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Abstract We 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.

Abstract We construct a set of parton distribution functions (PDFs), based on the recent NNPDF4.0 PDF set, that also include a photon PDF. The photon PDF is constructed using the LuxQED formalism, while QED evolution accounting for $${\mathcal {O}}\left( \alpha \right) $$ O α , $${\mathcal {O}}\left( \alpha \alpha _s\right) $$ O α α s , and $${\mathcal {O}}\left( \alpha ^2\right) $$ O α 2 corrections is implemented and benchmarked by means of the EKO code. We investigate the impact of QED effects on NNPDF4.0, and compare our results both to our previous NNPDF3.1QED PDF set and to other recent PDF sets that include the photon. We assess the impact of photon-initiated processes and electroweak corrections on a variety of representative LHC processes, and find that they can reach the 5% level in vector boson pair production at large invariant mass.

Abstract We present the software framework underlying the NNPDF4.0 global determination of parton distribution functions (PDFs). The code is released under an open source licence and is accompanied by extensive documentation and examples. The code base is composed by a PDF fitting package, tools to handle experimental data and to efficiently compare it to theoretical predictions, and a versatile analysis framework. In addition to ensuring the reproducibility of the NNPDF4.0 (and subsequent) determination, the public release of the NNPDF fitting framework enables a number of phenomenological applications and the production of PDF fits under user-defined data and theory assumptions.

Abstract We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order ( $$\hbox {aN}^3\hbox {LO}$$ aN 3 LO ). We construct an approximation to the $$\hbox {N}^3\hbox {LO}$$ N 3 LO splitting functions that includes all available partial information from both fixed-order computations and from small and large x resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known $$\hbox {N}^3\hbox {LO}$$ N 3 LO corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to $$\mathcal {O}\left( \alpha _s^3\right) $$ O α s 3 accuracy. We determine a set of $$\hbox {aN}^3\hbox {LO}$$ aN 3 LO PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of $$\hbox {N}^3\hbox {LO}$$ N 3 LO terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the $$\hbox {aN}^3\hbox {LO}$$ aN 3 LO PDFs from the MSHT group. We examine the phenomenological impact of $$\hbox {aN}^3\hbox {LO}$$ aN 3 LO corrections on parton luminosities at the LHC, and give a first assessment of the impact of $$\hbox {aN}^3\hbox {LO}$$ aN 3 LO PDFs on the Higgs and Drell–Yan total production cross-sections. We find that the $$\hbox {aN}^3\hbox {LO}$$ aN 3 LO NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell–Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order.