Ghost poles and chiral symmetry in $πN$ scattering

Details Ghost poles and chiral symmetry in $πN$ scattering Ghost poles and chiral symmetry in $πN$ scattering

1996-08-27

arxiv.org/abs/hep-ph/9608455v2

Physics

High Energy Physics

High Energy Physics - Phenomenology

6 pages, 4 embedded figures, Latex 2.09, Revtex.sty, epsf.sty. Contribution presented at the 14th International Conference on

Scientific paper

We solve the Schwinger-Dyson equation for the nucleon propagator in the vacuum using $\pi$, $\sigma$, and $\omega$ 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 $\pi N$ 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.

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