Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model

TL;DR

This paper investigates the analytic structure of pion-nucleon scattering amplitudes using a meson exchange model, focusing on pole positions and residues to accurately parameterize resonances and understand their behavior across different reactions.

Contribution

It provides a detailed analysis of the pole structure and Riemann sheet topology of the scattering amplitude, enhancing resonance extraction methods in meson exchange models.

Findings

Determined the pole positions and residues for pion-nucleon scattering.

Analyzed the sheet structure of the amplitude for resonance identification.

Discussed resonance interference effects in the S11 amplitude.

Abstract

The analytic properties of scattering amplitudes provide important information. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and residues allow for a parameterization of resonances in a well-defined way, free of assumptions for the background and energy dependence of the resonance part. This is a necessary condition to relate resonance contributions in different reactions. In the present study, we determine the pole structure of pion-nucleon scattering in an analytic model based on meson exchange. For this, the sheet structure of the amplitude is determined. To show the precision of the resonance extraction and discuss phenomena such as resonance interference, we discuss the S11 amplitude in greater detail.