  We study a few basic photon- and lepton-initiated processes at the LHC which
can be computed using the recently developed photon and lepton parton
densities. First, we consider the production of a massive scalar particle
initiated by lepton-antilepton annihilation and photon-photon fusion as
representative examples of searches of exotic particles. Then we study
lepton-lepton scattering, since this Standard-Model process may be observable
at the LHC. We examine these processes at leading and next-to-leading order
and, using the POWHEG method, we match our calculations to parton shower
programs that implement the required lepton or photon initial-states. We assess
the typical size of cross-sections and their uncertainties and discuss the
preferred choices for the factorization scale. These processes can also be
computed starting directly from the lepto-production hadronic tensor, leading
to a result where some collinear-enhanced QED corrections are missing, but all
strong corrections are included. Thus, we are in the unique position to perform
a comparison of results obtained via the factorization approach to a
calculation that does not have strong corrections. This is particularly
relevant in the case of lepton-scattering, that is more abundant at lower
energies where it is affected by larger strong corrections. We thus compute
this process also with the hadronic-tensor method, and compare the results with
those obtained with POWHEG. Finally, for some lepton-lepton scattering
processes, we compare the size of the signal to the main quark-induced
background, which is double Drell-Yan production, and outline a preliminary
search strategy to enhance the signal to background ratio.
