The gluon-fusion production of Higgs boson pair: N$^3$LO QCD corrections and top-quark mass effects

TL;DR

This paper presents the first N$^3$LO QCD calculations for Higgs boson pair production via gluon fusion, significantly reducing theoretical uncertainties and incorporating top-quark mass effects for precise predictions at various collider energies.

Contribution

It provides the first N$^3$LO QCD corrections for Higgs pair production in the infinite top-quark mass limit and introduces methods to include top-quark mass effects at this order.

Findings

Inclusive cross section uncertainties reduced by a factor of four.

Provides predictions for differential and inclusive cross sections at multiple energies.

Enhances the precision of theoretical inputs for Higgs pair event analyses.

Abstract

The Higgs boson pair production via gluon fusion at high-energy hadron colliders, such as the LHC, is vital in deciphering the Higgs potential and in pinning down the electroweak symmetry breaking mechanism. We carry out the next-to-next-to-next-to-leading order (N$^3$LO) QCD calculations in the infinite top-quark mass limit and present predictions for both the inclusive and differential cross sections, albeit the differential distributions other than the invariant mass distribution of the Higgs boson pair are approximated at N$^3$LO. Such corrections are indispensable in stabilising the perturbative expansion of the cross section in the strong coupling $\alpha_s$. At the inclusive level, the scale uncertainties are reduced by a factor of four compared with the next-to-next-to-leading order (NNLO) results. Given that the inclusion of the top-quark mass effects is essential for the phenomenological applications, we use several schemes to incorporate the N$^3$LO results in the infinite top-quark mass limit and the next-to-leading order (NLO) results with full top-quark mass dependence, and present theoretical predictions for the (differential) cross sections in the proton-proton collisions at the centre-of-mass energies $\sqrt{s}=13,14,27$ and $100$ TeV. Our results provide one of the most precise theoretical inputs for the analyses of the Higgs boson pair events.