Deuteron Uncertainties in the Determination of Proton PDFs

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.

Figures (9)

• Figure 1: A schematic representation of the iterative procedure adopted to determine the uncertainty due to deuteron corrections in proton PDF fits, see text for details. The global dataset is the union of the proton and deuteron datasets.
• Figure 2: The ratio between the SLAC, BCDMS, NMC and DYE866/NuSea deuteron observables computed either with the central prediction with deuteron PDFs, $T_i^d[f^0_d]$, or the central prediction with proton PDFs, $T_i^d[f^0_s]$. Data points are ordered in bins of increasing values of momentum fraction $x$ and energy $Q$.
• Figure 3: The square root of the diagonal elements of the covariance matrices normalised to the experimental data, $\sqrt{{\rm cov}_{ii}}/D_i$, for the deuteron measurements from SLAC, BCDMS, NMC and DYE866/NuSea. We show results for the experimental covaraince matrix $(C)$, for the deuteron covariance matrix $(S)$, computed from Eq. \ref{['eq:deuteroncovmatrix']}, and for their sum $(C+S)$.
• Figure 4: The experimental (left) and total (right) correlation matrices for the SLAC, BCDMS, NMC and DYE866/NuSea deuteron experiments. The deuteron covariance matrix, added to the experimental covariance matrix to obtain the total covariance matrix, is computed according to Eq. \ref{['eq:deuteroncovmatrix']}.
• Figure 5: Distances between the central values of the deuteron-ite1 and deuteron-ite2 fits (left) and of the global-ite1-dw and global-ite2-dw fits (right), see Table \ref{['tab:fits']} for details. For the deuteron fits, $u$ and $\bar{u}$ actually denote the combinations $(u+d)/2$ and $(\bar{u}+\bar{d})/2$, where $u=d$ and $\bar{u}=\bar{d}$ by definition. Results are displayed as a function of $x$ at a representative scale of the deuteron dataset, $Q=10$ GeV. The ReportEngine software zahari_kassabov_2019_2571601 was used to generate this figure.