On the Consistent Use of Scale Variations in PDF Fits and Predictions

TL;DR

This paper analyzes how to consistently apply scale variations in PDF fits to accurately estimate theoretical uncertainties, emphasizing the importance of accounting for correlations to avoid overestimating uncertainties.

Contribution

It provides a general framework for the consistent use of scale variations in PDF fits, highlighting the importance of correlations between fit and prediction uncertainties.

Findings

High correlation between scale variations in fits and predictions can lead to overestimated uncertainties.

A physical basis recasting of PDF fits reveals the importance of treating scale variations carefully.

Careful treatment of correlations is essential for accurate uncertainty estimation in PDF-based predictions.

Abstract

We present an investigation of the theoretical uncertainties in parton distribution functions (PDFs) due to missing higher-order corrections in the perturbative predictions used in the fit, and their relationship to the uncertainties in subsequent predictions made using the PDFs. We consider in particular the standard approach of factorization and renormalization scale variation, and derive general results for the consistent application of these at the PDF fit stage. To do this, we use the fact that a PDF fit may be recast in a physical basis, where the PDFs themselves are bypassed entirely, and one instead relates measured observables to predicted ones. In the case of factorization scale variation we find that in various situations there is a high degree of effective correlation between the variation in the fit and in predicted observables. In particular, including such a variation in both cases can lead to an exaggerated theoretical uncertainty. More generally, a careful treatment of this correlation appears mandatory, at least within the standard scale variation paradigm. For the renormalization scale, the situation is less straightforward, but again we highlight the potential for correlations between related processes in the fit and predictions to enter at the same level as between processes in the fit or prediction alone.