Pion, sigma and nucleon propagators in the linear σ-model

We study the pion, sigma and nucleon propagators of the linear σ-model in the one-loop approximation. We show that in the renormalized model the meson propagators exhibit imaginary poles. Such nonphysical poles disappear when a cutoff is introduced. The maximum of this cutoff value is shown to be of the orderλc≈1.2 Gev. Once this value is fixed it is possible to find a set of parameters which allow for a selfconsistent interpretation of physical properties associated with the propagators. A 400 MeV wide resonance appears in the sigma propagator, the nucleon is a bound state and in its continuum two Roper resonances can be identified.