On Dispersive and Nondispersive K-matrix Formalisms

TL;DR

This paper compares dispersive and nondispersive K-matrix formalisms for coupled-channel scattering, showing their equivalence in the physical region and highlighting ambiguities in model interpretation.

Contribution

It provides a detailed comparison of dispersive and nondispersive K-matrix methods within the N/D framework, clarifying their equivalence and discussing modeling ambiguities.

Findings

No clear preference for dispersive modeling.

Equivalence of dispersive and nondispersive methods in the physical region.

Interpretational ambiguities are common and require thorough data and model analysis.

Abstract

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 to interpret 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 reparameterization. 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 regards 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.