The chiral quark soliton model for the nucleon

We study the chiral invariant quark model lagrangians under the Hartree approximation for construction of a hedgehog solution with the baryon number B=1. We take into account the Dirac sea contributions to the energy and various densities in terms of the heat-kernel method. With the parameters of the Nambu-Jona-Lasinio model lagrangian fixed by the meson properties, we do not find any B=1 hedgehog solutions except for one case, even which is, however, unstable against small perturbation. We study then the Diakonov-Petrov model lagrangian, which is introduced by investigating the properties of the quark field in the instanton background in QCD. We find in this case stable hedgehog solutions under the heat-kernel regularization method in some parameter region. We study also the isoscalar-vector type (ω-meson type) correlations among quarks for the nucleon properties. The hedgehog energy, the baryon root mean square radius and the axial vector coupling constant gA are calculated as a function of the ω-quark coupling strength. (author)