Complete experiments in pseudoscalar meson photoproduction revisited

TL;DR

This paper revisits the determination of phase ambiguities in pseudoscalar meson photoproduction, establishing the minimal sets of observables needed and identifying conditions requiring additional measurements.

Contribution

It refines the understanding of the completeness of double-spin observables for phase resolution, including conditions requiring more measurements than previously thought.

Findings

Four observables suffice when phases are unequal in magnitude.

Additional observables are needed when phases have equal magnitudes.

A method to identify when extra observables are necessary is provided.

Abstract

By exploiting the underlying symmetries of the relative phases of the pseudoscalar meson photoproduction amplitude, we determine all the possible sets of four double-spin observables that resolve the phase ambiguity of the amplitude in transversity basis up to an overall phase. The present results corroborate the original findings by Chiang and Tabakin [Phys. Rev. C 55, 2054 (1997)]. However, it is found that the completeness condition of four double-spin observables to resolve the phase ambiguity holds only when the relative phases do not meet the condition of equal magnitudes. In situations where this condition occurs, it is shown that one needs extra chosen observables, resulting in the minimum number of observables required to resolve the phase ambiguity to reach up to eight, depending on the particular set of four double-spin observables considered. Furthermore, a way of gauging when the condition of equal magnitudes occurs is provided.