The non-perturbative three-point vertex in massless quenched QED and perturbation theory constraints

Dong, Munczek and Roberts 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 $U_1$.