Analytic structure of QCD propagators in Minkowski space

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.

Some comments on BRST invariance and some new references are added in the new version

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• The analytic structure of the lattice Landau gauge gluon and ghost propagators
• Complex poles and spectral function of Yang-Mills theory
• The gluon propagator in linear covariant $R_{\xi }$ gauges
• Effects of anomalous magnetic moment of quarks on the dilepton production from hot and dense magnetized quark matter using the NJL model
• Reconstructing confined particles with complex singularities
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• Gluon and Ghost Dynamics from Lattice QCD
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• Analytic continuation and physical content of the gluon propagator
• Screened massive expansion of Schwinger-Dyson equations
• QCD phase diagram from the gluon propagator at finite temperature and density
• Effects of a quark chemical potential on the analytic structure of the gluon propagator
• A window on infrared QCD with small expansion parameters
• Extracting a model quark propagator's spectral density
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• Quark mass function in Minkowski space
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• Screened massive expansion of the quark propagator in the Landau gauge
• Reconstructing propagators of confined particles in the presence of complex singularities
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• Extracting topological information from momentum space propagators