Minimal complete sets for two pseudoscalar meson photoproduction

TL;DR

This paper identifies minimal complete sets of polarization observables for two pseudoscalar meson photoproduction reactions, enabling unique amplitude determination with minimal measurements, including only one triple polarization observable.

Contribution

It introduces a method to derive minimal complete sets of polarization observables for these reactions, reducing previous over-complete sets to minimal, ambiguity-free sets for the first time.

Findings

Multiple minimal complete sets of 16 observables are presented.

Each set contains only one triple polarization observable.

Sets enable unique amplitude determination without ambiguities.

Abstract

For photoproduction reactions with final states consisting of two pseudoscalar mesons and a spin-1/2 baryon, 8 complex amplitudes need to be determined uniquely. A modified version of Moravcsik's theorem is employed for these reactions, resulting in slightly over-complete sets of polarization observables that are able to determine the amplitudes uniquely. Further steps were taken to reduce the found sets to minimal complete sets. As a final result, multiple minimal complete sets without any remaining ambiguities are presented for the first time. These sets consist of $2N=16$ observables, containing only one triple polarization observable.