Resolving interpretational ambiguity in two-channel K-matrix model via uniformized Jost function

Abstract

We propose a formal bridge between a two-channel Jost function and the K-matrix for scattering processes that correspond to a main pole-shadow pair. Different simple K-matrix parametrizations can yield similarly good fits in the physical region while implying different pole configurations, which makes physical interpretations ambiguous. By solving and comparing the Jost function to the K-matrix formalism, we created an effective mapping to the fitting parameters. The resulting framework is interpreted as a pole-informed constraint mechanism for these K-matrix parametrizations. In this way, a pole configuration chosen in the uniformization scheme can be used to restrict the phenomenological fitting parameters of the K-matrix. The present study is limited to the formal development of the bridge, while data fitting is reserved for future work in which a pole configuration selected within the uniformized framework will be used to constrain the K-matrix analysis.