Lattice three-gluon vertex in extended kinematics: Planar degeneracy

We present novel results for the three-gluon vertex, obtained from an extensive quenched lattice simulation in the Landau gauge. The simulation evaluates the transversely projected vertex, spanned on a special tensorial basis, whose form factors are naturally parametrized in terms of individually Bosesymmetric variables. Quite interestingly, when evaluated in these kinematics, the corresponding form factors depend almost exclusively on a single kinematic variable, formed by the sum of the squares of the three incoming four-momenta, q, r, and p. Thus, all configurations lying on a given plane in the coordinate system (q2, r2, p2) share, to a high degree of accuracy, the same form factors, a property that we denominate planar degeneracy. We have confirmed the validity of this property through an exhaustive study of the set of configurations satisfying the condition q2 = r2, within the range [0, 5 GeV]. This drastic simplification allows for a remarkably compact description of the main bulk of the data, which is particularly suitable for future numerical applications. A semi-perturbative analysis reproduces the lattice findings rather accurately, once the inclusion of a gluon mass has cured all spurious divergences. (c) 2023 Published by Elsevier B.V. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.

Automated summary

We present new results for the three-gluon vertex obtained from a large-scale lattice simulation in the Landau gauge. The simulation evaluates the transversely projected vertex using a special tensorial basis, with form factors parametrized in terms of Bose-symmetric variables. Interestingly, the form factors primarily depend on a single kinematic variable, the sum of the squares of the three incoming four-momenta. This property, known as planar degeneracy, allows for a simplified and compact description of the data, suitable for future numerical applications. Confirming this property through a detailed study of specific configurations, we find that a semi-perturbative analysis accurately reproduces the lattice findings when a gluon mass is included to eliminate spurious divergences. (c) 2023 Published by Elsevier B.V. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.