{
  "id": "2208.01020",
  "version": "v1",
  "published": "2022-08-01T17:52:35.000Z",
  "updated": "2022-08-01T17:52:35.000Z",
  "title": "Lattice three-gluon vertex in extended kinematics: planar degeneracy",
  "authors": [
    "F. Pinto-Gómez",
    "F. De Soto",
    "M. N. Ferreira",
    "J. Papavassiliou",
    "J. Rodríguez-Quintero"
  ],
  "comment": "8 pages, 7 figures",
  "categories": [
    "hep-ph",
    "hep-lat"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-01T17:52:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lattice three-gluon vertex",
      "extended kinematics",
      "planar degeneracy persist",
      "configurations",
      "special tensorial basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}