Soft-virtual corrections to Higgs production at N$^3$LO

TL;DR

This paper calculates the soft-virtual corrections at N$^3$LO for Higgs production via gluon fusion, also deriving analogous results for Drell-Yan and scalar pair production, revealing connections through Casimir scaling and transcendentality.

Contribution

It provides the first N$^3$LO soft-virtual corrections for Higgs production and extends the analysis to related processes in QCD and N=4 super Yang-Mills theory, highlighting structural similarities.

Findings

N$^3$LO soft-virtual corrections for Higgs production computed.

Derived soft-virtual terms for Drell-Yan and scalar pair production.

Identified maximal transcendentality weight correspondence in N=4 theory.

Abstract

In this paper, we compute the soft-virtual corrections to Higgs boson production in gluon fusion for infinite top quark mass at next-to-next-to-next-to-leading order in QCD. In addition, we present analogous soft-virtual terms for both Drell-Yan lepton production in QCD and scalar pair production in N = 4 super Yang-Mills theory. The result for Drell-Yan lepton production is derived from the result for Higgs boson production using Casimir scaling arguments together with well-known results available in the literature. For scalar pair production in the N = 4 model, we show by explicit calculation that the result is equal to the part of the Higgs boson soft-virtual term which is of maximal transcendentality weight.