Lattice three-gluon vertex in extended kinematics: planar degeneracy

• Published in: arXiv.org 2022-08
• Main Authors: Pinto-Gómez, F, De Soto, F, Ferreira, M N, Papavassiliou, J, Rodríguez-Quintero, J
• Format: Article
• Language: English
• Subjects: Configurations; Coordinates; Form factors; Gluons; Kinematics
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2208.01020

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 Bose-symmetric 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 \((q^2, r^2, p^2)\) share, to a high degree of accuracy, the same form factors, a property that we denominate \emph{planar degeneracy}. We have confirmed the validity of this property through an exhaustive study of the set of configurations satisfying the condition \(q^2 = r^2\), within the range \([0, 5\, \rm GeV]\). Moreover, a preliminary exploration reveals that the planar degeneracy persist in the case of more arbitrary configurations. 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.