  Within the background field formulation in harmonic superspace for quantum N
= 2 super Yang-Mills theories, the propagators of the matter, gauge and ghost
superfields possess a complicated dependence on the SU(2) harmonic variables
via the background vector multiplet. This dependence is shown to simplify
drastically in the case of an on-shell vector multiplet. For a covariantly
constant background vector multiplet, we exactly compute all the propagators.
In conjunction with the covariant multi-loop scheme developed in
hep-th/0302205, these results provide an efficient (manifestly N = 2
supersymmetric) technical setup for computing multi-loop quantum corrections to
effective actions in N = 2 supersymmetric gauge theories, including the N = 4
super Yang-Mills theory.
