Abstract
We show how to account for correlations between theoretical uncertainties incorporated in parton distribution function (PDF) fits, and the theoretical uncertainties in the predictions made using these PDFs. We demonstrate by explicit calculations, both analytical and numerical, that these correlations can lead to corrections to the central values of the predictions, and reductions in both the PDF uncertainties and the theoretical uncertainties in the prediction. 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 the inclusion of correlations can increase both the accuracy and precision of predictions involving PDFs, particularly for processes with data already included in the PDF fit.
Highlights
With and without various theoretical corrections, rather than to incorporate the uncertainties into the fit itself
Note that if we were to perform these studies with NNLO parton distribution function (PDF) which include missing higher order uncertainties (MHOUs), the MHOU in the PDF determination would have presumably been rather smaller than at NLO, and the effect of correlations in the MHOU, in particular the shift, and the effect on the size of the uncertainty would be even smaller than the small corrections we see here
In this paper we studied in detail the correlation between theoretical uncertainties in the calculations used in the determination of PDFs in a global fit, as formulated in Ref. [9], and the theoretical uncertainties in the predictions made using these PDFs
Summary
A new approach to estimating the impact of theoretical uncertainties on global PDF fits has been developed, through the construction of a ‘theory covariance matrix’ [4], analogous to the experimental covariance matrix used in global PDF fits. By adding the theory covariance matrix to the experimental covariance matrix as an additional source of uncertainty, theoretical uncertainties can be incorporated directly in the fit, where they impact the overall level of PDF uncertainty, and the relative weight of different datasets This novel approach has so far been applied to uncertainties associated with nuclear effects [5,6], and to the estimation of MHOUs by scale variation [7,8,9] (though other methods [10,11,12] of estimating MHOU are under development). When making predictions for hadronic observables there are again two sources of MHOU: uncertainties in the PDF evolution, which can be estimated by factorization scale variation, and uncertainties in the hard cross-section, again estimated by renormalization scale variation.
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