Studies of final-state photon radiation in the process $p\,p\hskip-7pt\hbox{$^{^{(\!-\!)}}$} \rightarrow W^{\pm} \rightarrow \ell^{\pm}\nu$

We study the effects of multiple soft, collinear photon radiation off a final state lepton in the process $p\,p\hskip-7pt\hbox{$^{^{(\!-\!)}}$}\rightarrow W^{\pm} \rightarrow \ell^{\pm}\nu$, as implemented in the MC program WGRAD3. EW virtual effects as well as up to two hard photons radiating off a final-state lepton are also included. These effects are compared with the MC program HORACE which also includes the complete ${\cal O}(\alpha)$ EW radiative corrections to $p\,p\hskip-7pt\hbox{$^{^{(\!-\!)}}$}\rightarrow W^{\pm} \rightarrow \ell^{\pm}\nu$ and multiple photon radiation.