  We re-examine the current state of the art for the calculation of
photon-initiated processes at the LHC, as formulated in terms of a photon PDF
in the proton that may be determined rather precisely from the known proton
structure functions. We in particular demonstrate that a by construction more
precise calculation is provided by a direct application of the structure
function approach, best known from the case of Higgs Boson production via
vector boson fusion. This avoids any artificial scale variation uncertainties,
which can otherwise be rather significant for processes calculated within the
standard approach thus far. To understand the source of these, we present a
detailed comparison of the structure function approach and its relation to the
photon PDF. We then provide precise predictions for the photon-initiated
contribution to lepton pair production at the LHC, including the lepton pair
transverse momentum distribution. Thus, by a direct application of the
structure function formalism we show how the contribution from initial-state
photons at the LHC may for the first time be included with high precision in a
universal and straightforward way, providing a high definition picture of the
photon content of the proton.
