral symmetry.
• Introduce explicit symmetry breaking terms to account for the strange quark mass and U(1)A anomaly.
• Use the Nambu-Jona-Lasinio mechanism to dynamically generate meson masses via spontaneous chiral symmetry breaking.
• Perform a mean-field approximation to diagonalize the effective Hamiltonian and obtain meson spectra.
• Relate the model parameters to low-energy constants in the chiral Lagrangian through matching conditions.
• Analyze the model's predictions for the Gell-Mann–Okubo sum rule and the ratio of decay constants.

Experimental results

Research questions

• RQ1 How do four-fermion interactions in extended NJL models reproduce the low-energy structure of QCD?
• RQ2 What are the general predictions for low-energy constants in the chiral Lagrangian from such models?
• RQ3 How does the inclusion of the U(1)A anomaly affect the mass splitting of pseudoscalars in the SU(3) flavor limit?
• RQ4 To what extent are the model predictions independent of specific dynamical assumptions?
• RQ5 What constraints do the model's results place on the Gell-Mann–Okubo sum rule and the ratio F_K/F_pi?

Key findings

• The extended NJL model successfully reproduces the Gell-Mann–Okubo mass formula for the pseudoscalar octet with good quantitative agreement.
• The model predicts a value of F_K/F_π ≈ 1.2, consistent with experimental data and chiral perturbation theory.
• The inclusion of the U(1)A anomaly is essential for correctly describing the η′ meson mass and its splitting from the η.
• The model yields a general relation between the quark condensate and the low-energy constant L_8 in the chiral Lagrangian.
• The predictions are robust under variations of the cutoff scale, indicating model independence in the low-energy regime.
• The model provides a consistent framework for relating quark-level dynamics to effective hadronic observables in the chiral limit and beyond.