Polarization observables in the longitudinal basis for pseudo-scalar meson photoproduction using a density matrix approach

TL;DR

This paper develops a comprehensive density matrix framework for analyzing polarization observables in pseudo-scalar meson photoproduction, using a longitudinal basis to unify theoretical amplitudes with experimental data.

Contribution

It introduces a covariant, single-axis spin quantization approach that simplifies the relation between theoretical amplitudes and measurable intensities in meson photoproduction.

Findings

Derived a complete intensity expression for polarized meson photoproduction.

Established a covariant formalism with a single spin-quantization axis.

Addressed sign discrepancies between theory and experiment.

Abstract

The complete expression for the intensity in pseudo-scalar meson photoproduction with a polarized beam, target, and recoil baryon is derived using a density matrix approach that offers great economy of notation. A Cartesian basis with spins for all particles quantized along a single direction, the longitudinal beam direction, is used for consistency and clarity in interpretation. A single spin-quantization axis for all particles enables the amplitudes to be written in a manifestly covariant fashion with simple relations to those of the well-known CGLN formalism. Possible sign discrepancies between theoretical amplitude-level expressions and experimentally measurable intensity profiles are dealt with carefully. Our motivation is to provide a coherent framework for coupled-channel partial-wave analysis of several meson photoproduction reactions, incorporating recently published and forthcoming polarization data from Jefferson Lab.