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The three-gluon vertex in Landau gauge

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abstract

We present the first Dyson-Schwinger calculation of the three-gluon vertex in Landau-gauge QCD in which its full covariant structure is back-coupled self-consistently. We truncate a Bose-symmetrized version of the DSE at the level of one-loop diagrams, model the four-gluon vertex, and neglect terms that contain non-primitively divergent n-point functions; the ghost-gluon vertex is taken bare to good approximation. Fit functions for the ghost and gluon propagators that interpolate between scaling and decoupling are presented. In all aspects of our study Bose symmetry is manifest, from the truncation to the basis decomposition and to the momentum invariants. We explore the uniform and soft-collinear infrared limits and obtain the expected infrared exponents. The presence of a zero crossing in the tree-level component of the vertex is confirmed for both scaling- and decoupling-type scenarios. The zero crossing appears at a scale ~1 GeV; however, its location might be sensitive to the four-gluon vertex and missing components in the DSE.

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hep-ph 1

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2026 1

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FunKit: A computer algebra toolkit for functional approaches

hep-ph · 2026-05-27 · unverdicted · novelty 6.0

FunKit is a computer algebra toolkit that automates derivation of functional equations such as Dyson-Schwinger and functional RG from arbitrary master equations, with tracing via FORM and export to numerical code.

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  • FunKit: A computer algebra toolkit for functional approaches hep-ph · 2026-05-27 · unverdicted · none · ref 38 · internal anchor

    FunKit is a computer algebra toolkit that automates derivation of functional equations such as Dyson-Schwinger and functional RG from arbitrary master equations, with tracing via FORM and export to numerical code.