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

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.

Comments: 23 pages, 6 figures