Scalar meson contributions in chiral quark condensate are calculated in the analytically regularized Nambu-Jona-Lasinio model using the framework of mean-field expansion in bilocal-source formalism. The sigma-meson contribution for physical values of the parameters is found to be small. Pion contribution is found to be significant and should be taken into account for the choice of the parameter values.

530.12The Nambu-Iona-Lasinio models with 4-dimensional cutting and dimensional-analytical regularization types are compared. It is demonstrated that they describe two different models of light quark interaction. In the average-field approximation, the behavior of the scalar amplitude differs in the threshold region. Unlike the 4-dimensional cutting regularization in which the pole term corresponding to a sigma-meson can be separated near the threshold, the singularity of the scalar amplitude in the dimensional-analytical regularization is non-pole; moreover, it disappears completely for a certain value of the regularization parameter. One more significant difference between the two models is in the first-order expansion of the average field. The calculated meson contributions to the quark chiral condensate and dynamic quark mass demonstrate that despite their relative smallness, they can destabilize the Nambu-Iona-Lasinio model with 4-dimensional cutting regularization. On the contrary, the model with dimensional-analytical regularization is stabilized, which is manifested through a shift of regularization parameter values toward the stability region in which the contributions themselves decrease.

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.

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