Calculations of Polarization Observables in Pseudoscalar Meson Photo-production Reactions

TL;DR

This paper derives relations between experimental observables and theoretical amplitudes in pseudoscalar meson photo-production, clarifying sign conventions and aiding the extraction of reaction amplitudes from experimental data.

Contribution

It provides explicit formulas for calculating matrix elements with arbitrary spin projections and clarifies sign discrepancies in existing literature.

Findings

Identified sign differences in double-polarization observables compared to previous analyses.

Presented formulas for direct calculation of matrix elements with arbitrary spin projections.

Highlighted the importance of consistent definitions in experimental and theoretical comparisons.

Abstract

In preparation for the extraction of pseudoscalar meson photo-production amplitudes from a new generation of complete experiments, we assemble the relations between experimental observables and the Chew-Goldberger-Low-Nambu amplitudes. We present expressions that allow the direct calculation of matrix elements with arbitrary spin projections and uses these to clarify sign differences that exist in the literature. Comparing to the MAID and SAID analysis codes, we have found that the implied definitions of six double-polarization observables are the negative of what has been used in comparing to recent experimental data.