Uncertainties of predictions from parton distributions. I: Theoretical errors

TL;DR

This study systematically quantifies theoretical uncertainties in parton distributions obtained from global fits, emphasizing data selection, perturbative-order truncation, and specific high-x/high- y corrections. By identifying conservative kinematic cuts and comparing NLO and NNLO results, the authors show NNLO partons yield more stable predictions and more robust determinations of $\alpha_S(M_Z^2)$, with notable improvements in W and Higgs production predictions as a luminosity monitor. They also probe beyond-fixed-order effects (ln(1/x), ln(1-x), absorptive and higher-twist corrections) and input assumptions (parameterization, heavy-target effects, strange sea, and isospin violation), finding that, while some effects can shift parton shapes or improve fits, the overall uncertainties shrink significantly at NNLO and within the conservative fit domain. The work highlights regions where theory errors dominate and suggests that further theoretical advances in low-$x$ and low-$Q^2$ physics are needed for precision predictions at colliders. Overall, NNLO analyses provide more reliable PDFs and predictions, with small residual uncertainties that motivate targeted improvements in resummation and non-perturbative modeling.

Abstract

We study the uncertainties in parton distributions, determined in global fits to deep inelastic and related hard scattering data, due to so-called theoretical errors. Amongst these, we include potential errors due to the change of perturbative order (NLO to NNLO), ln(1/x) and ln(1-x) effects, absorptive corrections and higher-twist contributions. We investigate these uncertainties both by including explicit corrections to our standard global analysis and by examining the sensitivity to changes of the x,Q^2,W^2 cuts on the data that are fitted. In this way we expose those kinematic regions where the conventional DGLAP description is inadequate. As a consequence we obtain a set of NLO, and of NNLO, conservative partons where the data are fully consistent with DGLAP evolution, but over a restricted kinematic domain. We also examine the potential effects of such issues as the choice of input parameterization, heavy target corrections, assumptions about the strange quark sea and isospin violation. Hence we are able to compare the theoretical errors with those uncertainties due to errors on the experimental measurements, which we studied previously. We use W and Higgs boson production at the Tevatron and the LHC as explicit examples of the uncertainties arising from parton distributions. For many observables the theoretical error is dominant, but for the cross section for W production at the Tevatron both the theoretical and experimental uncertainties are small, and hence the NNLO prediction may serve as a valuable luminosity monitor.

Figures (19)

• Figure 1: The gluon distribution obtained in NLO global fits with different values of $x_{\rm cut}$, that is $x_{\rm cut}$ taken to be 0.0002 (dashed curve), 0.001 (dotted) and 0.005 (dot-dashed), compared to the default set with $x_{\rm cut}=0$ (continuous curve).
• Figure 2: Comparison of MRST(cons) partons with the default NLO set MRST(2002). The former partons are only reliable for $x>0.005$ and $Q^2>10~\rm GeV^2$.
• Figure 3: Comparison of MRST gluons obtained from $x_{\rm cut}=0.005$ with the default gluons MRST(2002) at both NLO and NNLO.
• Figure 4: Comparison of the NNLO MRST(cons) partons with the default set MRST(2002) at NNLO. The former partons are only reliable for $x>0.005$ and $Q^2>7~\rm GeV^2$.
• Figure 5: Comparison of MRST gluons obtained from the fits with additional resummation corrections in $\ln(1/x)$ with the default gluons MRST(2002) at both NLO and NNLO.