Pion-nucleon interaction in a covariant hadron-exchange model

We develop a relativistic covariant and unitary description of the pion-nucleon interaction in a hadron-exchange model. The model is based on the solution of a dimensionally reduced (quasipotential) Bethe-Salpeter equation for the partial-wave off-shell πN scattering amplitudes with the potential consisting of the field-theoretical s- and u-channel nucleon, Roper, Delta, D₁₃, S₁₁ exchanges, and the t-channel ρ and σ meson exchanges. The contributions of the spin-3/2 Delta and D₁₃ resonances are treated within the Rarita-Schwinger formalism and different forms of the πNΔ vertex are investigated. The free parameters of the model are fitted to the πN phase-shift data of the KH80 and SM95 partial-wave analyses in the region up to 600 MeV pion kinetic energy. The resulting on-shell solution provides a good description of the πN scattering lengths, as well as the energy behavior of the S, P, and D partial waves. The sensitivity of the phase shifts on various model-dependent effects is examined.