On the consistent use of scale variations in PDF fits and predictions

Harland-Lang, L. A. (Aff1, 0000 0004 1936 8948, Rudolf Peierls Centre, Beecroft Building, Parks Road, OX1 3PU, Oxford, UK) ; Thorne, R. S. (Aff2, 0000000121901201, Department of Physics and Astronomy, University College London, WC1E 6BT, London, UK)

13 March 2019

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.

Published in: EPJC 79 (2019) 225
Published by: Springer/Società Italiana di Fisica
DOI: 10.1140/epjc/s10052-019-6731-6
License: CC-BY-3.0

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