# The Dark Side of the Propagators: exploring their analytic properties by a massive expansion

## TL;DR

This paper derives analytical expressions for QCD propagators using a one-loop massive expansion, demonstrating positivity violation and confinement through Minkowski space analysis, and revealing complex conjugate poles in the gluon propagator.

## Contribution

It introduces a novel one-loop massive expansion approach to study QCD propagators analytically in Minkowski space, providing first-principles evidence of confinement.

## Key findings

- Positivity violation confirmed for QCD propagators.
- Gluon propagator exhibits complex conjugate poles.
- Analytical functions derived in Minkowski space support confinement.

## Abstract

Analytical functions for the propagators of QCD, including a set of chiral quarks, are derived by a one-loop massive expansion in the Landau gauge, and are studied in Minkowski space, yielding a direct proof of positivity violation and confinement from first principles. Complex conjugated poles are found for the gluon propagator.