Scale dependence and collinear subtraction terms for Higgs production in gluon fusion at N3LO

TL;DR

This paper calculates the complete scale dependence of the Higgs production cross section at N3LO in gluon fusion, providing detailed convolution results and analyzing the expected scale uncertainties.

Contribution

It introduces explicit calculations of collinear subtraction terms and convolutions necessary for full N3LO Higgs production cross section determination.

Findings

Full scale dependence of N3LO Higgs cross section obtained

Convolutions of splitting kernels with lower-order cross sections provided

Estimated scale uncertainties at N3LO discussed

Abstract

The full, explicit, scale dependence of the inclusive N3LO cross section for single Higgs hadroproduction is obtained by calculating the convolutions of collinear splitting kernels with lower-order partonic cross sections. We provide results for all convolutions of splitting kernels and lower-order partonic cross sections to the order in epsilon needed for the full N3LO computation, as well as their expansions around the soft limit. We also discuss the size of the total scale uncertainty at N3LO that can be anticipated with existing information.