Abstract
We analyze the vacuum structure of a generalized lattice Nambu–Jona-Lasinio model with two flavors of Wilson fermions, such that its continuum action is the most general four-fermion action with “trivial” color interactions, and having a SU(2)V×SU(2)A symmetry in the chiral limit. The phase structure of this model in the space of the two four-fermion couplings shows, in addition to the standard Aoki phases, new phases with 〈ψ¯γ5ψ〉≠0, in close analogy to similar results recently suggested by some of us for lattice QCD with two degenerate Wilson fermions. This result shows how the phase structure of an effective model for low-energy QCD cannot be entirely understood from Wilson Chiral Perturbation Theory, based on the standard QCD chiral effective Lagrangian approach.
Highlights
Since the first numerical investigations of four-dimensional non-abelian gauge theories with dynamical Wilson fermions were performed in the early 80s [1,2], the understanding of the phase and vacuum structure of lattice QCD with Wilson fermions at nonzero lattice spacing, and of the way in which chiral symmetry is recovered in the continuum limit, has been a goal of lattice field theorists
The election of the Nambu–Jona-Lasinio model (NJL) model for our analysis was motivated by the fact that four-dimensional models without gauge fields, and with four-fermion interactions, are considered as effective models to describe the low-energy physics of QCD1 [35, 36]
With the aim of establishing the range of applicability of the standard QCD chiral effective Lagrangian approach, we have analyzed in this paper the vacuum structure of a generalized Nambu–Jona-Lasinio model (NJL) with Wilson fermions in the mean-field or leading-order 1/N expansion
Summary
Since the first numerical investigations of four-dimensional non-abelian gauge theories with dynamical Wilson fermions were performed in the early 80s [1,2], the understanding of the phase and vacuum structure of lattice QCD with Wilson fermions at nonzero lattice spacing, and of the way in which chiral symmetry is recovered in the continuum limit, has been a goal of lattice field theorists. Aoki’s conjecture has been supported by numerical simulations of lattice QCD, and by theoretical studies based on the Nambu–Jona-Lasinio model [5,33], on the linear sigma model [6], and on applying Wilson Chiral Perturbation Theory (W χPT) to the continuum effective Lagrangian [11] The latter analysis predicts, near the continuum limit, two possible scenarios, depending on the sign of an unknown low-energy coefficient. With the purpose of establishing the range of applicability of the standard QCD chiral effective Lagrangian approach, we will analyze in this paper the vacuum structure of a generalized Nambu–Jona-Lasinio model (NJL) with Wilson fermions in the mean-field or leading-order 1/N expansion.
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