Realistic simulation of NJL mechanism with vector-type coupling

Abstract

The concrete possibilities for a realistic simulation of the Nambu–Jona-Lasino mechanism of dynamical mass generation are examined from the viewpoint of a vector-type confining form of four-fermion Lagrangian with a natural mass scale which substitutes for the canonical NJL model of contact interaction, and is designed to keep a conscious link with spectroscopy. Such Lagrangians are known to lead (through the minimality condition on the effective action) to both the Schwinger–Dyson and Bethe–Salpeter equations for the quark-mass operator Σ(p) and the hadron-quark vertex function Γ_H(q, P) respectively. With a choice of the interaction which corresponds to a Lorentz-covariant generalization of the familiar instantaneous approximation, the related Bethe-Salpeter equation already provides a good description of both qq̅ and qqq spectra, as well a Lorentz-covariant access to different types of transition amplitudes via quark loops, within a common dynamical framework. With this precalibration, the model is subjected to the interlinked SDE and BSE for testing some key aspects of the NJL self-consistency mechanism by evaluating some basic constants. The results are: m_NJL = 300 MeV, ; M²_παm_c;M_σ = 857 MeV; ‹qq̅›₀ = (219 MeV)³. From these values two independent estimates of m_c are found as 21.8 and 17.8 (MeV).