Abstract
We present several key steps towards the computation of differential Higgs boson cross sections at N3LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N3LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions. We find that while a few terms in the threshold expansion are sufficient to approximate the exact rapidity distribution well, transverse momentum distributions require a signficantly higher number of terms in the expansion to be adequately described. We find that to improve state of the art predictions for the rapidity distribution beyond NNLO even more sub-leading terms in the threshold expansion than presented in this article are required. In addition, we report on an interesting obstacle for the computation of N3LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections as supplementary material attached to this paper.
Highlights
In order to truly exploit the potential of these excellent experimental results, it is imperative to confront them with precise theoretical predictions
We present several key steps towards the computation of differential Higgs boson cross sections at N3LO in perturbative QCD
We demonstrate how to perform an expansion of the analytic N3LO coefficient functions around the production threshold of the Higgs boson
Summary
We briefly review the definition of Higgs differential cross sections introduced in ref. [33]. The framework of Higgs differential cross sections allows to compute the scattering probability for any observable that is solely dependent on the four momentum of the Higgs boson. Such observables are related to the rapidity Y , transverse momentum pT and mass mh of the Higgs boson. Assume we are interested in computing the probability for a Higgs boson to be produced in the rapidity interval Y ∈ [1, 2] the measurement function would take the form. [33] the partonic Higgs differential cross sections were computed in heavy quark effective theory for the gluon fusion production mode to NNLO in QCD perturbation theory in terms of analytic functions of the variables z, x and λ. Higgs differential cross sections can be combined with subsequent decays of the Higgs boson in order to allow for the prediction of fiducial cross sections for Higgs boson decay products as demonstrated in ref. [33]
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