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We present a more reliable approach to approximate the unknownnext-to-next-to-next-to-leading order (N3LO) transverse momentum distributionof colourless final states, namely the Higgs boson produced via gluon fusionand the lepton pair produced via Drell--Yan (DY) mechanism. The approximationwe construct relies on the combination of various resummation formalisms --namely threshold, small-pt and high energy resummations -- by exploiting thesingularity structure of the large logarithms in Mellin space. We show that forthe case of Higgs boson production, the approximate N3LO transverse momentumdistribution amounts to a correction of a few percent with respect to the NNLOresult with a reduction in the scale dependence.

Approximating missing higher-orders in transverse momentum distributions using resummations