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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

S. Kondratyuk·K. Kubodera·F. Myhrer·O. Scholten
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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 $Δ$ resonance, including its dressing with meson loops, is discussed in some detail and found to be small.

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S. Kondratyuk, K. Kubodera, F. Myhrer, O. Scholten. 2004-03-03. 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. https://doi.org/10.1016/j.nuclphysa.2004.03.003

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