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
arXiv:nucl-th/0312104 · doi:10.1016/j.nuclphysa.2004.03.003
Abstract
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 $Î$ resonance, including its dressing with meson loops, is discussed in some detail and found to be small.
12 pages, 6 figures, using RevTEX4. References added, discussion extended, conclusions unchanged. To be published in Nuclear Physics A