Small parameters in infrared quantum chromodynamics

Abstract

We study the long-distance properties of quantum chromodynamics in an expansion in powers of the three-gluon, four-gluon, and ghost-gluon couplings, but without expanding in the quark-gluon coupling. This is motivated by two observations. First, the gauge sector is well-described by perturbation theory in the context of a phenomenological model with a massive gluon. Second, the quark-gluon coupling is significantly larger than those in the gauge sector at large distances. In order to resum the contributions of the remaining infinite set of QED-like diagrams, we further expand the theory in $1/N_c$, where $N_c$ is the number of colors. At leading order, this double expansion leads to the well-known rainbow approximation for the quark propagator. We take advantage of the systematic expansion to get a renormalization-group improvement of the rainbow resummation. A simple numerical solution of the resulting coupled set of equations reproduces the phenomenology of the spontaneous chiral symmetry breaking: for sufficiently large quark-gluon coupling constant, the constituent quark mass saturates when its valence mass approaches zero. We find very good agreement with lattice data for the scalar part of the propagator and explain why the vectorial part is poorly reproduced.

15 pages, 11 figures

References in corpus (19)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Baryons as relativistic three-quark bound states
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Infrared propagators of Yang-Mills theory from perturbation theory
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $⟨A^2⟩$ in the Landau gauge
• Chiral symmetry breaking with lattice propagators
• On the zero crossing of the three-gluon vertex
• Perspective on rainbow-ladder truncation
• Hadronic unquenching effects in the quark propagator
• On the massive gluon propagator, the PT-BFM scheme and the low-momentum behaviour of decoupling and scaling DSE solutions
• Infrared analysis of propagators and vertices of Yang--Mills theory in Landau and Coulomb gauge
• Refining the detection of the zero crossing for the symmetric and asymmetric three-gluon vertices
• A new method for determining the quark-gluon vertex
• Power-law running of the effective gluon mass
• How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators?
• Deconfinement transition in SU(2) Yang-Mills theory: A two-loop study

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