Aspects and consequences of a dressed-quark-gluon vertex

Abstract

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

Consequences of fully dressing quark–gluon vertex function with two-point gluon lines

“…The color factors of all contributions included in this improved ladder vertex are correctly generated by the iterations of − 1 2Nc implied by the above. Such a vertex, generated by 2-point gluon lines, is repulsive and as a consequence one finds [9] that the dominant vertex amplitude α 1 (p 2 ) < 1.…”

“…Certainly in the ultraviolet, where a one-loop analysis is reliable [13], α 1 (p 2 ) → 1 from above because of the strong attraction is provided by the 3-gluon coupling term with its dominant and large color factor + Nc 2 . In Refs.…”

“…[8], while in Ref. [9] the important attractive effects of dressing with 3-point gluon functions were added phenomenologically. The 4-point gluon functions have so far been neglected altogether.…”

“…Recent efforts have been made to perform calculations of meson masses beyond ladder-rainbow truncation [8,9,10]. These studies employ a quark-gluon vertex that is dressed by certain classes of diagrams constructed from 2-point gluon functions…”

“…In our previous work with the most general vertex dressing scheme to date [10], we extended the ladder-summed approximation of Refs. [8,9] (Fig. 1a) to self-consistently include the dressing of internal vertices (Figs.…”