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, ln 5, 4, 3(1−z), to the N3LO coefficient function in the threshold expansion. Also using knowledge from Higgs-exchange DIS to estimate the remaining terms not vanishing for z = m 2 /ŝ → 1, these results are combined with the recently completed soft + virtual contributions to provide an uncertainty band for the complete N3LO correction. For the 2008 MSTW parton distributions these N3LO contributions increase the cross section at 14 TeV by (10 ±2)% and (3 ±2.5)% for the standard choices μ R = m H and μ R = m H /2 of the renormalization 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.