Determination of complete experiments using graphs

TL;DR

This paper introduces a graph-based, automated method for determining complete experiments in reactions with multiple amplitudes, enhancing efficiency especially for complex reactions with many spin amplitudes.

Contribution

It presents a novel graph representation and an automated procedure based on a modified Moravcsik's theorem for identifying complete experiments across various reaction types.

Findings

Automated procedure determines complete experiments for any number of amplitudes.

Graph representation simplifies the visualization and analysis of experimental completeness.

New directional graphs can reduce the size of complete sets in complex cases.

Abstract

This work presents ideas for the determination of complete experiments using graphs, which are based on a recently published, modified form of Moravcsik's theorem. The lucid representation of complete experiments in terms of graphs, which is at the heart of the theorem, leads to a fully automated procedure that can determine complete experiments for in principle any reaction, i.e. for any number of amplitudes $N$. For larger $N$ (i.e. $N \geq 4$), the sets determined according to Moravcsik's theorem turn out to be slightly overcomplete. A new type of directional graph has been proposed recently, which can decrease the length of the complete sets of observables in some of these cases. The presented results are relevant for reactions with larger numbers of spin-amplitudes, which are at the center of interest in forthcoming measurements, such as single-meson electroproduction $(N=6)$, two-meson photoproduction $(N=8)$ or vector-meson photoproduction $(N=12)$.