VECTOR-MESONS IN THE NAMBU-JONA-LASINIO MODEL

We investigate solitonic solutions with baryon number equal to one of the semi-bosonized SU(2) Nambu-Jona-Lasinio model including sigma-, pi -, p-, A(1)- and omega-mesons both on the chiral circle (sigma(2)(r)+p i(2)(r)= f(pi)(2)) and beyond it (sigma(2)(r)+pi(2)(r)not equal f(pi)( 2)). The action is treated in the mesonic and baryonic sector in the l eading order of the large-N-c, expansion (one-quark-loop approximation ). The UV-divergent real part of the effective action is rendered fini te using different gauge-invariant regularization methods (Pauli-Villa rs and proper time). The parameters of the model are fixed in two diff erent ways: either approximately by a heat kernel expansion of the eff ective action up to second order or by an exact calculation of the mes onic on-shell masses. This leaves the constituent quark mass as the on ly free parameter of the model. In the solitonic sector we pay special attention to the way the Wick rotation from euclidean space back to M inkowski space has to be performed. We get solitonic solutions from he dgehog-like field configurations on the chiral circle for a wide range of couplings. We also find that if the chiral-circle constraint is re laxed vector mesons provide stable solitonic solutions. Moreover, whet her the baryon number is carried by the valence quarks or by the Dirac sea depends strongly on the particular values of the constituent quar k mass. We also study the low-energy limit of the model and its connec tion to chiral perturbation theory. To this end a covariant-derivative expansion is performed in the presence of external fields. After inte grating out the scalar, vector and axial degrees of freedom this leads to the corresponding low-energy parameters as e.g. pion radii and som e threshold parameters for pion-pion scattering. Vector mesons provide a natural explanation for an axial coupling constant at the quark lev el g(A)(Q) lower than one. However, we find for the g(A)(N) of the nuc leon noticeable deviations from the non-relativistic quark model predi ction g(A)(N) = 5/3g(A)(Q). For the values of the parameters where sol itons are found, pionic radii come out to be too small. Finally, the r elation of the present model to other chiral soliton models as well as some effective lagrangians is displayed.