Pion-nucleon partial-wave analysis with fixed-tdispersion relation constraints

We have performed a set of partial-wave analyses of the pion-nucleon elastic scattering data to 2 GeV employing rigorous constraints from simultaneous forward and fixed-t dispersion relations. Constraints were generated from the forward C^± amplitudes and the invariant amplitudes A and B at fixed t in the range 0 to -0.3 GeV². Solutions were generated for a range of pion-nucleon coupling constants (g²/4{π}) and isoscalar scattering lengths (a⁽⁺⁾). A chi-squared map for these (g²/4{π},a⁽⁺⁾) solutions exhibits a clear minimum near g²/4{π}=13.75 (f²/4{π}=0.076) for both the fits to the data and the dispersion relations. While favoring a particular g²/4{π}, this work shows that it is possible to obtain good, stable fits for nearby values, but at the cost of increased chi squared. Consequently, this approach provides a criterion for defining the preferred value and uncertainty of g²/4{π} from pion-nucleon scattering data. On this basis, we conclude that g²/4{π}=13.75±{}0.15 (f²/4{π}=0.076±{}0.001).