Higgs boson production at the LHC using the q_T subtraction formalism at N³LO QCD

We consider higher-order QCD corrections to Higgs boson production through gluon-gluon fusion in the large top quark mass limit in hadron collisions. We extend the transverse-momentum (q_T ) subtraction method to next-to-next-to-next-to-leading order (N³LO) and combine it with the NNLO Higgs-plus-jet calculation to numerically compute differential infrared-safe observables at N³LO for Higgs boson production in gluon fusion. To cancel the infrared divergences, we exploit the universal behaviour of the associated q_T distributions in the small-q_T region. We document all the necessary ingredients of the transverse-momentum subtraction method up to N³LO. The missing third-order collinear functions, which contribute only at q_T = 0, are approximated using a prescription which uses the known result for the total Higgs boson cross section at this order. As a first application of the third-order q_T subtraction method, we present the N³LO rapidity distribution of the Higgs boson at the LHC.