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

Understand

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.