The Adler–Weisberger and Goldberger–Miyazawa–Oehme sum rules as probes of constraints from analyticity and chiral symmetry in dynamical models for pion–nucleon scattering Original Research Article

The Adler–Weisberger and Goldberger–Miyazawa–Oehme sum rules are calculated within a relativistic, unitary and crossing symmetric dynamical model for pion–nucleon scattering using two different methods: (1) by evaluating the scattering amplitude at the corresponding low-energy kinematics and (2) by evaluating the sum-rule integrals with the calculated total cross section. The discrepancy between the results of the two methods provides a measure of the breaking of analyticity and chiral symmetry in the model. The contribution of the Δ resonance, including its dressing with meson loops, is discussed in some detail and found to be small.