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

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.