Dispersion Relations in Quantum Chromodynamics

TL;DR

This paper explores dispersion relations in Quantum Chromodynamics, demonstrating their applicability using BRST cohomology and confinement principles, and analyzing hadronic amplitudes without thresholds linked to quark-gluon structures.

Contribution

It extends dispersion relation proofs to QCD by incorporating BRST cohomology and confinement, showing hadronic amplitudes lack thresholds related to quark-gluon constituents.

Findings

Dispersion relations remain valid in QCD framework.

Hadronic amplitudes lack thresholds associated with quark-gluon structure.

BRST invariance and confinement are key to the analysis.

Abstract

Dispersion relations for the scattering of hadrons are considered within the framework of Quantum Chromodynamics. It is argued that the original methods of proof remain applicable. The setting and the spectral conditions are provided by an appropriate use of the BRST cohomology. Confinement arguments are used in order to exclude quarks and gluons from the physical subspace. Local, BRST-invariant hadron fields are considered as leading terms in operator product expansions for products of fundamental fields. The hadronic amplitudes have neither ordinary nor anomalous thresholds which are directly associated with the underlying quark-gluon-structure. Proofs involving the Edge of the Wedge Theorem and analytic completion are discussed briefly.