Analytic Structure of Amplitudes in Gauge Theories with Confinement

TL;DR

This paper investigates the analytic structure of amplitudes in confining gauge theories, demonstrating that physical amplitudes share properties with effective theories of composite particles, and clarifying the absence of anomalous thresholds related to confined constituents.

Contribution

It proves that physical amplitudes in confining gauge theories have the same analytic properties as effective theories with composite fields, and clarifies the nature of thresholds and singularities.

Findings

Physical amplitudes lack anomalous thresholds from confined particles.

Analytic properties are consistent with effective theories of composite fields.

Unphysical propagator functions have singularities indicating confined states.

Abstract

For gauge theories with confinement, the analytic structure of amplitudes is explored. It is shown that the analytic properties of physical amplitudes are the same as those obtained on the basis of an effective theory involving only the composite, physical fields. The corresponding proofs of dispersion relations remain valid. Anomalous thresholds are considered. They are related to the composite structure of particles. It is shown, that there are no such thresholds in physical amplitudes which are associated with confined constituents, like quarks and gluons in QCD. Unphysical amplitudes are considered briefly, using propagator functions as an example. For general, covariant, linear gauges, it is shown that these functions must have singularities at finite, real points, which may be associated with confined states.