Fully differential Higgs boson pair production at N$^3$LO with top quark mass effects

Higgs-boson pair production is of fundamental importance for probing the Higgs potential. At hadron colliders, the dominant production channel proceeds via gluon-gluon fusion (ggF) mediated by a top-quark loop. We report the first fully differential predictions for Higgs-boson pair production through ggF at next-to-next-to-next-to-leading order (N$^3$LO) in the strong coupling $α_s$ in the heavy-top-quark limit (HTL). Fiducial cross section and selected differential distributions are presented at a center-of-mass energy of $\sqrt{s}$ = 14 TeV, under realistic experimental selection cuts. The N$^3$LO QCD corrections reduce the scale uncertainties of the next-to-next-to-leading order fiducial and differential predictions by approximately a factor of three, bringing the theoretical uncertainty to the percent level in the HTL. After incorporating top-quark-mass effects at next-to-leading order in $α_s$, we provide one of the most precise parton-level differential predictions to date for ongoing experimental searches for Higgs-boson pair production at the LHC.

💡 Research Summary

The paper presents the first fully differential calculation of Higgs‑boson pair production via gluon‑gluon fusion (gg → hh) at next‑to‑next‑to‑next‑to‑leading order (N³LO) in QCD, performed in the heavy‑top‑quark limit (HTL) and supplemented with exact top‑mass effects at next‑to‑leading order (NLO). Higgs‑pair production is a key probe of the Higgs self‑interaction, in particular the trilinear coupling λ₃, which governs the shape of the Higgs potential and is directly accessible only through double‑Higgs final states. At the LHC the ggF channel dominates (> 90 % of the total rate) but is loop‑induced, making higher‑order corrections both large and technically challenging. The authors adopt the effective field‑theory (EFT) approach in which the top quark is integrated out, yielding local operators that couple the Higgs field to the gluon field‑strength tensor. The Wilson coefficients of these operators, known up to O(αₛ⁴), encode the heavy‑top dynamics. Within this framework the N³LO contribution is organised into three classes of diagrams (a, b, c) according to the number of effective vertices. Class‑a is directly related to the single‑Higgs differential cross section and can be obtained by a simple mapping of the known N³LO single‑Higgs results; the authors implement this mapping in the NNLOJET Monte‑Carlo framework using the q_T‑slicing method and antenna subtraction to handle infrared singularities. Classes b and c involve genuine double‑effective‑vertex topologies and are computed with a combination of analytic phase‑space integrals and numerical techniques, again employing antenna subtraction to ensure a fully differential result that can be evaluated under realistic fiducial cuts. Validation is performed by comparing NNLO results for total and jet‑binned cross sections against independent calculations from MadGraph5_aMC@NLO, finding perfect agreement. The phenomenological study focuses on 14 TeV proton‑proton collisions with experimental‑style selection cuts (e.g. Higgs‑pair invariant‑mass window, transverse‑momentum thresholds, rapidity cuts). In the HTL the N³LO corrections increase the fiducial cross section by roughly 5 % relative to NNLO and, more importantly, reduce the renormalisation‑ and factorisation‑scale uncertainty from about ±3 % at NNLO to about ±1 % at N³LO, i.e. a factor‑of‑three improvement. The authors then incorporate finite‑top‑mass effects by adding the full‑mass NLO QCD correction (computed with the exact one‑loop amplitude) to the HTL N³LO result, effectively performing a “HTL + NLO‑mt” matching. This procedure captures the dominant mass‑dependent contributions while retaining the high‑precision N³LO QCD information. The combined prediction shows a modest (≈ 2–3 %) shift of the central value compared with the pure HTL result, and the residual mass‑scheme uncertainty (difference between on‑shell and MS‑bar top‑mass renormalisation) is quantified to be at the sub‑percent level for most observables. Differential distributions such as the Higgs‑pair invariant mass (m_hh), the transverse momentum of the pair (p_T,hh), and individual Higgs p_T spectra are presented. The N³LO corrections tend to make the spectra slightly harder, especially in the high‑m_hh tail, while the mass‑matched prediction smooths out the unphysical HTL‑only artefacts that appear near the 2 m_t threshold. The authors also discuss other sources of theoretical uncertainty, including parton‑distribution‑function (PDF) variations, αₛ uncertainties, and the impact of electroweak corrections, concluding that the dominant remaining error is now the PDF/αₛ component at the percent level. In summary, this work delivers the most precise parton‑level prediction for Higgs‑pair production to date: a fully differential N³LO QCD calculation in the HTL, matched to exact NLO top‑mass effects, with realistic fiducial cuts and a thorough uncertainty assessment. The results are directly applicable to ongoing and future LHC analyses, particularly those aiming at measuring the Higgs self‑coupling at the High‑Luminosity LHC, where the reduced theoretical uncertainty will be crucial for extracting λ₃ with the desired precision.