Threshold resummation at N$^3$LL accuracy and soft-virtual cross sections at N$^3$LO

We consider QCD radiative corrections to the production of colourless high-mass systems in hadron collisions. We show that the recent computation of the soft-virtual corrections to Higgs boson production at N$^3$LO [1] together with the universality structure of soft-gluon emission can be exploited to extract the general expression of the hard-virtual coefficient that contributes to threshold resummation at N$^3$LL accuracy. The hard-virtual coefficient is directly related to the process-dependent virtual amplitude through a universal (process-independent) factorization formula that we explicitly evaluate up to three-loop order. As an application, we present the explicit expression of the soft-virtual N$^3$LO corrections for the production of an arbitrary colourless system. In the case of the Drell-Yan process, we confirm the recent result of Ref.[2].