Acknowledgements: RDB, LDD, and RS are supported by the U.K. Science and Technology Facility Council (STFC) grant ST/T000600/1. FH is supported by the Academy of Finland project 358090 and is funded as a part of the Center of Excellence in Quark Matter of the Academy of Finland, project 346326. ERN is supported by the Italian Ministry of University and Research (MUR) through the “Rita Levi-Montalcini” Program. MU and ZK are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (grant agreement n.950246), and partially by the STFC consolidated grant ST/T000694/1 and ST/X000664/1. JR is partially supported by NWO, the Dutch Research Council. CS is supported by the German Research Foundation (DFG) under reference number DE 623/6-2.Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek; Grant(s): http://dx.doi.org/10.13039/501100003246We include uncertainties due to missing higher order corrections to QCD computations (MHOU) used in the determination of parton distributions (PDFs) in the recent NNPDF4.0 set of PDFs. We use our previously published methodology, based on the treatment of MHOUs and their full correlations through a theory covariance matrix determined by scale variation, now fully incorporated in the new NNPDF theory pipeline. We assess the impact of the inclusion of MHOUs on the NNPDF4.0 central values and uncertainties, and specifically show that they lead to improved consistency of the PDF determination. PDF uncertainties on physical predictions in the data region are consequently either unchanged or moderately reduced by the inclusion of MHOUs
