Higgs boson production at the LHC using the $q_T$ subtraction formalism at N$^3$LO QCD

Leandro Cieri; Xuan Chen; Thomas Gehrmann; E. W. N. Glover; Alexander Huss

Paper

Higgs boson production at the LHC using the $q_T$ subtraction formalism at N$^3$LO QCD

Abstract

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 (

) subtraction method to next-to-next-to-next-to-leading order (N

LO) and combine it with the NNLO Higgs-plus-jet calculation to numerically compute differential infrared-safe observables at N

LO for Higgs boson production in gluon fusion. To cancel the infrared divergences, we exploit the universal behaviour of the associated

distributions in the small-

region. We document all the necessary ingredients of the transverse-momentum subtraction method up to N

LO. The missing third order collinear functions, which contribute only at

=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

subtraction method, we present the N

LO rapidity distribution of the Higgs boson at the LHC.