A re-examination of pion-nucleon dynamics

We calculate the scattering amplitude of elastic pion-nucleon scattering using two approaches of current importance. One is the extended linear sigma model (ELSM) in which one allows for the deviation of the axial coupling constant g_A from unity by adding vector and pseudo-vector pion-nucleon coupling terms. The other is heavy baryon chiral perturbation theory (HBχPT), which is a low-energy effective theory of quantum chromodynamics. Similarities and differences between the two amplitudes will be discussed. To this end, we expand the ELSM scattering amplitude up to order $1M$ (M = nucleon mass) and $1ms$ (m_σ =sigma mass) and compare this expanded ELSM amplitude with the HBχPT scattering amplitude calculated up to next-to-leading order.