Abstract
We investigate the importance of crossing symmetry in effective field models and the effects of phenomenological nucleon resonance widths on the paradigmatic case of pion photoproduction. We use reaction models containing four star resonances up to 1.8 GeV (Δ(1232), N(1440), N(1520), N(1535), Δ(1620), N(1650), Δ(1700), and N(1720)) with different prescriptions for crossed terms and widths, to fit the latest world database on pion photoproduction. We compare χ2 results from selected multipoles and fits. The χ2 is highly dependent on the fulfillment of crossing symmetry and the inclusion of u channels.
Highlights
In the non-perturbative regime of Quantum Chromodynamics (QCD) we have to rely on effective field models to describe physical processes governed by the strong interaction
The reliability of a complex calculation on nuclei starting from an elementary reaction model
Unitarity of the scattering matrix is not respected but, as long as we include all the Feynman diagrams emerging from the effective theory, crossing symmetry is fulfilled
Summary
In the non-perturbative regime of Quantum Chromodynamics (QCD) we have to rely on effective field models to describe physical processes governed by the strong interaction. When one considers direct and crossed terms one usually includes a resonance width in the s channel but not in the u channel [6,7]: Ares(s, u) J where j = π, ππ, η stands for the different decay channels, Xj (s) accounts for the energy dependence of the width, and Γπ ∝ h2.
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