Relevance of complex branch points for partial wave analysis

TL;DR

This paper investigates the impact of complex branch points on partial wave analysis in hadron spectroscopy, demonstrating their potential to mimic resonance poles and complicate the interpretation of experimental data.

Contribution

It highlights the significance of complex branch points in partial wave analysis and shows they can be mistaken for resonance poles in elastic scattering data.

Findings

Existence of complex branch points in the piN P11 partial wave.

Complex branch points can mimic resonance poles in elastic data.

Distinguishing between poles and branch points requires more than elastic data.

Abstract

A central issue in hadron spectroscopy is to deduce --- and interpret --- resonance parameters, namely pole positions and residues, from experimental data, for those are the quantities to be compared to lattice QCD or model calculations. However, not every structure in the observables derives from a resonance pole: the origin might as well be branch points, either located on the real axis (when a new channel comprised of stable particles opens) or in the complex plane (when at least one of the intermediate particles is unstable). In this paper we demonstrate first the existence of such branch points in the complex plane and then show on the example of the piN P11 partial wave that it is not possible to distinguish the structures induced by the latter from a true pole signal based on elastic data alone.