A framework is presented for including second-order perturbative corrections to the radiation patterns of parton showers. The formalism allows to combine O(alphaS^2)-corrected iterated 2->3 kernels for "ordered" gluon emissions with tree-level 2->4 kernels for "unordered" ones. The combined Sudakov evolution kernel is thus accurate to O(alphaS^2). As a first step towards a full-fledged implementation of these ideas, we develop an explicit implementation of 2->4 shower branchings in this letter.Comment: 11 pages, 3 figure

The Higgs boson pair production via gluon fusion at high-energy hadron colliders, such as the LHC, is vital in deciphering the Higgs potential and in pinning down the electroweak symmetry breaking mechanism. We carry out the next-to-next-to-next-toleading order (N 3 LO) QCD calculations in the infinite top-quark mass limit and present predictions for both the inclusive and differential cross sections. Such corrections are indispensable in stabilising the perturbative expansion of the cross section in the strong coupling α s . At the inclusive level, the scale uncertainties are reduced by a factor of four compared with the next-to-next-to-leading order (NNLO) results. Given that the inclusion of the top-quark mass effects is essential for the phenomenological applications, we use several schemes to incorporate the N 3 LO results in the infinite top-quark mass limit and the nextto-leading order (NLO) results with full top-quark mass dependence, and present theoretical predictions for the (differential) cross sections in the proton-proton collisions at the centreof-mass energies √ s = 13, 14, 27 and 100 TeV. Our results provide one of the most precise theoretical inputs for the analyses of the Higgs boson pair events.

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