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NNLO QCD corrections to $pp \to γ^* γ^*$ in the large $N_F$ limit

We compute the NNLO QCD corrections for the hadroproduction of a pair of off-shell photons in the limit of a large number of quark flavors. We perform a reduction of the two-loop amplitude to master integrals and calculate the latter analytically as a Laurent series in the dimensional regulator using modern integration methods. Real radiation corrections are evaluated numerically with a direct subtraction of infrared limits which we cast in a simple factorized form. The results presented here constitute a gauge invariant part of the full NNLO corrections but are not necessarily dominant. We view this calculation as a step towards a complete computation. Our partial corrections to the total cross-section are about $1\%-3\%$ and vary with the virtuality of the two off-shell photons.