# Experimental consistency in parton distribution fitting

## TL;DR

This paper applies the Data Set Diagonalization method to assess the consistency of experimental data used in parton distribution function fitting, revealing larger-than-expected discrepancies and supporting a specific tolerance criterion for uncertainties.

## Contribution

It introduces the application of the DSD method to evaluate data compatibility and influence in PDF fitting, highlighting the need for revised error tolerance criteria.

## Key findings

- Discrepancies among experiments are larger than Gaussian error predictions.
- A tolerance criterion of Δχ² ≈ 10 is supported for 90% confidence intervals.
- Muon scattering experiments show significant tension with other data sets.

## Abstract

The recently developed "Data Set Diagonalization" method (DSD) is applied to measure compatibility of the data sets that are used to determine parton distribution functions (PDFs). Discrepancies among the experiments are found to be somewhat larger than is predicted by propagating the published experimental errors according to Gaussian statistics. The results support a tolerance criterion of $\Delta\chi^2 \approx 10$ to estimate the 90% confidence range for PDF uncertainties. No basis is found in the data sets for the much larger $\Delta\chi^2$ values that are in current use; though it will be necessary to retain those larger values until improved methods can be developed to take account of systematic errors in applying the theory. The DSD method also measures how much influence each experiment has on the global fit, and identifies experiments that show significant tension with respect to the others. The method is used to explore the contribution from muon scattering experiments, which are found to exhibit the largest discrepancies in the current fit.