Landau gauge Yang-Mills correlation functions

Abstract

We investigate Landau gauge SU (3) Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalisation group. Particular focus is put on the dynamical creation of the gluon mass gap at non-perturbative momenta and the consistent treatment of quadratic divergences. The non-perturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated selfconsistently with the classical action as only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.

Baryons as relativistic three-quark bound states

“…Using ansätze for the three-and four-point vertices of the theory, first self-consistent solutions for the gluon and quark propagator have been obtained in [222]. Modern truncations also include numerical solutions for the three-and four-point functions [209,215,216] whose results compare well with those from lattice QCD [199,[223][224][225][226][227]. The typical behaviour of the quark mass function for different quark flavours is shown in the right panel of Fig.…”

“…Due to these differences, combinations of DSEs and FRGEs can be used to study, control and thus minimize artefacts from the necessary truncations. This strategy has been successfully employed in the past and FRGEs and DSEs together have been essential in the determination of QCD's Green functions, see [203,204,[213][214][215][216] and references therein. With respect to the main topic of this review, however, although FRG studies have begun to make progress in the meson sector they have not yet contributed to our understanding of the spectrum and properties of baryons.…”

“…Due to its much more complicated structure, the nonperturbative three-gluon vertex has only been begun to be explored in numerical simulations in recent years, see e.g. [205,206,209,215,216,226,237,238] and references therein. In the numerical calculations it turned out that the tensor structure of the bare vertex, [209] and compared to lattice calculations [199,228].…”

“…The gluon propagator has been studied intensely in the past both on the lattice, with DSEs and the FRG due to its supposed connection with confinement of the non-Abelian gauge theory, see e.g. [200,216,227,[229][230][231][232][233][234][235][236] and references therein. Due to its much more complicated structure, the nonperturbative three-gluon vertex has only been begun to be explored in numerical simulations in recent years, see e.g.…”

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

“…The most pressing one is surely the question of how reliable this method can be on a quantitative level. Recent results indicate that, at least in the vacuum, a reasonable accuracy can be achieved [2][3][4]. However, to realize corresponding truncations requires to solve large sets of functional equations.…”