Further evidence for zero crossing on the three gluon vertex

Abstract

The three gluon one particle irreducible function is investigated using lattice QCD simulations over a large region of momentum in the Landau gauge for four dimensional pure Yang-Mills equations and the SU(3) gauge group. The results favor a zero crossing of the gluon form factor for momenta in the range 220 − 260 MeV. This zero crossing is required to happen in order to have a properly defined set of Dyson-Schwinger equations. It is also shown that in the high momentum region the lattice results are compatible with the predictions of renormalisation group improved perturbation theory.The non-perturbative computation of the QCD Green's functions is an important step towards the understanding of the dynamics of strong interactions. The calculation of the Green's functions over the full momentum range is a non-trivial task, independently of taking into account or not the contribution of quarks. The lattice approach to QCD allows for first principles determination of the n-point complete Green functions as for example

QCD propagators and vertices from lattice QCD (in memory of Michael Müller-Preußker)

“…Recently, this zero-crossing has been confirmed by two independent lattice studies [67,68]. In 2014 Michael and I were granted computing time for a study of the 3-gluon and quark-gluon vertex.…”

Schwinger mechanism in linear covariant gauges

“…Let us start with the simplest case, setting As a second model for the three-gluon vertex form factor let us consider the function (ii ) The third and final form factor f 3 is motivated by recent nonperturbative studies of the three-gluon vertex in the Landau gauge [68][69][70][71][72][73][74]. Specifically, in certain kinematic limits characterized by a single momentum scale, the vertex form factors display in the IR the so-called "zero crossing", followed by a negative logarithmic divergence at the origin.…”

An exploratory study of Yang-Mills three-point functions at non-zero temperature

“…From lattice simulations it was known that the vertex dressing shows an enhancement in the nonperturbative regime below the phase transition [30]. However, as there is strong evidence that at zero temperature and in the infinite temperature limit the vertex becomes negative [27,[39][40][41][42][43][44][45], it is not clear from the lattice data if this changes for intermediate temperatures or if the vertex goes down again at even lower momenta. The calculation of its DSE favors the second possibility as a clear zero crossing is observed, although at very low momenta, see Fig.…”