Quenched lattice-QCD data on the dressed-quark Schwinger
function can be correlated with dressed-gluon data via a rainbow
gap equation so long as that equation's kernel possesses
enhancement at infrared momenta above that exhibited by the gluon
alone. The required enhancement can be ascribed to a dressing of
the quark-gluon vertex. The solutions of the rainbow gap equation
exhibit dynamical chiral symmetry breaking and are consistent with
confinement. The gap equation and related, symmetry-preserving,
ladder Bethe-Salpeter equation yield estimates for chiral and
physical pion observables that suggest these quantities are
materially underestimated in the quenched theory: |〈q̄q〉| by a factor of two and fπ by 30%.
Features of
the dressed-quark-gluon vertex and their role in the gap and
Bethe-Salpeter equations are explored. It is argued that quenched
lattice data indicate the existence of net attraction in the
colour-octet projection of the quark-antiquark scattering kernel.
The study employs a vertex model whose diagrammatic content is
explicitly enumerable. That enables the systematic construction of
a vertex-consistent Bethe-Salpeter kernel and thereby an
exploration of the consequences for the strong interaction spectrum
of attraction in the colour-octet channel. With rising
current-quark mass the rainbow-ladder truncation is shown to
provide an increasingly accurate estimate of a bound state's mass.
Moreover, the calculated splitting between vector and pseudoscalar
meson masses vanishes as the current-quark mass increases, which
argues for the mass of the pseudoscalar partner of the Υ(1S)
to be above 9.4 GeV.
A model for the dressed quark-gluon vertex,
at zero gluon momentum, is formed from a nonperturbative extension
of the two Feynman diagrams that contribute at 1-loop in
perturbation theory. The required input is an existing
ladder-rainbow model Bethe-Salpeter kernel from an approach based
on the Dyson-Schwinger equations; no new parameters are introduced.
The model includes an Ansatz for the triple-gluon vertex. Two of
the three vertex amplitudes from the model provide a point-wise
description of the recent quenched lattice-QCD data. An estimate of
the effects of quenching is made. To be phenomenologically tested
this model has to be extended to non-zero gluon momentum. Various
options for such an extension are under consideration.