On the Soliton in the NJL model with the ω Meson

We study the soliton solution in the perturbative treatment of the Eur Euclidean energy functional in the Nambu-Jona-Lasinio model with the omega -meson. The resulting energy functional is the sum of the usual pion energy functional and omega -meson terms up to the second order. The equations of motion involve an inhomogeneous integral equation for the omega -meson and the evaluation of a triple sum over sea quark states for the pion. The dependences of the soliton solutions on the constituent quark mass M are studied. A solution is found M approximate to 390 MeV and thc valence quark energy becomes negative when M is greater than 450 MeV. This solution satisfies all consistent condtions and confirms that the omega meson has a repulsive character. We discuss related problems and the possible analytical solution without the perturbation, which involves a frequency dependent soliton solution.