Low-energy pion-nucleon scattering

An analysis of low-energy charged pion-nucleon data from recent π^±p experiments is presented. From the scattering lengths and the Goldberger-Miyazawa-Oehme (GMO) sum rule we find a value of the pion-nucleon coupling constant of f²=0.0756±0.0007. We also find, contrary to most previous analyses, that the scattering volumes for the P₃₁ and P₁₃ partial waves are equal, within errors, corresponding to a symmetry found in the Hamiltonian of many theories. For the potential models used, the amplitudes are extrapolated into the subthreshold region to estimate the value of the Σ term. Off-shell amplitudes are also provided.