Nonperturbative study of the four gluon vertex

Abstract

In this paper we study the nonperturbative structure of the SU(3) four-gluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric. We employ an approximation scheme where "one-loop" diagrams are computed using fully dressed gluon and ghost propagators, and tree-level vertices. When a suitable kinematical configuration depending on a single momentum scale $p$ is chosen, only two structures emerge: the tree-level four-gluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zero-crossing) in the deep infrared, and finally diverges logarithmically. The origin of this characteristic behavior is proven to be entirely due to the masslessness of the ghost propagators forming the corresponding ghost-loop diagram, in close analogy to a similar effect established for the three-gluon vertex. However, in the case at hand, and under the approximations employed, this particular divergence does not affect the form factor proportional to the tree-level tensor, which remains finite in the entire range of momenta, and deviates moderately from its naive tree-level value. It turns out that the kinematic configuration chosen is ideal for carrying out lattice simulations, because it eliminates from the connected Green's function all one-particle reducible contributions, projecting out the genuine one-particle irreducible vertex. Motivated by this possibility, we discuss in detail how a hypothetical lattice measurement of this quantity would compare to the results presented here, and the potential interference from an additional tensorial structure, allowed by Bose symmetry, but not encountered within our scheme.

36 pages, 8 figures; additional references added

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Cited by in corpus (9)

• Chiral symmetry breaking in continuum QCD
• A Dyson-Schwinger study of the four-gluon vertex
• Further Evidence For Zero Crossing On The Three Gluon Vertex
• On non-primitively divergent vertices of Yang-Mills theory
• On bounds and boundary conditions in the continuum Landau gauge
• Symmetric point 4-point functions at one loop in QCD
• Gluon mass scale through the Schwinger mechanism
• Four-gluon vertex from the Curci-Ferrari model at one-loop order
• Gluon correlation functions from lattice quantum chromodynamics