# One-loop QCD contributions to differential cross-sections for Higgs production at N$^3$LO

## TL;DR

This paper calculates one-loop QCD contributions to the differential cross-section of Higgs production via gluon fusion, advancing the precision of theoretical predictions at N$^3$LO by handling complex singularities and providing numerical results.

## Contribution

It introduces a method to compute one-loop contributions to Higgs production at N$^3$LO, including singularity treatment and numerical evaluation of finite parts.

## Key findings

- Computed one-loop contributions to Higgs differential cross-section.
- Demonstrated numerical corrections at N$^3$LO for Higgs rapidity and transverse momentum.
- Identified universal infrared divergent structures in the calculation.

## Abstract

We present one-loop contributions to the fully differential Higgs boson gluon-fusion cross-section for Higgs production via gluon fusion. Our results constitute a necessary ingredient of a complete N$^3$LO determination of the cross-section. We perform our computation using a subtraction method for the treatment of soft and collinear singularities. We identify the infrared divergent parts in terms of universal splitting and eikonal functions, and demonstrate how phase-space integrations yield poles (up to $1/\epsilon^6$ ) in the dimensional regulator $\epsilon=(4-d)/2$. We compute the coefficients of the $\epsilon$ expansion, including the finite part numerically. As a demonstration of our numerical implementation, we present the corrections at N$^3$LO due to one-loop amplitudes in the rapidity and transverse momentum of the Higgs boson.