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

Emanuele Bagnaschi,Laura Jenniches,Alberto Guffanti,Matteo Cacciari

doi:10.1007/jhep02(2015)133

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.

Highlights

In Quantum Chromodynamics (QCD), which we take as a model here given its central role in LHC physics, theoretical uncertainties stemming from missing higher orders in the perturbative series are usually estimated by varying the unphysical renormalisation and factorisation scales that appear in the calculation of cross sections and decay rates
We summarise the results of our study, comparing the size of the 68% and 95% Degree of Belief (DoB) intervals obtained with the Cacciari-Houdeau approach (CH) method with the uncertainty interval of the scale-variation procedure for r = 2
We summarise the results of our studies comparing, for each process, the size of the uncertainty intervals obtained with the CH method (68% and 95% DoB) to the ones obtained using the scale-variation procedure (r = 2) at different perturbative orders

Summary

Introduction

In Quantum Chromodynamics (QCD), which we take as a model here given its central role in LHC physics, theoretical uncertainties stemming from missing higher orders in the perturbative series are usually estimated by varying the unphysical renormalisation and factorisation scales that appear in the calculation of cross sections and decay rates. This approach has served the QCD community well for more than thirty years, and can still be regarded as the most effective way to quickly estimate the missing higher order uncertainties (MHOUs). We introduce and describe two different approaches to the estimation of the uncertainty stemming from the missing higher orders of a perturbatively calculated observable:

Objectives

Results

Conclusion