The Chiral Soliton of the Nambu-Jona-Lasinio Model

Abstract

The baryon number one soliton of the NJL model is investigated. The Euclidian effective action is regularized using Schwinger's proper time method. Numerical results for the static soliton energy are presented for the cases without and with vector and axialvector fields. It is found that the baryon number is carried by the polarized Dirac sea of the quarks if the $a_1$ meson is included in contrast to the case without $a_1$ where the baryon number resides on valence quarks. Thus the model strongly supports the picture of the baryon as a topological soliton of the meson fields. Including the $ω$ vector meson leads to a non--vanishing imaginary part of the Euclidian effective action even for static solitons. Leaving the chiral circle, i.e.\ including the isoscalar scalar meson, the soliton first seems unstable. However, we demonstrate that a $ϕ^4$ term stabilizes the soliton. Finally, the self--consistent two--flavor chiral soliton is embedded in the SU(3) flavor group and collectively quantized. The predicted mass splittings for the low--lying baryons with different hypercharge are in excellent agreement with the experimental data if the physical value for the kaon decay constant is substituted.