The modeling of coupled-channel effects has become increasingly important due to the availability of highly precise data for a large variety of hadronic (re)scattering processes. The $K$-matrix is a powerful, yet comparatively simple, method to describe scattering amplitudes, including coupled-channel effects, with the aim of interpreting experimental data. Throughout the literature, a range of dispersive and nondispersive $K$-matrix methods are employed. Here, we compare the dispersive and nondispersive formulations in the context of the N/D method. It is shown that the methods are equivalent in the physical region under $K$-matrix reparametrization. Differences away from the physical region are examined. Applications to synthetic data are used to illustrate the effects of model choices concerning form factors and the application of dispersion relations, with the goal of clarifying best practices. We find no clear preference with regard to dispersive modeling. In contrast, we find that interpretational ambiguity of the bare model parameters—and even of the form of the bare model—is endemic, and recommend a thorough sampling of data and model spaces to assess conclusion robustness.

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• QCD phenomenology
• Scattering amplitudes
• Strong interaction