Crossing symmetry and phenomenological widths in effective Lagrangian models of the pion photoproduction process

TL;DR

This study examines how crossing symmetry and phenomenological resonance widths influence effective Lagrangian models of pion photoproduction, highlighting their impact on model fit quality to experimental data.

Contribution

It demonstrates the significance of crossing symmetry and resonance width prescriptions in improving the accuracy of pion photoproduction models.

Findings

Crossing symmetry significantly affects fit quality.

Inclusion of u channels improves model fits.

Different width prescriptions alter the chi-squared results.

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 ($\Delta$(1232), N(1440), N(1520), N(1535), $\Delta$(1620), N(1650), $\Delta$(1700), and N(1720)) with different prescriptions for crossed terms and widths, to fit the latest world database on pion photoproduction. We compare $\chi^2$ results from selected multipoles and fits. The $\chi^2$ is highly dependent on the fulfillment of crossing symmetry and the inclusion of $u$ channels.