We present the cross section for the production of a Higgs boson at hadron colliders at next-to-next-to-next-to-leading order (N^{3}LO) in perturbative QCD. The calculation is based on a method to perform a series expansion of the partonic cross section around the threshold limit to an arbitrary order. We perform this expansion to sufficiently high order to obtain the value of the hadronic cross at N^{3}LO in the large top-mass limit. For renormalization and factorization scales equal to half the Higgs boson mass, the N^{3}LO corrections are of the order of +2.2%. The total scale variation at N^{3}LO is 3%, reducing the uncertainty due to missing higher order QCD corrections by a factor of 3.

We present the most precise value for the Higgs boson cross-section in the gluon-fusion production mode at the LHC. Our result is based on a perturbative expansion through N 3 LO in QCD, in an effective theory where the top-quark is assumed to be infinitely heavy, while all other Standard Model quarks are massless. We combine this result with QCD corrections to the cross-section where all finite quark-mass effects are included exactly through NLO. In addition, electroweak corrections and the first corrections in the inverse mass of the top-quark are incorporated at three loops. We also investigate the effects of threshold resummation, both in the traditional QCD framework and following a SCET approach, which resums a class of π 2 contributions to all orders. We assess the uncertainty of the cross-section from missing higher-order corrections due to both perturbative QCD effects beyond N 3 LO and unknown mixed QCD-electroweak effects. In addition, we determine the sensitivity of the cross-section to the choice of parton distribution function (PDF) sets and to the parametric uncertainty in the strong coupling constant and quark masses. For a Higgs mass of m H = 125 GeV and an LHC center-of-mass energy of 13 TeV, our best prediction for the gluon fusion cross-section is σ = 48.58 pb +2.22 pb (+4.56%) −3.27 pb (−6.72%) (theory) ± 1.56 pb (3.20%) (PDF+α s ) .

We present the cross-section for the threshold production of the Higgs boson at hadron-colliders at next-to-next-to-next-to-leading order (N 3 LO) in perturbative QCD. We present an analytic expression for the partonic cross-section at threshold and the impact of these corrections on the numerical estimates for the hadronic cross-section at the LHC. With this result we achieve a major milestone towards a complete evaluation of the cross-section at N 3 LO which will reduce the theoretical uncertainty in the determination of the strengths of the Higgs boson interactions.High precision theoretical predictions for the production rate of the Higgs boson are crucial in the study of the recently discovered particle from the ATLAS and CMS Collaborations [1] and for inferring the existence of phenomena beyond the Standard Model. With the collection of further data at the upgraded LHC, the theoretical uncertainty for the gluon-fusion cross-section will become soon dominant. It is thus highly timely to improve the theoretical accuracy of the cross-section predictions.The quest for accurate Higgs boson cross-sections has been long-standing and it is paralleled with major advances in perturbative QCD. State-of-the-art calculations of the gluon-fusion cross-section (for a review, see Ref.[2] and references therein) comprise next-to-leading-order (NLO) QCD corrections in the full Standard-Model theory, next-to-next-to-leading order (NNLO) QCD corrections as an expansion in inverse powers of the top-quark mass 1/m t , two-loop electroweak corrections and mixed QCD/electroweak corrections. To improve upon the present accuracy, the most significant correction is expected from the N 3 LO QCD contribution in the leading order of the 1/m t expansion.Universal factorization of radiative corrections due to soft emissions, as well as knowledge of the three-loop splitting functions [3], have made possible the derivation of logarithmic contributions to the cross-section beyond NNLO [4]. However, further progress in determining the N 3 LO correction can only be achieved by direct evaluation of the Feynman diagrams at this order.

We present the two first terms in the threshold expansion of Higgs production partonic cross-sections at hadron colliders for processes with three partons in the final state. These are contributions to the inclusive Higgs cross-section in gluon fusion at N3LO. We have developed a new technique for the expansion of the squared matrix-elements around the soft limit and for the reduction of the required phase-space integrals to only ten single-scale master integrals. We compute the master integrals building upon modern techniques for the integration of multidimensional integrals in dimensional regularization. Our results constitute an important step towards a systematic computation of the Higgs boson cross-section as an expansion around the threshold limit.Comment: 78 page

We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. We demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.