Transverse-momentum resummation for photon pair production at NNLL+NLO

We are interested in the transverse-momentum ($q_T$) distribution of a diphoton pair produced in hadron collisions. We resum the logarithmically-enhanced perturbative QCD contributions at small values of $q_T$ up to next-to-next-to-leading logarithmic accuracy. We consistently combine resummation with the known next-to-leading order perturbative result at intermediate and large values of $q_T$ . We include all perturbative terms up to order $\alpha_S^2$ in our computation which, after integration over $q_T$ , reproduces the known next-to-next-to-leading order result for the diphoton pair production total cross section. A comparison with LHC data is presented. We estimate the perturbative accuracy of the theoretical calculation by performing the corresponding variation of scales. We anticipate that the effect of the transverse momentum resummation is not only to recover the predictivity of the calculation at small $q_T$ , but also to improve substantially the agreement with the experimental data.