Nonperturbative results on the quark-gluon vertex

Abstract

We present analytical and numerical results for the Dirac form factor of the quark-gluon vertex in the quark symmetric limit, where the incoming and outgoing quark momenta have the same magnitude but opposite sign. To accomplish this, we compute the relevant components of the quark-ghost scattering kernel at the one-loop dressed approximation, using as basic ingredients the full quark propagator, obtained as a solution of the quark gap equation, and the gluon propagator and ghost dressing function, obtained from large-volume lattice simulations.

Phase structure of three and four flavor QCD

“…The ghost dressing function at finite temperature is known from lattice calculations [10] and exhibits an (almost) temperature independent enhancement at infrared momenta. Approximate treatments of the ghostquark scattering kernel at zero temperature show a similar enhancement in the infrared [39,40]. In the absence of more information we approximate the combined effects of the ghost dressing function and the scattering kernel by a function Γ(k 2 ), Eq.…”

“…where G(k 2 ) denotes the dressing function of the ghost propagator and H(q, p) a ghost-quark scattering kernel with "conjugate" H. The momenta of the two quarks are given by p, q and k = p−q is the corresponding gluon momentum. Since the nonperturbative behavior of H(p, q) and its conjugate is currently unknown, there is no exact solution of this identity available (see, however, [39,40] for recent progress in this direction). A valid strategy to work along this identity at least approximately is to start with the corresponding Abelian identity, where G = H = H = 1.…”

On the quark-gluon vertex and quark-ghost kernel: combining lattice simulations with Dyson-Schwinger equations

“…We mention that, with respect to the approximation just discussed, various kinematic configurations of H(p 1 , p 2 , p 3 ) have also been investigated [63,64]. Of course, the approach to the quark-ghost kernel can be amended in various ways.…”

“…Note that this is not the usual value, α s (4.3 GeV) = 0.22, but our choice for the strong coupling constant will allow for a direct comparison with the results of Ref. [62,63]. In what concerns X0 , a different definition for α(µ) requires, accordingly, the rescaling of X0 , i.e.…”

“…Based on perturbative one-loop calculations [61], Aguilar and Papavassiliou [62,63] calculated the leading nonperturbative corrections to the longitudinal quark-gluon vertex (the "one-loop dressed" approximation to X 0 , see Fig. 5) using a particular kinematic configuration.…”