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

TL;DR

This paper tackles the precision challenge of Higgs-boson pair production via gluon-gluon fusion by delivering the first fully differential predictions at $N^3LO$ in QCD within the heavy-top-quark limit, including three-way (class-$a$, class-$b$, class-$c$) contributions and $q_T$-slicing techniques. The authors show that the $N^3LO$ corrections reduce scale uncertainties to the percent level and offer improved fiducial cross sections and differential distributions at $14$ TeV, while also incorporating finite top-quark mass effects at NLO to produce highly precise parton-level predictions. They examine three schemes for merging HTL $N^3LO$ results with full mt dependence, revealing significant yet manageable top-mass effects on differential observables and highlighting the importance of top-quark-mass scheme choices for uncertainty estimation. The work delivers the most precise theoretical predictions to date for di-Higgs production at the LHC and informs ongoing experimental searches and future improvements including NNLO finite-mt corrections and electroweak effects.

Abstract

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.

Figures (13)

• Figure 1: LO representative Feynman diagrams for the Higgs boson pair production in the SM.
• Figure 2: LO representative Feynman diagrams for the Higgs pair production in the HTL.
• Figure 3: Representative Born-level Cutkosky-cut diagrams for the three classes of Higgs-pair production in the HTL.
• Figure 4: The $p_T^{\mathrm{veto}}$ dependence of the N$^3$LO ($\mathcal{O}(\alpha_s^5)$) corrections $\Delta\sigma_{hh}^{a,\mathrm{N}^3\mathrm{LO}}$ (green circles) to the total cross section of the class-$a$ contribution in $pp$ collisions at $\sqrt{s}=14$ TeV. The left panel displays the breakdown of $\Delta\sigma_{hh}^{a,\mathrm{N}^3\mathrm{LO}}$ into $p_{T,hh}<p_T^{\mathrm{veto}}$ (blue triangles) and $p_{T,hh}>p_T^{\mathrm{veto}}$ (red diamonds) contributions. In the right panel, our $q_T$-slicing result (green circles) is compared with the inclusive cross section from ref. Chen:2019fhs, obtained using iHixs2 and eq. \ref{['eq:htohh']} (black line). Error bars indicate Monte Carlo integration uncertainty.
• Figure 5: Fit of $\Delta\sigma^{\mathrm{a,N^{3}LO}}_{hh}(p_{T}^{\rm veto})$ using the ansatz in eq. \ref{['eq:DN3LOaansatz']}. The lower panel shows the residuals of the fit. The numerical data points are shown as black dots, with error bars indicating the Monte Carlo integration statistical uncertainties. The red line represents the central value of the fit curve, and the light red band denotes the fit error. The blue line corresponds to the result in ref. Chen:2019fhs.