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. This attraction affects the uniformity with which solutions of truncated equations converge pointwise to solutions of the complete gap and vertex equations. For current-quark masses less than the scale set by dynamical chiral symmetry breaking, the dependence of the dressed-quark-gluon vertex on the current-quark mass is weak. 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 \Upsilon(1S) to be above 9.4 GeV. The absence of colour-antitriplet diquarks from the strong interaction spectrum is contingent upon the net amount of attraction in the octet projected quark-antiquark scattering kernel. There is a window within which diquarks appear. The amount of attraction suggested by lattice results is outside this domain.Comment: 22 pages, 12 figure

We survey contemporary studies of hadrons and strongly interacting quarks using QCD's DysonSchwinger equations, addressing: aspects of confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small-to large-Q 2 ; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.

The in-pseudoscalar-meson condensate can be represented through the pseudoscalar-meson's scalar form factor at zero momentum transfer. With the aid of a mass formula for scalar mesons, revealed herein, the analogue is shown to be true for in-scalar-meson condensates. The concept is readily extended to all hadrons so that, via the zero momentum transfer value of any hadron's scalar form factor, one can readily extract the value for a quark condensate in that hadron which is a measure of dynamical chiral symmetry breaking.PACS numbers: 12.38. Aw, 11.30.Rd, 11.15.Tk, 24.85.+p Dynamical chiral symmetry breaking (DCSB) and its connection with the generation of hadron masses was first considered in Ref. [1]. The effect was represented as a vacuum phenomenon. Two essentially inequivalent classes of ground-state were identified in the mean-field treatment of a meson-nucleon field theory: symmetry preserving (Wigner phase); and symmetry breaking (Nambu phase). Notably, within the symmetry breaking class, each of an uncountable infinity of distinct configurations is related to every other by a chiral rotation. This is arguably the origin of the concept that strongly-interacting quantum field theories possess a nontrivial vacuum.With the introduction of the parton model for the description of deep inelastic scattering (DIS), this notion was challenged via an argument [2] that DCSB can be realised as an intrinsic property of hadrons, instead of via a nontrivial vacuum exterior to the observable degrees of freedom. This perspective is tenable because the essential ingredient required for dynamical symmetry breaking in a composite system is the existence of a divergent number of constituents and DIS provided evidence for the existence within every hadron of a divergent sea of low-momentum partons. This view has, however, received scant attention. On the contrary, the introduction of QCD sum rules [3] as a method to estimate nonperturbative strong-interaction matrix elements entrenched the belief that the QCD vacuum is characterised by numerous, independent, non-vanishing condensates.Notwithstanding the prevalence of this belief, it does lead to problems; e.g., entailing a cosmological constant that is 10 46 -times greater than that which is observed [4,5]. This unwelcome consequence is partly responsible for reconsideration of the possibility that the so-called vacuum condensates are in fact an intrinsic property of hadrons. Namely, in a confining theory, condensates are not constant, physical mass-scales that fill all spacetime; instead, they are merely mass-dimensioned parameters that serve a practical purpose in some theoretical truncation schemes but otherwise do not have an existence independent of hadrons [5][6][7][8]. Regarding the quark condensate, this perspective was recently elucidated for light pseudoscalar mesons [7]. Herein we propose an extension of the concept to all hadrons.We start with Ref.[9], which presents the relationwhere m π is the pion's mass and H χsb is that part of the hadronic Hamiltonian dens...