The incompleteness of complete pseudoscalar-meson photoproduction

TL;DR

This paper investigates the limitations of complete sets of observables in pseudoscalar-meson photoproduction, showing that even complete measurements cannot unambiguously determine reaction amplitudes due to phase ambiguities under realistic experimental conditions.

Contribution

The study demonstrates that complete sets of observables are insufficient for unambiguous amplitude extraction in pseudoscalar-meson photoproduction when considering experimental errors.

Findings

Moduli of transversity amplitudes can be determined from single-polarization data.

Relative phases face discrete ambiguities, hindering unambiguous determination.

Complete sets of observables do not guarantee statistically significant amplitude solutions.

Abstract

[Background] A complete set is a minimum set of observables which allows one to determine the underlying reaction amplitudes unambiguously. Pseudoscalar-meson photoproduction from the nucleon is characterized by four such amplitudes and complete sets involve single- and double-polarization observables. [Purpose] Identify complete sets of observables, and study how measurements with finite error bars impact their potential to determine the reaction amplitudes unambiguously. [Method] The authors provide arguments to employ the transversity representation in order to determine the amplitudes in pseudoscalar-meson photoproduction. It is studied whether the amplitudes in the transversity basis for the $\gamma p \to K^+\Lambda$ reaction can be estimated without ambiguity. To this end, data from the GRAAL collaboration and mock data from a realistic model are analyzed. [Results] It is illustrated that the moduli of normalized transversity amplitudes can be determined from precise single-polarization data. Starting from mock data with achievable experimental resolution, it is quite likely to obtain imaginary solutions for the relative phases of the amplitudes. Also the real solutions face a discrete phase ambiguity which makes it impossible to obtain a statistically significant solution for the relative phases at realistic experimental conditions. [Conclusions] Single polarization observables are effective in determining the moduli of the amplitudes in a transversity basis. Determining the relative phases of the amplitudes from double-polarization observables is far less evident. The availability of a complete set of observables does not allow one to unambiguously determine the reaction amplitudes with statistical significance.