Phase Variation of Hadronic Amplitudes

TL;DR

This paper investigates how the phase of hadronic scattering amplitudes varies with angle, highlighting the limitations of current models and suggesting a link to interaction radii, with implications for nuclear medium effects.

Contribution

It provides a detailed analysis of phase variation in hadronic amplitudes, emphasizing the constraints from unitarity and proposing model-based explanations related to interaction radii.

Findings

Unitarity constrains phase determination in amplitude analyses.

Current nucleon-nucleon analyses lack the necessary phase variation.

Phase behavior near forward angles relates to interaction radii.

Abstract

The phase variation with angle of hadronic amplitudes is studied with a view to understanding the underlying physical quantities which control it and how well it can be determined in free space. We find that unitarity forces a moderately accurate determination of the phase in standard amplitude analyses but that the nucleon-nucleon analyses done to date do not give the phase variation needed to achieve a good representation of the data in multiple scattering calculations. Models are examined which suggest its behavior near forward angles is related to the radii of the real and absorptive parts of the interaction. The dependence of this phase on model parameters is such that if these radii are modified in the nuclear medium (in combination with the change due to the shift in energy of the effective amplitude in the medium) then the larger magnitudes of the phase needed to fit the data might be attainable, but only for negative values of the phase variation parameter.