Spectral representation for u- and t-channel exchange processes in a partial-wave decomposition

TL;DR

This paper develops a spectral representation for partial-wave amplitudes in u- and t-channel exchange processes, addressing complex analytic structures relevant for QCD and hadron physics.

Contribution

It introduces a general spectral representation applicable to complex threshold structures, enhancing the analysis of coupled-channel systems in dispersion theory.

Findings

Spectral representation valid with anomalous thresholds

Applicable to decaying particles and overlapping cuts

Demonstrated on ten specific processes

Abstract

We study the analytic structure of partial-wave amplitudes derived from u- and t-channel exchange processes. The latter plays a crucial role in dispersion-theory approaches to coupled-channel systems that model final state interactions in QCD. A general spectral representation is established that is valid in the presence of anomalous thresholds, decaying particles or overlapping left-hand and right-hand cut structures as it occurs frequently in hadron physics. The results are exemplified at hand of ten specific processes.