New method to extract information of near-threshold resonances: Uniformized Mittag-Leffler expansion of Green's function and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi></mml:math> matrix

Abstract

We propose a new, model-independent approach that appropriately incorporates the resonant and threshold behaviors. We show that when choosing the appropriate variable, the complete Green's function and the $T$ matrix can be expressed as single-valued functions (uniformization) in the form of a simple series explicitly written by the bound and resonant poles: the uniformized Mittag-Leffler expansion. The poles' symmetries, arising from the unitarity of the $S$ matrix, impose the series to obey the proper threshold behaviors. We then demonstrate this method in a model case of a double-channel meson-baryon scattering, with channels, $\overline{K}N(I=0)$, and $\ensuremath{\pi}\mathrm{\ensuremath{\Sigma}}(I=0)$, by fitting the numerically calculated $T$ matrix with the simple series and comparing the fitted results to the exact results.