New graphical criterion for the selection of complete sets of polarization observables and its application to single-meson photoproduction as well as electroproduction

TL;DR

This paper introduces a new graphical method combining graph theory and phase-ambiguity analysis to identify minimal complete sets of polarization observables for amplitude extraction in meson photoproduction and electroproduction.

Contribution

It presents a novel graphical criterion for selecting complete observable sets and applies it to specific meson production processes, including the first extensive list for electroproduction.

Findings

Derived minimal complete sets of 2N observables for N=4 and N=6.

Published the first extensive list of minimal sets for electroproduction.

Outlined generalization to processes with N > 6 amplitudes.

Abstract

This paper combines the graph-theoretical ideas behind Moravcsik's theorem with a completely analytic derivation of discrete phase-ambiguities, recently published by Nakayama. The result is a new graphical procedure for the derivation of certain types of complete sets of observables for an amplitude-extraction problem with $N$ helicity-amplitudes. The procedure is applied to pseudoscalar meson photoproduction ($N = 4$ amplitudes) and electroproduction ($N = 6$ amplitudes), yielding complete sets with minimal length of $2N$ observables. For the case of electroproduction, this is the first time an extensive list of minimal complete sets is published. Furthermore, the generalization of the proposed procedure to processes with a larger number of amplitudes, i.e. $N > 6$ amplitudes, is sketched. The generalized procedure is outlined for the next more complicated example of two-meson photoproduction ($N = 8$ amplitudes).