Model-independent tests of the on-shell pion-nucleon Ward identities

A dispersion-theoretic method is developed to determine the axial-vector background amplitudes appearing in the on-shell $\pi N$ Ward identities. These current-algebra constraints are then found to be completely consistent with low-energy data and a nucleon $\sigma$ term of 73±21 MeV. All threshold $s$- and $p$-wave scattering lengths are correctly predicted by our model-independent approach.