Differential Higgs production at N3LO beyond threshold

TL;DR

This paper advances the calculation of differential Higgs boson production cross sections at N$^3$LO in QCD by developing a threshold expansion framework, providing analytic coefficients, and addressing computational challenges.

Contribution

It introduces a method to compute N$^3$LO differential Higgs cross sections using threshold expansions and solves a key obstacle related to parton distribution functions.

Findings

First two analytic threshold expansion coefficients obtained.

Framework allows high-order expansion in Higgs production.

Addresses and resolves a computational obstacle with LHAPDF.

Abstract

We present several key steps towards the computation of differential Higgs boson cross sections at N$^3$LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N$^3$LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions. In addition, we report on an interesting obstacle for the computation of N$^3$LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections together with the arXiv submission.