  With an eye toward the precision physics of the LHC, such as the recent
measurement of $M_W$ by the ATLAS Collaboration, we present here systematic
studies relevant to the assessment of the expected size of multiple photon
radiative effects in heavy gauge boson production with decay to charged lepton
pairs. We use the new version 4.22 of ${\cal KK}$MC-hh so that we have CEEX EW
exact ${\cal O}(\alpha^2 L)$ corrections in a hadronic MC and control over the
corresponding EW initial-final interference (IFI) effects as well. In this way,
we illustrate the interplay between cuts of the type used in the measurement of
$M_W$ at the LHC and the sizes of the expected responses of the attendant
higher order corrections. We find that there are per cent to per mille level
effects in the initial-state radiation, fractional per mille level effects in
the IFI and per mille level effects in the over-all ${\cal O}(\alpha^2 L)$
corrections that any treatment of EW corrections at the per mille level should
consider. Our results have direct applicability to current LHC experimental
data analyses.
