N${}^3$LO+N${}^3$LL QCD improved Higgs pair cross sections

Abstract

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 (N${}^3$LL) accuracy. After matching N${}^3$LL to the next-to-next-to-next-to-leading order (N${}^3$LO) 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 N${}^3$LO, 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.

arXiv comment40 pages, 6 figures, 2 tables. v2: journal version (minor corrections wrt v1)

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