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

Abstract

We show how to account for correlations between the theoretical uncertainties incorporated in parton distribution function (PDF) fits, and the theoretical uncertainties of theoretical predictions made using these PDFs. We demonstrate that these correlations are very weak due to a combination of three distinct mechanisms: decorrelation due to the experimental uncertainties in the data, decorrelation due to the projection of the theoretical uncertainties into the universal PDFs, and decorrelation due to the functional uncertainty in these PDFs. We provide explicit formulae for computing the shift in central value and correction to the overall theoretical uncertainty of the theoretical predictions due to the small residual correlation. We illustrate our results with predictions for top production rapidity distributions and the Higgs total cross-section at the LHC, using the NLO NNPDF3.1 PDF set which incorporates missing higher order uncertainties. We conclude that when making predictions using PDFs that incorporate theoretical uncertainties, the PDF uncertainties and the theoretical uncertainties in the hard cross-sections can in practice be simply added in quadrature. However the small shift in central value due to the correlations may offer a useful way of improving theoretical predictions, particularly when there are data for similar processes already included in the PDF fit.