Abstract
We explore the behavior of the iterative procedure to obtain the solution to the gap equation of the Nambu-Jona-Lasinio (NLJ) model for arbitrarily large values of the coupling constant and in the presence of a magnetic field and a thermal bath. We find that the iterative procedure shows a different behavior depending on the regularization scheme used. It is stable and very accurate when a hard cut-off is employed. Nevertheless, for the Paul-Villars and proper time regularization schemes, there exists a value of the coupling constant (different in each case) from where the procedure becomes chaotic and does not converge any longer.
Highlights
The Nambu-Jona-Lasinio (NJL) model represents one of the earliest attempts to describe the strong interactions between protons and neutrons inside an atomic nucleus
The model has as a dynamical parameter a regulator that gives physical reliability to its predictions, namely, by choosing appropriately the coupling and regularization scale, one is able to predict static the properties of pions, for example
Such a regulator can be implemented through several prescriptions
Summary
The Nambu-Jona-Lasinio (NJL) model represents one of the earliest attempts to describe the strong interactions between protons and neutrons inside an atomic nucleus. As an outcome of this symmetry breaking, the fundamental fermion fields acquire a mass that turns out to be a constant. To give this prediction a physically reliable character, it should be valid only up to some scale. In this sense, the model is non-renormalizable, and for the loop integrals to converge, the introduction of a regularization scheme is necessary. It can be coupled to the Polyakov loop through an effective potential to describe confinement [3] It can be regularized non-locally such that the quark mass function smoothly varies with energy [4]. For a review on the NJL model, we refer the readers to the seminal works in [5,6]
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