Abstract
In this paper, the results of the investigation of multi-quark equations in the Nambu–Jona-Lasinio (NJL) model in the mean-field expansion are presented. The multi-quark functions have been considered up to the third order of expansion. One of the purposes of our computations is the study of corrections of higher orders to parameters of the model. The important problem of the application of the NJL model is regularization. We compare the NJL model with 4-dimensional cutoff regularization and the dimensionally analytical regularization. We also discuss so-called “predictive regularization” in the NJL model, and a modification of this regularization, which is free of the Landau pole, is proposed. To calculate the high-order corrections, we use the Legendre transform method in the framework of bilocal-source formalism, which allows one effectively to take into consideration the symmetry constraints. A generalization of the mean-field expansion for other types of multi-quark sources is also discussed.
Highlights
Quantum chromodynamics as the theory of strong interactions has achieved great successes in the description of various hadronic processes
As it follows from results of this section, the NJL model with DAR is stable with respect to quantum fluctuations caused by scalar-amplitude contributions in chiral condensate, whereas for the NJL model with 4D cutoff the meson contributions can lead to destabilization
Some physical applications of the NJL model exist that connected with multi-quark functions, for which a neglecting by the meson contributions in quark propagator is certainly non-correct from the point of view of the mean-field expansions (MFE) and, the stability of basic model parameters with respect to these contributions becomes essential
Summary
Quantum chromodynamics as the theory of strong interactions has achieved great successes in the description of various hadronic processes. As is shown, this method is an effective way to take into account the constraints following from the chiral Ward identity (see [44]). Such generalization can be fruitful, in particular, for the quantum-field description of nucleons
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