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

Abstract

We consider a two-flavor Nambu \& Jona-Lasinio model in Hartree approximation involving scalar-isoscalar and pseudoscalar-isovector quark-quark interactions. Average meson fields are defined by minimizing the effective Euklidean action. The fermionic part of the action, which contains the full Dirac sea, is regularized within Schwinger's proper-time scheme. The meson fields are restricted to the chiral circle and to hedgehog configurations. The only parameter of the model is the constituent quark mass $M$ which simultaneously controls the regularization. We evaluate meson and quark fields self-consistently in dependence on the constituent quark mass. It is shown that the self-consistent fields do practically not depend on the constituent quark mass. This allows us to define a properly parameterized reference field which for physically relevant constituent masses can be used as a good approximation to the exactly calculated one. The reference field is chosen to have correct behaviour for small and large radii. To test the agreement between self-consistent and reference fields we calculate several observables like nucleon energy, mean square radius, axial-vector constant and delta-nucleon mass splitting in dependence on the constituent quark mass. The agreement is found to be very well. Figures available on request.