Correlation and Combination of Sets of Parton Distributions

TL;DR

This paper investigates how different parton distribution function (PDF) sets are correlated, distinguishing between data-driven and methodology-driven correlations, and evaluates the reliability of combining PDFs for high-energy physics analyses.

Contribution

It analyzes the sources of correlation among PDF sets, highlighting the limitations of data-driven combination methods and validating the PDF4LHC15 combination approach.

Findings

Significant non-data-driven correlations exist among PDF sets.

Data-driven correlations can assess the efficiency of PDF determination methodologies.

Combining PDFs using statistical methods remains the most reliable approach.

Abstract

We study the correlation between different sets of parton distributions (PDFs). Specifically, viewing different PDF sets as distinct determinations, generally correlated, of the same underlying physical quantity, we examine the extent to which the correlation between them is due to the underlying data. We do this both for pairs of PDF sets determined using a given fixed methodology, and between sets determined using different methodologies. We show that correlations have a sizable component that is not due to the underlying data, because the data do not determine the PDF uniquely. We show that the data-driven correlations can be used to assess the efficiency of methodologies used for PDF determination. We also show that the use of data-driven correlations for the combination of different PDFs into a joint set can lead to inconsistent results, and thus that the statistical combination used in constructing the widely used PDF4LHC15 PDF set remains the most reliable method.