A new method for extracting poles from single-channel data based on Laurent expansion of T-matrices with Pietarinen power series representing the non-singular part

TL;DR

This paper introduces a novel method for extracting pole parameters from single-channel data using Laurent expansion combined with Pietarinen series to represent non-singular parts, improving robustness and automatic determination of series terms.

Contribution

The paper presents a new approach that replaces traditional guesswork with Pietarinen series for modeling non-singular parts in Laurent expansion, enhancing accuracy and automation.

Findings

Method is robust up to three Pietarinen series.

Successfully applied to toy model with known poles.

Confirmed effectiveness on realistic resonance data.

Abstract

We present a new approach to quantifying pole parameters of single-channel processes based on Laurent expansion of partial wave T-matrices. Instead of guessing the analytical form of non-singular part of Laurent expansion as it is usually done, we represent it by the convergent series of Pietarinen functions. As the analytic structure of non-singular term is usually very well known (physical cuts with branhcpoints at inelastic thresholds, and unphysical cuts in the negative energy plane), we show that we need one Pietarinen series per cut, and the number of terms in each Pietarinen series is automatically determined by the quality of the fit. The method is tested on a toy model constructed from two known poles, various background terms, and two physical cuts, and shown to be robust and confident up to three Pietarinen series. We also apply this method to Zagreb CMB amplitudes for the N(1535) 1/2- resonance, and confirm the full success of the method on realistic data. This formalism can also be used for fitting experimental data, and the procedure is very similar as when Breit-Wigner functions are used, but with one modification: Laurent expansion with Pietarinen series is replacing the standard Breit-Wigner T-matrix form.