Analytic structure of QCD propagators in Minkowski space

TL;DR

This paper derives analytic QCD propagators in Minkowski space using a one-loop massive expansion, demonstrating positivity violation and confinement, and unifying chiral symmetry breaking with gluon mass generation.

Contribution

It introduces a novel one-loop massive expansion in Landau gauge that provides analytic propagators consistent with lattice data and confinement principles.

Findings

Spectral functions show positivity violation.

Gluon propagator has complex conjugate poles.

Universal scaling matches lattice data.

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, deep in the infrared. By analytic continuation, the spectral functions are studied in Minkowski space, yielding a direct proof of positivity violation and confinement from first principles.The dynamical breaking of chiral symmetry is described on the same footing of gluon mass generation, providing a unified picture. While dealing with the exact Lagrangian, the expansion is based on massive free-particle propagators, is safe in the infrared and is equivalent to the standard perturbation theory in the UV. By dimensional regularization, all diverging mass terms cancel exactly without including mass counterterms that would spoil the gauge and chiral symmetry of the Lagrangian. Universal scaling properties are predicted for the inverse dressing functions and shown to be satisfied by the lattice data. Complex conjugated poles are found for the gluon propagator, in agreement with the i-particle scenario.