Pushing and Cranking Corrections to the Meson Fields of the Bosonized Nambu \& Jona-Lasinio Model

Abstract

We study the effect of center-of-mass motion and rotational corrections on hedgehog meson fields in the bosonized two-flavor Nambu \& Jona-Lasinio model. To remove the spurious motion and to restore good spin and isospin we consider a boosted and rotating soliton instead a static soliton at rest. Modified meson fields are obtained by minimizing a corrected effective energy functional. The importance of the modification is estimated by evaluating expectation values of several observables. Stabile solitonic configurations are obtained for $M\gapp$ 300\,MeV, while static solitons exists for $M\gapp$ 350\,MeV only. Despite the considerable size of the energy corrections (30-50\% of the soliton energy) the main features of the static soliton are preserved. Modified meson profiles are somewhat narrower than static ones and have a different asymptotic behavior, which depends on the isospin quantum number. The modifications increase with increasing constituent quark mass. The valence-quark picture dominates up to very large constituent quark masses. In the physically relevant mass region, the root-mean square radius of the quark distribution is reduced by less than 10 percent. The $\Delta$--nucleon mass-splitting is still weaker affected.