Generalized Nambu-Jona-Lasinio model in a study of the boson-exchange model of nuclear forces.

Abstract

In this paper we discuss the role of chiral symmetry in the description of the nucleon-nucleon interaction. We make use of a generalized Nambu---Jona-Lasinio model which exhibits chiral symmetry at the quark level and demonstrate how the various components of the boson-exchange model of the nucleon-nucleon interaction arise in this model. In this paper we make use of our recent analysis of correlated two-pion exchange. We have found that when correlated two-pion exchange is represented by an effective low-mass sigma meson, that meson may be seen to be the chiral partner of the pion. (That result pertains if the meson momentum $q$ is spacelike such that $t={q}^{2}<0$.) We give particular attention to the vertex functions appearing in the boson-exchange model. For monopole forms of the vertex functions the cutoff parameter ${\ensuremath{\Lambda}}^{\mathrm{OBE}}$ varies from about 1.3 GeV to 2.0 GeV. In our model the nucleon form factors are characterized by a parameter $\ensuremath{\lambda}$. We show how large cutoff parameters, such as ${\ensuremath{\Lambda}}^{\mathrm{OBE}}$, can arise in our analysis even if the meson-nucleon vertex is soft, with a characteristic cutoff of about 800 MeV. We present the values of $\ensuremath{\lambda}$ that puts the NJL analysis in good agreement with the boson-exchange model of the nucleon-nucleon force.