No spontaneous breakdown of chiral symmetry in Nambu–Jona-Lasinio model

Abstract

We argue that the spontaneous breakdown of symmetry in the chirally symmetric Nambu-JonaLasinio model which was supposed to illustrate the origin of the low mass of pions in hadron physics does not occur due to strong fluctuations in the σ -π field space. Although quarks acquire a constituent mass, σ and π turn out to have equal heavy masses of the order of the constituent quark mass.

Mean-field expansion and meson effects in chiral condensate of analytically regularized Nambu-Jona-Lasinio model

“…At the same time, the presented analysis demonstrates that in the analytically regularized NJL model, for physical values of the parameters, taking into account next-to-leading order of the mean-field expansion, does not lead to any pathologies such as a disappearance of the DCSB order parameters or of the Goldstone boson in the spirit of ref. [15,16].…”

“…One can see that the contribution of the sigma-meson is small, while the contribution of the pion in the region 0 < ξ ≤ 0.3 ÷ 0.5 is significant and, strictly speaking, in this last region we cannot consider this contribution as a mere correction, i.e., at such values of the parameter ξ the quantum fluctuations are large and can lead to a principal modification of the entire physical picture of the NJL model (in spirit of work [15], for example). Table 1 Relative contributions of sigma-meson (r σ ) and pion (r π ) to the chiral condensate c 3 of U(1)-model and a ratio (c (1) /c (0) ) of first iteration condensate to leading-approximation condensate as functions of the regularization parameter ξ.…”

Mesonic fluctuations in a nonlocal Nambu–Jona-Lasinio model

“…In the language of Ref. [16], the Fock terms contribute at NLO in 1/N c to an increased "stiffness" against mesonic fluctuations. This raises a question about the estimate of the critical stiffness in that work, which relies on an expression for the stiffness obtained from the LO pion propagator.…”

“…In this context, it is worth making a remark about the recent claim of Kleinert and Van den Bossche [16] that meson fluctuation effects in the NJL model are large enough to restore manifest chiral symmetry, at least for small values of N c . Although our approach is based on a loop expansion, one might have expected to see large decreases in the magnitudes of quantities like the quark condensate, the quark self-energy and the pion decay constant if mesonic fluctuations were driving the system towards symmetry restoration.…”

“…Encouragingly, there seems to be a general consensus emerging from recent studies that NLO corrections are indeed relatively small for standard choices of the model parameters [6,8,[10][11][12][13][14][15], at least for properties of the ground state and of the pion. A contrary view, however, has been expressed by Kleinert and Van den Bossche [16].…”