a Soliton Bag Model of the Nucleon and Delta Dressed by a Quark-Antiquark Pion.
The Friedberg-Lee soliton bag model is used to describe the nucleon, delta and pion. We build upon the mean-field solutions to the model, taking into account the one-gluon-exchange interaction by the use of a free gluon propagator in the Coulomb gauge and allowing the nucleon or delta to consist of a bare three quark bag and a three quark bag dressed by one quark-antiquark pion. This way of treating the pion cloud differs from most other works on the subject by the fact that we take the quark substructure of the pion into account. The generator coordinate method enables us to find an approximate solution to the ground state of the nucleon and the delta from which static physical properties can be calculated. The soliton field part of the ground state is treated in a coherent state approximation (similar to the mean-field approximation, but remaining a true quantum state). The generator coordinate or Hill-Wheeler integral equations are solved numerically with the help of the Tikhonov regularization. Detailed numerical results are given for different sets of parameters. The agreement with experiment is as good as in the mean-field approximation but new quantities are now accessible to computation (e.g., the neutron charge radius and the NN(pi) and N(DELTA)(pi) coupling constants). Since chiral symmetry was not built into the Lagrangian density, we do not recover PCAC and the soft pion limit. However, by carrying away a large part of the axial current exchanged by the quarks as they bounce off the bag's surface, the pion helps reduce the surface peak of the divergence of the axial current: we obtain a global axial current "conservation".
- Pub Date:
- Physics: Nuclear