  With an eye toward the usual unphysical divergence of hard fixed-order
corrections in predictions for the processes probed in high energy colliding
hadron beam devices as one approaches the soft limit, we present a new approach
to the realization of such corrections, with some emphasis on the LHC and the
future FCC devices. We show that the respective divergence is removed in our
approach. This means that we would render the standard results to be closer to
the observed exclusive distributions. While we stress that the approach has
general applicability, we use the single Z and virtual gamma production and
decay to lepton pairs as our prototypical example. Accordingly, our work opens
another part of the way to rigorous baselines for the determination of the
theoretical precision tags for LHC physics, with an attendant generalization to
the future FCC.
