Fully differential Higgs boson pair production at N³LO 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 $\alpha_s$ 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 $\alpha_s$, 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.