  Precision measurements of diphoton distributions at the LHC display some
tension with theory predictions, obtained at next-to-next-to-leading order
(NNLO) in QCD. We revisit the theoretical uncertainties arising from the
approximation of the experimental photon isolation by smooth-cone isolation,
and from the choice of functional form for the renormalisation and
factorisation scales. We find that the resulting variations are substantial
overall, and enhanced in certain regions. We discuss the infrared sensitivity
at the cone boundaries in cone-based isolation in related distributions.
Finally, we compare predictions made with alternative choices of dynamical
scale and isolation prescriptions to experimental data from ATLAS at 8 TeV,
observing improved agreement. This contrasts with previous results,
highlighting that scale choice and isolation prescription are potential sources
of theoretical uncertainty that were previously underestimated.
