Analytic structure of QCD propagators in Minkowski space

Understand

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.