Deuteron uncertainties in the determination of proton PDFs

Richard D Ball,Rosalyn L Pearson,Emanuele R Nocera

doi:10.1140/epjc/s10052-020-08826-7

Abstract

We evaluate the uncertainties due to nuclear effects in global fits of proton parton distribution functions (PDFs) that utilise deep-inelastic scattering and Drell–Yan data on deuterium targets. To do this we use an iterative procedure to determine proton and deuteron PDFs simultaneously, each including the uncertainties in the other. We apply this procedure to determine the nuclear uncertainties in the SLAC, BCDMS, NMC and DYE866/NuSea fixed target deuteron data included in the NNPDF3.1 global fit. We show that the effect of the nuclear uncertainty on the proton PDFs is small, and that the increase in overall uncertainties is insignificant once we correct for nuclear effects.

Highlights

In a previous study [16] we showed how theoretical uncertainties due to heavy nuclear targets in deep-inelastic scattering (DIS) and DY measurements can be incorporated into global fits of proton parton distribution functions (PDFs)
In a previous study [16] we showed how theoretical uncertainties due to heavy nuclear targets in DIS and DY measurements can be incorporated into global fits of proton PDFs
This suggests that these three sets might not be sufficiently consistent to determine a precise nuclear correction, but can be used to estimate the uncertainty due to nuclear effects, and the second procedure led to a worse global fit than the first

Summary

37 Page 2 of 12

If the deuteron data were all pure deuteron data, in practice only the SLAC and BCDMS datasets, we could produce a similar set of pure deuteron PDFs { fd(k) : k = 1 · · · Nrep} These by construction will include the nuclear effects and the size of the nuclear correction would be Tid [ fd(0)] − Tid [ fs(0)], with fs(0) determined from the proton PDFs using Eq (1) averaged over proton PDF replicas. Our aim here is not so much to determine the deuteron PDF, but rather to use it to determine a theoretical covariance matrix that takes into account the nuclear effects in the deuteron data (both pure and mixed) when using these data in a global fit of the proton PDF. As in [16], we implement the second procedure: in this case, the theoretical (deuteron) covariance matrix is defined as

37 Page 4 of 12

37 Page 6 of 12

37 Page 8 of 12

Findings

37 Page 12 of 12