Schwinger–Dyson equation and NJL approximation in massive gauge theory with fermions

Abstract

We consider massive SU (N ) gauge theory with fermions. Gauge bosons become massive due to the interaction with the scalar field, whose vacuum average provides the spontaneous breakdown of gauge symmetry. We investigate Dyson -Schwinger equation for the fermion propagator written in ladder approximation and in Landau gauge. Our analysis demonstrates that the chiral symmetry breaking in the considered theory is the strong coupling phenomenon. There are the indications that there appears the second order phase transition between chirally broken and symmetric phases of the theory at the value of coupling constant α c = (1 + γ) ×

Scalar excitation with Leggett frequency inHe3−Band the 125 GeV Higgs particle in top quark condensation models as pseudo-Goldstone bosons

“…A less unusual scenario of physics behind the four -fermion interactions of the top -seesaw model involves the exchange by massive gauge bosons, which appear in the conventional renormalizable field theory (see, for example, [39] and references therein).…”

“…(As it was mentioned in the introduction we imply this kind of the NJL model. For the discussion of this issue see also [16,39,50] and references therein.) Notice that the results of [2] are valid under the same assumptions.…”

“…The appearance of the one -loop gap equation of NJL model may follow from the direct investigation of the theory with massive gauge fields interacting with fermions. Indeed, recently the indications were found that in the theory with exchange by massive gauge bosons the NJL approximation may be applied understood through its one -loop expressions [39]. Anyway, we assume that the model with the four -fermion interactions considered here should be explored in this way, i.e.…”

Fundamental scalar field with zero dimension from anomaly cancelations

“…At this point the discussion follows the method of [89], itself based on [90]. The idea of this method is to write down the Schwinger-Dyson equation in order express the inverse of the full propagator, D −1 (p) in terms of the selfenergy function Σ(p) in the form of a simplified ansatz, through which Σ(p) can be determined.…”

Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

“…[43,163,164,165,166,167,168,169,170,171,172]. In the following, we take the NJL model, which is successful as well as popular in chiral phase transition studies [173,174,175,176,177,178,179,161,180,181,182], as an example, and give some discussions on the applications of some susceptibilities [36], similar discussions with in the framework of QED 3 can be found in Ref. [183].…”