  We consider the production of prompt-photon pairs at the LHC and we report on
a study of QCD radiative corrections up to the next-to-next-to-leading order
(NNLO). We present a detailed comparison of next-to-leading order (NLO) results
obtained within the standard and smooth cone isolation criteria, by studying
the dependence on the isolation parameters. We highlight the role of different
partonic subprocesses within the two isolation criteria, and we show that they
produce large radiative corrections for both criteria. Smooth cone isolation is
a consistent procedure to compute QCD radiative corrections at NLO and beyond.
If photon isolation is sufficiently tight, we show that the NLO results for the
two isolation procedures are consistent with each other within their
perturbative uncertainties. We then extend our study to NNLO by using smooth
cone isolation. We discuss the impact of the NNLO corrections and the
corresponding perturbative uncertainties for both fiducial cross sections and
distributions, and we comment on the comparison with some LHC data. Throughout
our study we remark the main features that are produced by the kinematical
selection cuts that are applied to the photons. In particular, we examine
soft-gluon singularities that appear in the perturbative computations of the
invariant mass distribution of the photon pair, the transverse-momentum spectra
of the photons, and the fiducial cross section with asymmetric and symmetric
photon transverse-momentum cuts, and we present their behaviour in analytic
form.
