Complete set of observables in pseudo-scalar meson photoproduction -- Controversy solved

TL;DR

This paper clarifies the controversy over the number of observables needed in pseudo-scalar meson photoproduction, demonstrating that all eight observables are necessary in practical scenarios due to data uncertainties.

Contribution

It shows that the reduction to four observables in partial-wave analysis is unjustified when realistic data uncertainties are considered.

Findings

All eight observables are necessary for complete amplitude determination.

The claimed reduction to four observables is invalid with real-world data.

Mathematical assumptions in partial-wave analysis lead to artificial controversy.

Abstract

The long-standing debate over whether the complete set of observables in pseudo-scalar meson photoproduction consists of eight or merely four elements continues to persist. From the perspective of amplitude analysis, it is argued that all eight observables are necessary to completely determine the others. On the other hand, proponents of partial-wave analysis, working with theoretically precise data of infinite accuracy, claim that only four observables are needed. However, this claim is not acceptable from an experimental viewpoint, as all data in the real world contain some uncertainty. This paper illustrates that the controversy is artificial and is due to additional mathematical assumptions used in partial-wave analysis. Our research advances this discussion by moving from exact synthetic numerical data to also synthetic, but more realistic data in partial-wave analysis and shows that the claimed reduction in observables is unjustified. Consequently, the final conclusion is that the complete set of observables in pseudo-scalar meson photoproduction, whether using amplitude analysis or partial-wave analysis with practical data, must consist of eight observables.