On the Higgs cross section at N3LO+N3LL and its uncertainty

We consider the inclusive production of a Higgs boson in gluon-fusion and we study the impact of threshold resummation at next-to-next-to-next-to-leading logarithmic accuracy ((NLL)-L-3) on the recently computed fixed-order prediction at next-to-next-to-nextto- leading order ((NLO)-L-3). We propose a conservative, yet robust way of estimating the perturbative uncertainty from missing higher (fixed-or logarithmic-) orders. We compare our results with two other different methods of estimating the uncertainty from missing higher orders: the Cacciari-Houdeau Bayesian approach to theory errors, and the use of algorithms to accelerate the convergence of the perturbative series, as suggested by David and Passarino. We con firm that the best convergence happens at mu(R) = mu(F) = m(H)/2, and we conclude that a reliable estimate of the uncertainty from missing higher orders on the Higgs cross section at 13TeV is approximately +/- 4%.