  Complex mass poles, or ghost poles, are present in the Hartree-Fock solution
of the Schwinger-Dyson equation for the nucleon propagator in renormalizable
models with Yukawa-type meson-nucleon couplings, as shown many years ago by
Brown, Puff, and Wilets (BPW). These ghosts violate basic theorems of quantum
field theory and their origin is related to the ultraviolet behavior of the
model interactions. Recently, Krein et.al, proved that the ghosts disappear
when vertex corrections are included in a self-consistent way, softening the
interaction sufficiently in the ultraviolet region. In previous studies of
pion-nucleon scattering using "dressed" nucleon propagator and bare vertices,
did by Nutt and Wilets in the 70's (NW), it was found that if these poles are
explicitly included, the value of the isospin-even amplitude A+ is satisfied
within 20% at threshold. The absence of a theoretical explanation for the
ghosts and the lack of chiral symmetry in these previous studies led us to
re-investigate the subject using the approach of the linear-sigma model and
study the interplay of low-energy theorems for pion-nucleon scattering and
ghost poles. For bare interaction vertices we find that ghosts are present in
this model as well and that the A+ value is badly described. As a first
approach to remove these complex poles, we dress the vertices with
phenomenological form factors and a reasonable agreement with experiment is
achieved. In order to fix the two cutoff parameters, we use the A+ value for
the chiral limit (m_pion -> 0) and the experimental value of the isoscalar
scattering length. Finally, we test our model by calculating the phase shifts
for the S waves and we find a good agreement at threshold.
