Introducing Pietarinen expansion method into single-channel pole extraction problem

TL;DR

This paper introduces a novel Pietarinen expansion method for extracting pole parameters in single-channel processes, improving the analytic modeling of partial-wave T-matrices near the real axis.

Contribution

The paper develops and tests a Pietarinen series-based approach for pole extraction, offering a more reliable and flexible analytic structure representation compared to traditional methods.

Findings

Method is robust with up to three Pietarinen series.

Effective in analyzing both toy models and real experimental data.

Simplifies fitting procedures for partial-wave amplitudes.

Abstract

We present a new approach to quantifying pole parameters of single-channel processes based on a Laurent expansion of partial-wave T-matrices in the vicinity of the real axis. Instead of using the conventional power-series description of the non-singular part of the Laurent expansion, we represent this part by a convergent series of Pietarinen functions. As the analytic structure of the non-singular part is usually very well known (physical cuts with branch points at inelastic thresholds, and unphysical cuts in the negative energy plane), we find that one Pietarinen series per cut represents the analytic structure fairly reliably. The number of terms in each Pietarinen series is determined by the quality of the fit. The method is tested in two ways: on a toy model constructed from two known poles, various background terms, and two physical cuts, and on several sets of realistic piN elastic energy-dependent partial-wave amplitudes (GWU/SAID - [1, 2], and Dubna-Mainz-Taipei - [3, 4]). We show that the method is robust and confident using up to three Pietarinen series, and is particularly convenient in fits to amplitudes, such as single-energy solutions, coming more directly from experiment; cases where the analytic structure of the regular part is apriori unknown.