Dispersion Relations in Gauge Theories with Confinement

TL;DR

This paper demonstrates that in gauge theories with confinement, the analytic structure of physical amplitudes remains consistent with effective theories, confirming the validity of dispersion relations in QCD despite confinement.

Contribution

It introduces BRST-invariant composite fields to analyze the analytic structure of amplitudes, showing confinement does not alter the singularity structure of physical amplitudes.

Findings

Physical amplitudes share the same singularities as in effective theories with only physical fields.

No anomalous thresholds associated with confined constituents like quarks and gluons.

Dispersion relations for hadronic amplitudes remain valid in QCD.

Abstract

The analytic structure of {\it physical} amplitudes is considered for gauge theories with confinement of excitations corresponding to the elementary fields. Confinement is defined in terms of the BRST algebra. BRST-invariant, local, composite fields are introduced, which interpolate between physical asymptotic states. It is shown that the singularities of physical amplitudes are the same as in an effective theory with only physical fields. In particular, there are no structure singularities (anomalous thresholds) associated with confined constituents, like quarks and gluons. The old proofs of dispersion relations for hadronic amplitudes remain valid in QCD.