Meaningful characterisation of perturbative theoretical uncertainties

TL;DR

This paper introduces a Bayesian approach to quantify perturbative theoretical uncertainties, providing a more rigorous and conceptually sound method compared to traditional scale variation estimates in high energy physics calculations.

Contribution

It formulates a Bayesian model for perturbative uncertainties, offering a rigorous way to determine credibility intervals for series remainders, improving upon conventional methods.

Findings

Bayesian model yields comparable uncertainty estimates to traditional methods.

Conceptual differences highlight the Bayesian approach's rigor.

First step towards systematic uncertainty quantification in perturbative calculations.

Abstract

We consider the problem of assigning a meaningful degree of belief to uncertainty estimates of perturbative series. We analyse the assumptions which are implicit in the conventional estimates made using renormalisation scale variations. We then formulate a Bayesian model that, given equivalent initial hypotheses, allows one to characterise a perturbative theoretical uncertainty in a rigorous way in terms of a credibility interval for the remainder of the series. We compare its outcome to the conventional uncertainty estimates in the simple case of the calculation of QCD corrections to the e+e- -> hadrons process. We find comparable results, but with important conceptual differences. This work represents a first step in the direction of a more comprehensive and rigorous handling of theoretical uncertainties in perturbative calculations used in high energy phenomenology.