Parton distributions need representative sampling

Abstract

In global QCD fits of parton distribution functions (PDFs), a large part of the estimated uncertainty on the PDFs originates from the choices of parametric functional forms and fitting methodology. We argue that these types of uncertainties can be underestimated with common PDF ensembles in high-stake measurements at the Large Hadron Collider and Tevatron. A fruitful approach to quantify these uncertainties is to view them as arising from sampling of allowed PDF solutions in a multidimensional parametric space. This approach applies powerful insights gained in recent statistical studies of large-scale population surveys and quasi-Monte Carlo integration methods. In particular, PDF fits may be affected by the big data paradox, which stipulates that more experimental data do not automatically raise the accuracy of PDFs -close attention to the data quality and sampling of possible PDF solutions is as essential. To test if the sampling of the PDF uncertainty of an experimental observable is truly representative of all acceptable solutions, we introduce a technique ("a hopscotch scan") based on a combination of parameter scans and stochastic sampling. With this technique, we show that the PDF uncertainty on key LHC cross sections at 13 TeV obtained with the public NNPDF4.0 fitting code is larger than the nominal uncertainty obtained with the published NNPDF4.0 Monte-Carlo replica sets. In the PDF ensembles obtained in the analytic minimization (Hessian) formalism, the tolerance on the PDF uncertainty must be based on sufficiently complete sampling of PDF functional forms and choices of the experiments.

The Future of US Particle Physics: The Energy Frontier Report – 2021 US Community Study on the Future of Particle Physics

“…New types of complexity issues emerge in comparisons of multiparametric models with many parameters to very large data samples expected at the LHC Run 3 and HL-LHC. Undetected biases due to non-representative exploration of contributing systematic factors must be watched for, as has been recently demonstrated on an example of a PDF global fit [233]. Figure 1-28 illustrates that elevating the accuracy of QCD calculations to one percent requires both individual precise theoretical calculations as well as accurate supporting theoretical infrastructure that would allow to explore exhaustively the relevant systematic factors.…”

“…Control of uncertainties requires, in particular, to either fit the experiments that are minimally affected by the unknown factors (for example, to include cross sections only on proton, rather than on nuclear targets), or to estimate the associated uncertainties from these factors directly in the fit. The PDF uncertainties must representatively reflect all PDF behaviors compatible with the fitted data [233]. PDFs must be developed for a wide range of users in a format that optimizes for accuracy, versatility, and speed across a broad range of applications -a highly non-trivial task.…”

Snowmass 2021 Whitepaper: Proton Structure at the Precision Frontier

“…New complexity issues emerge in the global analyses of large data sets. Representative exploration of all contributions to the uncertainties is necessary for confident and accurate predictions [375].…”

“…In another recent development, it was pointed out that precisely approximating the full probability with 100-1000 MC replicas is very challenging in models with several tens or hundreds of parameters because of large dimensionality of the associated parameter space [375]. Representative sampling is needed to adequately explore the space of available PDF solutions, and differences in sampling with independent methodologies are related to the issue of (the absence of) methodological correlations.…”

“…To begin with, one could extend the analysis of PDF fits based on a common reduced data set by adding other measurements, since an even wider "reduced" data set could further highlight which differences observed between PDF groups can be traced back to the underlying methodological choices. One could also consider investigations of why the PDF uncertainties between various groups differ even when a similar input data set is considered, such as the one recently pursued in [375]. Also, the PDF4LHC21 combination will have to be eventually updated once new releases from the various PDF fitting collaborations are presented.…”