Quasiparticle properties of the quarks of the Nambu–Jona-Lasinio model

Abstract

In spite of the apparent limitations of the model, in recent years there have been many applications of the Nambu–Jona-Lasinio (NJL) model in the study of hadron structure and in the study of the behavior of nuclear matter at finite temperature and density. A number of researchers have studied a generalized SU(3) version of the NJL model. For example, Vogl, Lutz, Klimt, and Weise [Nucl. Phys. A516 469 (1990)] have performed extensive calculations that include a calculation of a scalar form factor of a constituent quark, ${\mathit{F}}_{\mathit{s}}$(${\mathit{q}}^2$), and a calculation of a quark sigma term ${\mathrm{\sigma }}_{\mathit{q}}$. (In their work, the latter quantity is related to the nucleon sigma term ${\mathrm{\sigma }}_{\mathit{N}}$ as in a constituent quark model: ${\mathrm{\sigma }}_{\mathit{N}}$=3${\mathrm{\sigma }}_{\mathit{q}}$.) These calculations are made in what may be termed a sigma-dominance approximation. In the work reported here, we review the important role played by the nucleon sigma term in understanding the behavior of the quark condensate in the presence of matter. We make use of the original SU(2) version of the NJL model to study how various quark properties are modified when we take into account the dressing of the constituent quarks by the pion, the Goldstone boson of the model. We calculate the quark self-energy arising from emission and absorption of a pion and also show how the calculation of the scalar form factor of the quark and ${\mathrm{\sigma }}_{\mathit{q}}$ are modified due to the coupling of the quark to the pion. The correction terms considered here serve to reduce the value of ${\mathrm{\sigma }}_{\mathit{q}}$ by a small amount relative to the value obtained in the simplest version of the sigma dominance model. For example, for a Euclidean momentum cutoff, Λ=1050 MeV, the uncorrected result is ${\mathrm{\sigma }}_{\mathit{N}}$=54.6 MeV. That value is then reduced to ${\mathrm{\sigma }}_{\mathit{N}}$=51.5 MeV, if the corrections due to the pion ‘‘dressing’’ are included. It is also found that the residue at the quasiparticle pole of the quark propagator Z is about 0.86 when the coupling to the pion field is taken into account.