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

TL;DR

This paper analyzes the Higgs boson production cross section at N$^3$LO+N$^3$LL accuracy, proposing a robust method to estimate theoretical uncertainties and comparing different approaches to improve prediction reliability.

Contribution

It introduces a conservative method for estimating perturbative uncertainties in Higgs production and compares it with other existing methods, enhancing the robustness of theoretical predictions.

Findings

Uncertainty estimate is approximately ±4% at 13 TeV.

Best convergence occurs at μ_R=μ_F=m_H/2.

Threshold resummation at N$^3$LL improves fixed-order predictions.

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 $\mu_R=\mu_F=m_H\,/\,2$, and we conclude that a reliable estimate of the uncertainty from missing higher orders on the Higgs cross section at 13 TeV is approximately $\pm4$%.