Two regularization types as two different Nambu-Iona-Lasinio models

Abstract

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.

Mean-Field Expansion, Regularization Issue, and Multi-Quark Functions in Nambu–Jona-Lasinio Model

“…We study in this section the NJL model with dimensional regularization in approach of Krewald and Nakayama [34] (see also [45][46][47][48][49][50][51]). Contrary to renormalized models, a regularization parameter of the NJL model is involved in formulas for observable quantities.…”

Regularization dependence on phase diagram in Nambu–Jona-Lasinio model

“…The dimensional regularization analytically continues the spacetime dimension in the loop integrals to a non-integer value, then try to obtain finite contribution from the integrals [14]. Beside from the frequently used 3D cutoff way, there have been a lot of works by using the 4D [6,7], PV [6,[15][16][17], PT [6,[18][19][20][21][22][23][24][25][26], and DR [27][28][29][30][31][32]. Thus, the physical consequences depend on the regularization [34].…”

Phase diagram of Nambu–Jona-Lasinio model with dimensional regularization

“…The model in the cutoff scheme may miss an important contribution when the quark density becomes comparable to the cutoff scale. There is an alternative method, the dimensional regularization (DR) [19,[26][27][28], to avoid the issue [29]. In the DR, divergences coming from fermion loop integrals are regularized by lowering the dimension of the integration through an analytic continuation in the dimension variable.…”