Goldstone bosons and fermions in QCD

Abstract

We consider the version of QCD in Euclidean Landau gauge in which the restriction to the Gribov region is implemented by a local, renormalizable action. This action depends on the Gribov parameter $\gamma$, with dimensions of (mass)${}^4$, whose value is fixed in terms of ${\Lambda }_{QCD}$, by the gap equation, known as the horizon condition, ${\p Γ\over \p γ} = 0$, where $\Gamma$ is the quantum effective action. The restriction to the Gribov region suppresses gluons in the infrared, which nicely explains why gluons are not in the physical spectrum, but this only makes makes more mysterious the origin of the long-range force between quarks. In the present article we exhibit the symmetries of $\Gamma$, and show that the solution to the gap equation, which defines the classical vacuum, spontaneously breaks some of the symmetries $\Gamma$. This implies the existence of massless Goldstone bosons and fermions that do not appear in the physical spectrum. Some of the Goldstone bosons may be exchanged between quarks, and are candidates for a long-range confining force. As an exact result we also find that in the infrared limit the gluon propagator vanishes like $k^2$.

22 pages, typos corrected, improved comparison with lattice data

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• Infrared analysis of Dyson-Schwinger equations taking into account the Gribov horizon in Landau gauge
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Cited by in corpus (18)

• Modeling the Gluon Propagator in Landau Gauge: Lattice Estimates of Pole Masses and Dimension-Two Condensates
• On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory
• A remark on the BRST symmetry in the Gribov-Zwanziger theory
• Alternative refined Gribov-Zwanziger Lagrangian
• Properties of the Faddeev-Popov operator in the Landau gauge, matter confinement and soft BRST breaking
• BRST-Symmetry Breaking and Bose-Ghost Propagator in Lattice Minimal Landau Gauge
• BRST Cohomology and Physical Space of the GZ Model
• Features of ghost-gluon and ghost-quark bound states related to BRST quartets
• Renormalizability of the linearly broken formulation of the BRST symmetry in presence of the Gribov horizon in Landau gauge Euclidean Yang-Mills theories
• On the reanimation of a local BRST invariance in the (Refined) Gribov-Zwanziger formalism
• Loop calculations in the three dimensional Gribov-Zwanziger Lagrangian
• Low momentum propagators at two loops in gluon mass model
• Gribov as a Phase Transition
• Study of the all orders multiplicative renormalizability of a local confining quark action in the Landau gauge
• Natural solution in the refined Gribov-Zwanziger theory
• The quenched SU(2) adjoint scalar propagator in minimal Landau gauge
• The quenched SU(2) scalar-gluon vertex in minimal Landau gauge
• Numerical Evaluation of the Bose-Ghost Propagator in Minimal Landau Gauge on the Lattice