# A connection between angular dependent phase ambiguities and the uniqueness of the partial wave decomposition

## TL;DR

This paper explores how angular-dependent phase ambiguities affect the uniqueness of partial wave decompositions in scattering data, demonstrating methods to resolve non-uniqueness through phase rotations and analyzing implications for experimental observables.

## Contribution

It establishes a connection between angular-dependent phase ambiguities and the non-uniqueness of partial wave analysis, providing a method to remove ambiguities via phase rotations.

## Key findings

- Phase ambiguities cause non-unique partial wave solutions.
- Phase rotations can restore uniqueness in partial wave analysis.
- Implications for Legendre expansions of experimental data.

## Abstract

Unconstrained partial-wave amplitudes obtained at discrete energies from fits to complete sets of experimental data may not vary smoothly with energy, and are in principle non-unique. We demonstrate how this behavior can be ascribed to the continuum ambiguity. Starting from the spinless scattering case, we demonstrate how an unknown overall phase depending on energy and angle mixes the structures seen in the associated partial-wave amplitudes making the partial wave decomposition non-unique, and illustrate it on a simple toy model. We then apply these principles to pseudo-scalar meson photoproduction and show that the non-uniqueness effect can be removed through a phase rotation, allowing a consistent comparison with model amplitudes. The effect of this phase ambiguity is also considered for Legendre expansions of experimental observables. 5 pages,