Effect of the Quark-Gluon Vertex on Dynamical Chiral Symmetry Breaking

Abstract

In this work we investigate how the details of the quark-gluon interaction vertex affect the quantitative description of chiral symmetry breaking and dynamical mass generation through the gap equation. We employ the Maris-Tandy (MT) [1] and Qin-Chang (QC) [2] models for the gluon propagator and the effective strong running coupling. The gap equation is solved by employing several vertex Ansätze which have been constructed in order to implement some of the key aspects of a gauge field theory such as gauge invariance and multiplicative renormalizability. We find that within a small variation of MT and QC model parameters, all truncations point towards the same quantitative pattern of chiral symmetry breaking, the running quark mass function, ensuring the robustness of this approach.

Quark-gluon vertex from Nf=2 lattice QCD

“…It is thus natural that attention has in recent years turned to the structure of the 3-and 4-point vertices of QCD, including the quark-gluon vertex. There have been a number of recent studies within the DSE framework exploring the full structure of this vertex [20][21][22][23][24][25][26][27][28][29][30][31][32] and the potential impact of the various non-leading form factors on chiral symmetry breaking and hadron phenomenology [23,33,34]. Two critical ingredients in determining the full structure of the vertex have been the Slavnov-Taylor identity, which relates the longitudinal part of the vertex to the quark propagator, and the transverse Ward-Takahashi identities [35][36][37][38] which constrain the purely transverse part of the vertex.…”

The soft-gluon limit and the infrared enhancement of the quark-gluon vertex

“…At a qualitative level, the various approaches seem to produce compatible results. See also [14,15,16,17] for other recent studies of the quark-gluon vertex.…”

Interplay of dynamical and explicit chiral symmetry breaking effects on a quark

“…In continuum approaches to Quantum Chromodynamics (QCD), such as the Dyson-Schwinger equation (DSE) for the quark, the strength of DCSB is governed by two ingredients in its integral kernel: the gluon dressing function [15][16][17] and the dressed quark-gluon vertex [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Failure to produce sufficient support result in a Wigner solution of the gap equation and thus any symmetrypreserving truncation must compensate for lacking interaction strength [37].…”