Abstract
The soft gluon limit of the longitudinal part of the quark-gluon vertex is studied by resorting to non-perturbative approaches to quantum chromodynamics (QCD). Based on a Slavnov–Taylor identity (STI), the longitudinal form factors is expressed in terms of the quark-ghost kernel, the quark self energy and the quark wave function. An exact relation between the non-vanishing longitudinal form factors is derived for the soft gluon limit and explored to understand the behaviour of the vertex. Within a Ball–Chiu vertex, the form factor lambda _1 was analysed using recent lattice simulations for full QCD for the soft gluon limit. The lattice data shows that the gluon propagator resumes the momentum dependence of such component of the vertex. This connection is understood via a fully dressed one-loop Bethe–Salpeter equation. The behaviour of the remaining longitudinal form factors lambda _2(p^2) and lambda _3(p^2) is investigated combining both the information of lattice simulations and the derived relations based on the STI.
Highlights
Introduction and motivationThe quark-gluon vertex is at the heart of all hadron phenomena
Progress in computing the quark-gluon vertex and the fundamental quantum chromodynamics (QCD) kernels has been slow and it revealed quite a difficult problem per se [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. In this perspective, gathering information and combining various non-perturbative approaches can be useful to learn more about this fundamental QCD quantity. Efforts along this line has already been pursued in the Landau gauge in [3], where lattice results for the gluon, ghost and quark propagator have been used together with the Slavnov–Taylor Identity (STI) for the quark-gluon vertex to solve the quark gap equation that relates all these quantities and implicitly defines a coupled set of integral equations to be solved for the unknown form factors of the quark-ghost kernel
We aim to go further on the above delineated approach studying the soft gluon limit of the quark-gluon vertex provided by full QCD lattice simulations for N f = 2 in combination with the information that the STI adds on
Summary
Introduction and motivationThe quark-gluon vertex is at the heart of all hadron phenomena. Progress in computing the quark-gluon vertex and the fundamental QCD kernels has been slow and it revealed quite a difficult problem per se [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. In this perspective, gathering information and combining various non-perturbative approaches can be useful to learn more about this fundamental QCD quantity. A similar approach to the gluon-ghost vertex can be found in [17]
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