Approximate N3LO Higgs-boson production cross section using physical-kernel constraints

The single-logarithmic enhancement of the physical kernel for Higgs production by gluon-gluon fusion in the heavy top-quark limit is employed to derive the leading so far unknown contributions, in (5,4,3)(1-z) to the (NLO)-L-3 coefficient function in the threshold expansion. Also using knowledge from Higgs-exchange DIS to estimate the remaining terms not vanishing for z = m(H)(2)/(S) over cap -> 1, these results are combined with the recently completed soft + virtual contributions to provide an uncertainty band for the complete (NLO)-L-3 correction. For the 2008 MSTW parton distributions these (NLO)-L-3 contributions increase the cross section at 14 TeV by (10 +/- 2)% and (3 +/- 2.5)% for the standard choices mu(R) = m(H) and mu(R) = m(H)/2 of the renorrnalization scale. The remaining uncertainty arising from the hard-scattering cross sections can be quantified as no more than 5%, which is smaller than that due to the strong coupling and the parton distributions.