Abstract
In this article, we compute the gluon fusion Higgs boson cross-section at N3LO through the second term in the threshold expansion. This calculation constitutes a major milestone towards the full N3LO cross section. Our result has the best formal accuracy in the threshold expansion currently available, and includes contributions from collinear regions besides subleading corrections from soft and hard regions, as well as certain logarithmically enhanced contributions for general kinematics. We use our results to perform a critical appraisal of the validity of the threshold approximation at N3LO in perturbative QCD.
Highlights
JHEP03(2015)091 sufficient to predict the value of the Higgs-boson cross-section at N3LO in QCD
A few months ago, we completed the computation of the first term in the threshold expansion, the so-called soft-virtual term, by computing in addition the constant term proportional to δ(1 − z) [23], which includes in particular the complete three-loop corrections to Higgs production via gluon fusion [24, 25]
We have computed for the first time the full next-to-soft corrections to Higgs-boson production, as well as the exact results for the coefficients of the first three leading logarithms at N3LO
Summary
We present the main results of our paper. We start by giving a short review of the inclusive gluon-fusion cross-section and its analytic properties, and we present our results in subsequent sections. Ηi(j3)(z) does contain the three-loop corrections to inclusive Higgs production, and contributions from the emission of up to three partons in the final state at the same order in perturbation theory. Only the single-emission contributions at two loops are known for generic values of z [27,28,29,30, 34,35,36], and only a few terms in the threshold expansion for the contributions with up to two additional partons in the final state are known [23, 44, 45] Each of these contributions is ultra-violet (UV) and infra-red (IR) divergent, and the divergences manifest themself as poles in the dimensional regulator ǫ. The coefficients of these logarithms are the main subject of this paper, and in the rest of this section we show how to explicitly determine some of the regular coefficients of the threshold logarithms
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