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.
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