An extensive survey of the estimation of uncertainties from missing higher orders in perturbative calculations

TL;DR

This paper compares traditional scale variation and Bayesian methods for estimating uncertainties in perturbative QCD calculations, finding that a modified Bayesian approach provides more reliable uncertainty estimates across various observables.

Contribution

It introduces a modified Bayesian framework for better uncertainty estimation in perturbative QCD, validated against a wide range of observables.

Findings

Scale variation often underestimates uncertainties.

Modified Bayesian approach improves uncertainty estimates.

Method performs well for both hadronic and non-hadronic observables.

Abstract

We consider two approaches to estimate and characterise the theoretical uncertainties stemming from the missing higher orders in perturbative calculations in Quantum Chromodynamics: the traditional one based on renormalisation and factorisation scale variation, and the Bayesian framework proposed by Cacciari and Houdeau. We estimate uncertainties with these two methods for a comprehensive set of more than thirty different observables computed in perturbative Quantum Chromodynamics, and we discuss their performance in properly estimating the size of the higher order terms that are known. We find that scale variation with the conventional choice of varying scales within a factor of two of a central scale gives uncertainty intervals that tend to be somewhat too small to be interpretable as 68% confidence-level-heuristic ones. We propose a modified version of the Bayesian approach of Cacciari and Houdeau which performs well for non-hadronic observables and, after an appropriate choice of the relevant expansion parameter for the perturbative series, for hadronic ones too.