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

Abstract

Abstract We show how an inaccurate determination of experimental uncertainty correlations in high-precision LHC measurements may undermine the reliability of the associated $$\chi ^2$$ χ 2 . We formulate the problem rigorously, and devise a regularisation procedure that increases the stability of the $$\chi ^2$$ χ 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 $$\chi ^2$$ χ 2 of the NNPDF4.0 determination is lowered by about $$3\sigma $$ 3 σ , without significantly altering the resulting PDFs upon refitting.