Abstract
We construct an approximate expression for the cross section for Higgs production in gluon fusion at next-to-next-to-next-to-leading order (N3LO) in αs with finite top mass. We argue that an accurate approximation can be constructed by exploiting the analyticity of the Mellin space cross section, and the information on its singularity structure coming from large N (soft gluon, Sudakov) and small N (high energy, BFKL) all order resummation. We support our argument with an explicit comparison of the approximate and the exact expressions up to the highest (NNLO) order at which the latter are available. We find that the approximate N3LO result amounts to a correction of 17% to the NNLO QCD cross section for production of a 125 GeV Higgs at the LHC (8 TeV), larger than previously estimated, and it significantly reduces the scale dependence of the NNLO result.
Highlights
The dominant Higgs production mechanism at the LHC is gluon fusion via a heavy fermion loop [1], and the recent announcement of the discovery of a Higgs-like particle [2, 3] is largely based on events in this channel
We have determined an approximate expression for the N3LO Higgs production cross section in gluon fusion, with finite top mass
Our approximation is based on combining information on the large N and small N singularities of the coefficient function, which are determined from resummation, while making sure that they do not interfere with each other, so that large N terms do not introduce spurious small N singularities, and
Summary
The dominant Higgs production mechanism at the LHC is gluon fusion via a heavy fermion loop (mainly a top quark) [1], and the recent announcement of the discovery of a Higgs-like particle [2, 3] is largely based on events in this channel. Next-to-leading order (NLO) corrections to the inclusive cross section, originally computed in Refs. [6] for general mt are known to be as large as the leading order, and the NNLO corrections [20,21,22]) that accurate approximations to partonic cross sections may be obtained from knowledge of their N space singularity structure, both at finite perturbative order, and at the resummed level. We will pursue this idea in the context of Higgs production in gluon fusion: we will determine the dominant small N and large N singularities up to N3LO from resummation arguments, and, after testing our methodology against known results up to NNLO, we will use them to construct a N3LO approximation
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