On the Higgs cross section at N${}^3$LO+N${}^3$LL and its uncertainty

Abstract

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 (N${}^3$LL) on the recently computed fixed-order prediction at next-to-next-to-next-to-leading order (N${}^3$LO). 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. We confirm that the best convergence happens at $\hat{I}{¼}_R=\hat{I}{¼}_F=m_H/2$, and we conclude that a reliable estimate of the uncertainty from missing higher orders on the Higgs cross section at 13 TeV is approximately $\pm 4$%.

27 pages, 6 figures. Version to be published in JHEP