A window on infrared QCD with small expansion parameters

Lattice simulations of the QCD correlation functions in the Landau gauge have established two remarkable facts. First, the coupling constant in the gauge sector-defined, e.g., in the Taylor scheme-remains finite and moderate at all scales, suggesting that some kind of perturbative description should be valid down to infrared momenta. Second, the gluon propagator reaches a finite nonzero value at vanishing momentum, corresponding to a gluon screening mass. We review recent studies which aim at describing the long-distance properties of Landau gauge QCD by means of the perturbative Curci-Ferrari model. The latter is the simplest deformation of the Faddeev-Popov Lagrangian in the Landau gauge that includes a gluon screening mass at tree-level. There are, by now, strong evidences that this approach successfully describes many aspects of the infrared QCD dynamics. In particular, several correlation functions were computed at one- and two-loop orders and compared with ab-initio lattice simulations. The typical error is of the order of ten percent for a one-loop calculation and drops to few percents at two loops. We review such calculations in the quenched approximation as well as in the presence of dynamical quarks. In the latter case, the spontaneous breaking of the chiral symmetry requires to go beyond a coupling expansion but can still be described in a controlled approximation scheme in terms of small parameters. We also review applications of the approach to nonzero temperature and chemical potential.

Automated summary

Lattice simulations in the Landau gauge have shown that the coupling constant in the QCD sector remains finite and moderate at all scales, while the gluon propagator reaches a finite nonzero value at vanishing momentum. Studies have successfully described infrared QCD dynamics using the perturbative Curci-Ferrari model, with calculations showing good agreement with lattice simulations. The approach has also been applied to scenarios with dynamical quarks, showing controlled approximation schemes can account for chiral symmetry breaking. Applications to nonzero temperature and chemical potential have also been explored.