Higgs boson production at the LHC using the qT 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 ((NLO)-L-3) and combine it with the NNLO Higgs-plus-jet calculation to numerically compute differential infrared-safe observables at (NLO)-L-3 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 (NLO)-L-3. 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 (NLO)-L-3 rapidity distribution of the Higgs boson at the LHC.