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We present a $q_T$-resummed calculation of diphoton production at orderN$^3$LL$^\prime$+NNLO. To reach the primed level of accuracy we haveimplemented the recently published three-loop $\mathcal{O}(\alpha_s^3)$ virtualcorrections in the $q\bar{q}$ channel and the three-loop transverse momentumdependent beam functions and combined them with the existing infrastructure ofCuTe-MCFM, a code performing resummation at order N$^3$LL. While the primedpredictions are parametrically not more accurate, one typically observes fromlower orders and other processes that they are the dominant effect of the nextorder. We include in both the $q\bar{q}$ and loop-induced $gg$ channel the hardcontributions consistently together at order $\alpha_s^3$ and find that theresummed $q\bar{q}$ channel without matching stabilizes indeed. Due to largematching corrections and large contributions and uncertainties from the $gg$channel, the overall improvements are small though. We furthermore study theeffect of hybrid-cone photon isolation and hard-scale choice on our fullymatched results to describe the ATLAS 8 TeV data and find that the hybrid-coneisolation destroys agreement at small $q_T$.

The Diphoton $q_T$ spectrum at N$^3$LL$^\prime$+NNLO