N3LO+N3LL QCD improved Higgs pair cross sections

We report a new calculation of the soft-gluon threshold resummation for the Higgs boson pair production in the dominant production mode - gluon-gluon fusion - up to the next-to-next-to-next-to-leading logarithmic ((NLL)-L-3) accuracy. After matching (NLL)-L-3 to the next-to-next-to-next-to-leading order ((NLO)-L-3) QCD calculation in the infinite top quark mass approximation, we show that the central values of the inclusive cross sections are quite stable with respect to (NLO)-L-3, while the conventional renormalisation and factorisation scale uncertainties are reduced by a factor of two, reaching to the subpercent level. Our study further consolidates the good asymptotic perturbative convergence. After combining with the full top-quark mass dependent next-to-leading order QCD results, our most advanced predictions are presented for both the inclusive total cross sections and the differential invariant mass distributions of the Higgs pair.

Automated summary

We present a new calculation of the soft-gluon threshold resummation for Higgs boson pair production in the dominant gluon-gluon fusion mode up to the next-to-next-to-next-to-leading logarithmic ((NLL)-L-3) accuracy. By matching (NLL)-L-3 to the next-to-next-to-next-to-leading order ((NLO)-L-3) QCD calculation in the infinite top quark mass approximation, we find that the inclusive cross sections are stable with respect to (NLO)-L-3 and the scale uncertainties are reduced by a factor of two, reaching subpercent level. Our study confirms the good asymptotic perturbative convergence. We provide advanced predictions for the inclusive total cross sections and differential invariant mass distributions of Higgs pair by combining with the full top-quark mass dependent next-to-leading order QCD results.