Generalization of the model-independent Laurent-Pietarinen single-channel pole-extraction formalism to multiple channels

TL;DR

This paper extends a model-independent Laurent-Pietarinen pole-extraction method from single-channel to multi-channel analyses, enabling simultaneous analysis of multiple amplitudes with unitarity constraints for better resonance characterization.

Contribution

The paper introduces a generalized multi-channel Laurent-Pietarinen formalism for resonance pole extraction, incorporating unitarity constraints, enhancing the analysis of coupled-channel partial-wave amplitudes.

Findings

Successfully generalized the method to multiple channels

Provides a model-independent analysis framework

Incorporates unitarity constraints effectively

Abstract

A method to extract resonance pole information from single-channel partial-wave amplitudes based on a Laurent (Mittag-Leffler) expansion and conformal mapping techniques has recently been developed. This method has been applied to a number of reactions and provides a model-independent extraction procedure which is particularly useful in cases where a set of amplitudes is available only at descrete energies. This method has been generalized and applied to the case of a multi-channel fit, where several sets of amplitudes are analysed simultaneously. The importance of unitarity constraints is discussed. The final result provides a powerful, model-independent tool for analyzing partial-wave amplitudes of coupled or connected channels based entirely on the concepts of analyticity and unitarity.