The inclusion of theory errors in PDF fits

We present ongoing work towards incorporating the missing higher-order uncertainty (MHOU) determined through scale variations in the assessment of parton distribution functions (PDFs). Our PDFs fitting employs the NNPDF4.0 methodology and our theory covariance matrix framework to account for theory errors. This approach relies on the integration of MHOUs and their correlations via a theory covariance matrix. We validate our estimation and assess the impact of theory errors on the PDFs and on LHC phenomenology.