Uncertainties of predictions from parton distributions. I: experimental errors

TL;DR

The paper assesses how experimental data errors propagate into predictions from global NLO parton fits (MRST2001) using both Hessian and Lagrange multiplier methods. It generates 30 eigenvector-based parton sets to propagate uncertainties to key observables (F2^{CC}, sigma_W, sigma_H, W−/W+ ratio, and non-singlet u−d moments) and cross-validates with direct observable minimization, finding generally small experimental uncertainties (1–5%) but larger ones (up to ~10%) for high-x partons. The study also shows that differences in data selection and parameterization across global fits (MRST vs CTEQ, MRST2001 vs MRST2002) can dominate over data-driven errors, highlighting substantial theory-related uncertainties and the need for NNLO and resummation-based refinements. Overall, the results provide a practical framework for error propagation in parton distributions and underscore the impact of theoretical assumptions on predicted cross-sections and fundamental quantities like alpha_S(MZ^2).

Abstract

We determine the uncertainties on observables arising from the errors on the experimental data that are fitted in the global MRST2001 parton analysis. By diagonalizing the error matrix we produce sets of partons suitable for use within the framework of linear propagation of errors, which is the most convenient method for calculating the uncertainties. Despite the potential limitations of this approach we find that it can be made to work well in practice. This is confirmed by our alternative approach of using the more rigorous Lagrange multiplier method to determine the errors on physical quantities directly. As particular examples we determine the uncertainties on the predictions of the charged-current deep-inelastic structure functions, on the cross-sections for W production and for Higgs boson production via gluon--gluon fusion at the Tevatron and the LHC, on the ratio of W-minus to W-plus production at the LHC and on the moments of the non-singlet quark distributions. We discuss the corresponding uncertainties on the parton distributions in the relevant x,Q^2 domains. Finally, we briefly look at uncertainties related to the fit procedure, stressing their importance and using sigma_W, sigma_H and extractions of alpha_S(M_Z^2) as examples. As a by-product of this last point we present a slightly updated set of parton distributions, MRST2002.

Figures (15)

• Figure 1: The uncertainty on $u_V(x,Q^2)$ at $Q^2= 5\ \rm GeV^2$ and $100\ \rm GeV^2$ obtained using the Hessian approach with $\Delta \chi^2=50$. Also shown is the CTEQ6M distribution. The uncertainties are shown relative to the MRST2001 set of partons MRST2001; the label C is explained in footnote 5.
• Figure 2: The uncertainty on $d_V(x,Q^2)$ at $Q^2= 2\ \rm GeV^2$ and $100\ \rm GeV^2$ obtained using the Hessian approach with $\Delta \chi^2=50$. Also shown is the CTEQ6M distribution. The uncertainties are shown relative to the MRST2001 set of partons MRST2001; the label C is explained in footnote 5.
• Figure 3: The uncertainty on $g(x,Q^2)$ at $Q^2= 5\ \rm GeV^2$ and $100\ \rm GeV^2$ obtained using the Hessian approach with $\Delta \chi^2=50$. Also shown is the CTEQ6M distribution. The uncertainties are shown relative to the MRST2001 set of partons MRST2001; the label C is explained in footnote 5.
• Figure 4: The uncertainty on $g(x,Q^2)$ at $Q^2= 2\ \rm GeV^2$ obtained using the Hessian approach with $\Delta \chi^2=50$. Also shown is the CTEQ6M distribution.
• Figure 5: $\Delta\chi^2=50,100,\dots$ contours, where $\Delta\chi^2$ is the increase in $\chi^2$ from the global MRST2001 minimum, obtained by performing new global fits with $F_2^{CC}(e^\pm p)$ fixed at values in the neighbourhood of their value in unconstrained MRST2001 fit. The $\Delta\chi^2=50$ contour is taken to represent the errors on $F_2^{CC}(e^\pm p)$ (arising from the experimental errors on the data used in the global fit). The extrema sets of partons (T,U,$\dots$) are discussed in the text. The dashed contours are obtained if $\alpha_S(M_Z^2)$ is allowed to vary. The superimposed solid $\Delta\chi^2=50,100$ contours are obtained if $\alpha_S(M_Z^2)$ is fixed at 0.119.