The complete tensor structure of the quark-gluon vertex in Landau gauge is determined at two kinematical points ('asymmetric' and 'symmetric') from lattice QCD in the quenched approximation. The simulations are carried out at β = 6.0, using a meanfield improved Sheikholeslami-Wohlert fermion action, with two quark masses ∼ 60 and 115 MeV. We find substantial deviations from the abelian form at the asymmetric point. The mass dependence is found to be negligible. At the symmetric point, the form factor related to the chromomagnetic moment is determined and found to contribute significantly to the infrared interaction strength.

The one loop vertex in QED is calculated in arbitrary covariant gauges as an analytic function of its momenta. The vertex is decomposed into a longitudinal part, that is fully responsible for ensuring the Ward and Ward-Takahashi identities are satisfied, and a transverse part. The transverse part is decomposed into 8 independent components each being separately free of kinematic singularities in any covariant gauge in a basis that modifies that proposed by Ball and Chiu. Analytic expressions for all 11 components of the O(α) vertex are given explicitly in terms of elementary functions and one Spence function. These results greatly simplify in particular kinematic regimes.

The quark-gluon vertex in Landau gauge is studied in the quenched approximation using the Sheikholeslami-Wohlert (SW) fermion action with mean-field improvement coefficients in the action and for the quark fields. We see that the form factor that includes the running coupling is substantially enhanced in the infrared, over and above the enhancement arising from the infrared suppression of the quark propagator alone. We define two different momentum subtraction renormalisation schemes -MOM (asymmetric) and MOM (symmetric) -and determine the running coupling in both schemes. We find Λ−180 ± 55 ± 30 MeV from the asymmetric scheme. This is somewhat higher than other determinations of this quantity, but the uncertainties -both statistical and systematic -are large. In the symmetric scheme, statistical noise prevents us from obtaining a meaningful estimate for Λ MS .

Dong, Munczek and Roberts [1] have shown how the full 3-point vertex that appears in the Schwinger-Dyson equation for the fermion propagator can be expressed in terms of a constrained function W 1 in massless quenched QED. However, this analysis involved two key assumptions : that the fermion anomalous dimension vanishes in the Landau gauge and that the transverse vertex has a simplified dependence on momenta. Here we remove these assumptions and find the general form for a new constrained function U 1 that ensures the multiplicative renormalizability of the fermion propagator non-perturbatively.We then study the restriction imposed on U 1 by recent perturbative calculations of the vertex and compute its leading logarithmic expansion. Since U 1 should reduce to this expansion in the weak coupling regime, this should serve as a guide to its non-perturbative construction. We comment on the perturbative realization of the constraints on U 1 .