A method for extracting the resonance parameters from experimental cross section

TL;DR

This paper introduces a method to extract resonance parameters from experimental cross sections by analytically modeling the S-matrix with explicit channel threshold behavior and Taylor expansions, enabling accurate resonance identification.

Contribution

The paper presents a novel approach that explicitly factorizes channel threshold effects in the Jost matrices and uses Taylor expansions to fit experimental data for resonance extraction.

Findings

Accurately locates multi-channel resonances.

Reproduces partial widths and cross sections.

Ensures proper analytic structure of the S-matrix.

Abstract

The matrix elements of the multi-channel Jost matrices are written in such a way that their dependencies on all possible odd powers of channel momenta are factorized explicitly. As a result the branching of the Riemann energy surface at all the channel thresholds is represented in them via exact analytic expressions. The remaining single-valued functions of the energy are expanded in the Taylor series near an arbitrary point on the real axis. Using the thus obtained Jost matrices, the $S$-matrix is constructed and then the scattering cross section is calculated, which therefore depends on the Taylor expansion coefficients. These coefficients are considered as the adjustable parameters that are optimized to fit a given set of experimental data. After finding the coefficients, the resonances are located as zeros of the Jost matrix determinant at complex energies. Within this approach the $S$-matrix has proper analytic structure. This enables us not only to locate multi-channel resonances but also to reproduce their partial widths as well as the scattering cross section in the channels for which the data are not available.