Approximating missing higher-orders in transverse momentum distributions using resummations

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