Low-energy pion-nucleon scattering

An analysis of low-energy charged pion-nucleon data from recent ${\pi }^{\pm }p$ 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 $f^2=0.0756\mathrm{}\pm 0.0007$. We also find, contrary to most previous analyses, that the scattering volumes for the $P_{31}$ and $P_{13}$ 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 $\Sigma$ term. Off-shell amplitudes are also provided.