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

TL;DR

This paper presents a highly precise calculation of Higgs boson pair production cross sections using advanced QCD resummation techniques, significantly reducing theoretical uncertainties and improving prediction stability.

Contribution

It introduces the first N$^3$LO+N$^3$LL QCD calculation for Higgs pair production, combining resummation with fixed-order results for enhanced accuracy.

Findings

Cross section uncertainties reduced by a factor of two.

Predictions show stable central values at N$^3$LO.

Improved differential invariant mass distribution predictions.

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.