Soft Expansion of Double-Real-Virtual Corrections to Higgs Production at N$^3$LO

TL;DR

This paper develops methods to compute higher-order threshold expansions for Higgs production at N$^3$LO, focusing on one-loop processes with two partons, advancing precision in theoretical predictions.

Contribution

It introduces new techniques for calculating master integrals in the threshold expansion of Higgs production, including two novel methods for integral evaluation.

Findings

Expanded the phase-space integrals in small kinematic parameters.

Reduced complex integrals to a small set of master integrals.

Provided Laurent expansions in the dimensional regulator.

Abstract

We present methods to compute higher orders in the threshold expansion for the one-loop production of a Higgs boson in association with two partons at hadron colliders. This process contributes to the N$^3$LO Higgs production cross section beyond the soft-virtual approximation. We use reverse unitarity to expand the phase-space integrals in the small kinematic parameters and to reduce the coefficients of the expansion to a small set of master integrals. We describe two methods for the calculation of the master integrals. The first was introduced for the calculation of the soft triple-real radiation relevant to N$^3$LO Higgs production. The second uses a particular factorization of the three body phase-space measure and the knowledge of the scaling properties of the integral itself. Our result is presented as a Laurent expansion in the dimensional regulator, although some of the master integrals are computed to all orders in this parameter.