Extracting the resonance parameters from experimental data on scattering of charged particles

TL;DR

This paper introduces a novel parametrization of the multi-channel S-matrix using Taylor series expansion of Jost matrices to accurately extract resonance parameters from scattering data, addressing multi-valuedness issues.

Contribution

The paper presents a semi-analytic, Taylor series-based method for fitting scattering data and locating resonances, improving upon existing techniques by explicitly handling multi-valued functions.

Findings

Successfully tested on a two-channel model with artificial data.

Accurately locates resonance poles using the new parametrization.

Addresses multi-valuedness and branching issues in S-matrix analysis.

Abstract

A new parametrization of the multi-channel S-matrix is used to fit scattering data and then to locate the resonances as its poles. The S-matrix is written in terms of the corresponding "in" and "out" Jost matrices which are expanded in the Taylor series of the collision energy E around an appropriately chosen energy E0. In order to do this, the Jost matrices are written in a semi-analytic form where all the factors (involving the channel momenta and Sommerfeld parameters) responsible for their "bad behaviour" (i.e. responsible for the multi-valuedness of the Jost matrices and for branching of the Riemann surface of the energy) are given explicitly. The remaining unknown factors in the Jost matrices are analytic and single-valued functions of the variable E and are defined on a simple energy plane. The expansion is done for these analytic functions and the expansion coefficients are used as the fitting parameters. The method is tested on a two-channel model, using a set of artificially generated data points with typical error bars and a typical random noise in the positions of the points.