Analytic properties of the vertex function in gauge theories. I

Dynamical chiral symmetry breaking and the fermion–gauge-boson vertex

“…(18), (27). We now demand a little more; namely, that our Ansatz produce a Landau-gauge value of α c which agrees with that produced by the Ball-Chiu Ansatz [12] and minimises ∂α c /∂ξ on ξ ∈ [0, 10].…”

“…Dotted curve -For comparison with the dashed and dot-dashed curves, the distribution obtained with any one of the Ansätze in Refs. [12,29,34]. tively massless fermion: it is impossible for a truly massless fermion to possess a measurable anomalous magnetic moment [24].…”

“…This was actually realised early on, with studies of the fermion-gauge-boson vertex in Abelian gauge theories [12] that have inspired numerous ensuing analyses. The importance of this dressing to the reliable computation of hadron physics observables was exposed in Refs.…”

“…In this connection, perhaps, it is clearest that such considerations are not sufficient to fully determine the vertex. As an example, the Ball-Chiu vertex [12] augmented by the Curtis-Pennington extension [29] is unable to explain the mass splitting between the ρ-and a 1 -mesons, parity partners in the spectrum. The minimum required to understand this is inclusion of a dressed-quark anomalous chromomagnetic moment [26], the presence and strength of which are driven by DCSB [24,36,37] and confirmed by numerical simulations of lattice-QCD [38].…”

“…The best are informed by analyses that emphasise the constraints of quantum field theory, amongst which are that the vertex should [12,[29][30][31][32][33][34][35]: be free of kinematic singularities; ensure gauge covariance and invariance; and assist in providing for the multiplicative renormalisability of solutions to the DSEs within which it appears. Ansätze that are largely consistent with these constraints have also been used to represent the dressed quarkgluon vertex.…”