On size and shape of the average meson fields in the semibosonized Nambu & Jona-Lasinio model

We consider the bosonized form of a two-flavor Nambu & Jona-Lasinio model involving scalar-isoscalar and pseudoscalar-isovector quark-quark interaction. Solitonic meson fields are obtained by minimizing the effective Euclidean action. In dependence on the constituent quark mass, which is the only free parameter in the model, we evaluate a series of meson profiles and compare them with a properly parameterized reference profile. We show that the self-consistent fields do in fact practically not depend on the constituent quark mass. Their shape can be very well approximated by this reference profile which interpolates between the correct asymptotic behavior for small and large radii. To demonstrate the accuracy of the approximation we evaluate several static properties like energy, mean square radius, axial-vector constant and delta-nucleon mass splitting using both self-consistent and reference profiles. The agreement is found to be very well in the physically relevant mass region.