Self-Consistent Calculation for the Nucleon Mass, π−N Coupling Constant, and the Low-Energy P12, T=12, π−N Scattering Phase Shifts

Abstract

A self-consistent calculation is performed for the low-energy $P_{\frac{1}{2}}$, $T=\frac{1}{2}$, pion-nucleon scattering amplitude, using the $\frac{N}{D}$ method. The distant part of the left-hand cut for the partial-wave amplitude is dealt with in the manner of Balázs. The mass of the nucleon bound state is found to be ≈880 MeV, the coupling constant ≈12. The low-energy phase shifts and the scattering length are also in good qualitative agreement with the observed ones.