  We discuss the production of photon pairs in gluon-gluon scattering in the
context of the position-space resummation formalism at small transverse
momentum. We derive the remaining unknown coefficients that arise at
$O(\alpha_S)$, as well as the remaining $O(\alpha_S^2)$ coefficient that occurs
in the Sudakov factor. We comment on the impact of these coefficients on the
normalization and shape of the resummed transverse momentum distribution of
photon pairs, which comprise an important background to Higgs boson production
at the LHC.
