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We show how to account for correlations between theoretical uncertaintiesincorporated in parton distribution function (PDF) fits, and the theoreticaluncertainties in the predictions made using these PDFs. We demonstrate byexplicit calculations, both analytical and numerical, that these correlationscan lead to corrections to the central values of the predictions, andreductions in both the PDF uncertainties and the theoretical uncertainties inthe prediction. We illustrate our results with predictions for top productionrapidity distributions and the Higgs total cross-section at the LHC, using theNLO NNPDF3.1 PDF set which incorporates missing higher order uncertainties. Weconclude that the inclusion of correlations can increase both the accuracy andprecision of predictions involving PDFs, particularly for processes with dataalready included in the PDF fit.

Correlation of Theoretical Uncertainties in PDF Fits and Theoretical Uncertainties in Predictions