Is the pole content of each single-energy, single-channel partial wave analysis inherently model dependent?

TL;DR

This paper demonstrates that the pole content in single-energy, single-channel partial wave analysis is inherently model dependent due to phase ambiguity, affecting the interpretation of resonance structures.

Contribution

It provides a realistic model analysis showing how phase choices influence pole structures, confirming the model dependence of partial wave analysis in experimental data.

Findings

Pole structure varies with phase choice.

Phase fixing to a specific solution affects pole content.

Improving data fit can alter the analytic structure.

Abstract

Unfortunately, yes, it is. In ref.[1] it has been shown that without fixing the reaction-amplitude phase, many combinations of partial waves at neighboring energies in single-energy, single-channel partial wave analysis reproduce experimental data identically, but are discontinuous and disconnected. To obtain the continuous solution, the phase has to be fixed to some continuous value. In the same reference it has also been shown that the change of angular part of reaction-amplitude phase mixes partial waves, so the pole structure of any single-energy single-channel partial wave analysis depends on the chosen phase. As in any single-channel analysis the overall reaction-amplitude phase cannot be determined because of continuum ambiguity, it is in principle free and has to be taken from some coupled-channel model. Because of the difference in the angular part of the phase, choosing different phases results in the change of the pole content of the obtained solution. Therefore, single-energy single-channel partial wave analysis is inherently model dependent, and the number of poles it contains strongly depends on the choice of the phase. In that reference these facts have been illustrated on the pseudo-scalar meson production toy model. This truth is now for the measured observables demonstrated on the realistic model of ref. [2] which combines amplitude and partial wave analysis in one self-consistent scheme for the the world collection of {\eta}-photoproduction data, and fixes the phase to BG2014-2 solution [3]. We show that the pole structure of the solution whose phase is very close to the BG2014-2 theoretical ED phase is very similar to the pole structure of BG2014-2 solution, but the agreement with the data is not ideal. However, improving the agreement with the data requires the departure from BG2014-2 ED phase, and this spoils analytic structure of the obtained solution.