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

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,

arXiv comment5 pages, 6 figures

References in corpus (8)

• Properties of baryon resonances from a multichannel partial wave analysis
• Electromagnetic Excitation of Nucleon Resonances
• Determining pseudoscalar meson photo-production amplitudes from complete experiments
• Ambiguities in the partial-wave analysis of pseudoscalar-meson photoproduction
• Model dependence of single-energy fits to pion photoproduction data
• Towards an understanding of discrete ambiguities in truncated partial wave analyses
• Phase Variation of Hadronic Amplitudes
• Photoproduction of $\eta$ and ${\eta }^{\prime }$ Mesons on Proton

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• On the spin-observables in pseudoscalar meson photoproduction
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• Is the pole content of each single-energy, single-channel partial wave analysis inherently model dependent?
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• Single-channel, single-energy partial-wave analysis with continuity improved through minimal phase constraints
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• Mathematical aspects of phase rotation ambiguities in partial wave analyses