A Study of the Nambu--Jona-Lasinio Model on the Lattice

Abstract

We present our full analysis of the two flavor Nambu--Jona-Lasinio model with $SU(2)\times SU(2)$ chiral symmetry on the four--dimensional hypercubic lattice with naive and Wilson fermions. We find that this model is an excellent toy field theory to investigate issues related to lattice QCD. We use the large $N$ approximation to leading order in $1/N$ to obtain non perturbative analytical results over almost the whole parameter range. By using numerical simulations we estimate that the size of the $1/N$ corrections for most of the quantities we consider are small and in this way we strengthen the validity of the leading order large $N$ calculations. We obtain results regarding the approach to the continuum chiral limit, the effects of the zero momentum fermionic modes on finite lattices and the scalar and pseudoscalar spectrum. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your complete E-mail address. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called NJL_long.ps (to get it type: get NJL_long.ps)

35 pages, LaTex file. (Added section with title: "The zero pion mass line on a finite lattice at large $N$".)

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• Chiral Gauge Theories and Fermion-Higgs Systems
• Constituent Quark Couplings and QCD in the Large $N_c$ Limit
• On the O(1/N^2) Beta-Function of the Nambu-Jona-Lasinio Model with Non-Abelian Chiral Symmetry
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Cited by in corpus (14)

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• The $B_K$ Parameter in the $1/N_c$ Expansion
• Two- and Three-Point Functions in the Extended NJL Model
• Coupling the Deconfining and Chiral Transitions
• Absence of Parity-Flavor Breaking Phase in QCD with two Flavors of Wilson fermions for beta greater than or equal to 5.0
• Fermion-scalar interactions with domain wall fermions
• Kondo effect with Wilson fermions
• Dynamical Wilson fermions and the problem of the chiral limit in compact lattice QED
• Nambu-Jona-Lasinio model with Wilson fermions
• The Phase Structure of the Schwinger Model on the Lattice with Wilson Fermions in the Hartree-Fock Approximation
• Elucidating the Vacuum Structure of the Aoki Phase
• Phase structure of a generalized Nambu Jona-Lasinio model with Wilson fermions in the mean field or large $N$-expansion
• Flavor-Parity Breaking in the NJL Model with Wilson Fermions