The three loop soft function for N$^3$LL$^\prime$ gluon fusion Higgs production in SCET

TL;DR

This paper derives a three-loop soft function for gluon fusion Higgs production, enabling high-precision N$^3$LL$^ extprime$ resummation in SCET, including collinear effects and finite mass corrections.

Contribution

It provides the first derivation of the three-loop soft function for Higgs production in gluon fusion and incorporates collinear and mass effects into N$^3$LL$^ extprime$ resummation.

Findings

Enhanced Higgs cross section predictions at N$^3$LL$^ extprime$ accuracy.

Inclusion of finite top, bottom, and charm mass effects.

Public availability of the ResHiggs code for practical use.

Abstract

We derive the three loop soft function for inclusive Higgs production in gluon fusion, and use it to perform the resummation of the Higgs cross section at N$^3$LL$^\prime$ in SCET. We improve the accuracy of the resummation by including contributions of collinear origin. We include finite top, bottom and charm mass effect where available. These results are available through the public code ResHiggs.