On the Analytic Structure of the Quark Self-Energy in Nambu-Jona- Lasinio Models

The self-energy of quarks is investigated for various models which are inspired by the Nambu--Jona-Lasinio (NJL) model. Including, beyond the Hartree-Fock approximation, terms up to second-order in the quark interaction, the real and imaginary parts of scalar and vector components of the self-energy are discussed. The second-order contributions depend on the energy and momentum of the quark under consideration. This leads to solutions of the Dirac equation which are significantly different from those of a free quark or a quark with constant effective mass, as obtained in the Hartree-Fock approximation.