Regularising experimental correlations in LHC data: theory and application to a global analysis of parton distributions

TL;DR

This paper introduces a regularisation method to improve the stability of the chi-squared statistic in high-precision LHC data analysis by adjusting the covariance matrix, enhancing the reliability of parton distribution fits.

Contribution

It presents a novel regularisation procedure for covariance matrices that stabilizes chi-squared calculations in global analyses of LHC data, with minimal impact on the resulting PDFs.

Findings

Regularised chi-squared lowered by about 3 sigma.

PDFs remained largely unchanged after regularisation.

Enhanced stability of uncertainty correlations in high-precision measurements.

Abstract

We show how an inaccurate determination of experimental uncertainty correlations in high-precision LHC measurements may undermine the reliability of the associated $\chi^2$. We formulate the problem rigorously, and devise a regularisation procedure that increases the stability of the $\chi^2$ by altering the covariance matrix of the measurement as little as possible. We apply the procedure to the NNPDF4.0 global analysis of parton distribution functions that utilises a large amount of LHC measurements. We find that the regularised $\chi^2$ of the NNPDF4.0 determination is lowered by about $3\sigma$, without significantly altering the resulting PDFs upon refitting.