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Ghost poles and chiral symmetry in $πN$ scattering

C. A. da Rocha·G. Krein·L. Wilets
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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.

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C. A. da Rocha, G. Krein, L. Wilets. 1996-09-16. Ghost poles and chiral symmetry in $πN$ scattering. https://arxiv.org/abs/hep-ph/9608455

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