  Under certain assumptions and independent of the instantons, we show that the
logarithm expansion of dimensional regularization in quantum field theory needs
a nonperturbative completion to have a renormalization-group flow valid at all
energies. Then, we show that such nonperturbative completion has the analytic
properties of the renormalons, which we find with only a marginal reference to
diagrammatic calculations. We demonstrate that renormalon corrections
necessarily lead to analyzable functions, namely, resurgent transseries. A
detailed analysis of the resurgent properties of the renormalons is provided.
The self-consistency of the theory requires these nonperturbative contributions
to render the running coupling well-defined at any energy, thus with no Landau
pole. We illustrate the point within the case of QED. This way, we explicitly
realize the correspondence between the nonperturbative Landau pole scale and
the renormalons. What is seen as a Landau pole in perturbation theory is cured
by the nonperturbative, resurgent contributions.
