Systematic Studies of Exact ${cal O}(alpha^2L)$ CEEX EW Corrections in a Hadronic MC for Precision $Z/gamma^*$ Physics at LHC Energies

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.