Mathematical aspects of phase rotation ambiguities in partial wave analyses

TL;DR

This paper explores the mathematical nature of phase rotation ambiguities in partial wave analyses, revealing how continuum ambiguities mix partial waves and encompass discrete ambiguities, with a numerical method proposed for their determination.

Contribution

It demonstrates that continuum ambiguities in partial wave analyses are more general than previously thought, unifying discrete ambiguities under a broader phase ambiguity framework.

Findings

Continuum ambiguities mix partial waves.

Discrete ambiguities are special cases of continuum ambiguities.

A numerical method can determine connecting phases.

Abstract

The observables in a single-channel $2$-body scattering problem remain invariant once the amplitude is multiplied by an overall energy- and angle-dependent phase. This invariance is known as the continuum ambiguity. Also, mostly in truncated partial wave analyses (TPWAs), discrete ambiguities originating from complex conjugation of roots are known to occur. In this note, it is shown that the general continuum ambiguity mixes partial waves and that for scalar particles, discrete ambiguities are just a subset of continuum ambiguities with a specific phase. A numerical method is outlined briefly, which can determine the relevant connecting phases.