Ghost poles and chiral symmetry in $πN$ scattering

Abstract

We solve the Schwinger-Dyson equation for the nucleon propagator in the vacuum using $π$, $σ$, and $ω$ mesons. For bare interaction vertices (Hartree-Fock approximation) we obtain a pair of complex-conjugated poles (ghost poles) and for vertices dressed by phenomenological form-factors these ghosts disappeared. We use these two different approaches to evaluate the scattering lengths and the phase shifts for the $πN$ scattering at threshold. Our results show that only when the form factors are present is possible to obtain a good agreement with the low-energy observables.

6 pages, 4 embedded figures, Latex 2.09, Revtex.sty, epsf.sty. Contribution presented at the 14th International Conference on Particles and Nuclei (PANIC 96), Williamsburg, VA, 22-28 May 1996