A precise knowledge of the quark and gluon structure of the proton, encoded by the parton distribution functions (PDFs), is of paramount importance for the interpretation of high-energy processes at present and future lepton–hadron and hadron–hadron colliders. Motivated by recent progress in the PDF determinations carried out by the CT, MSHT, and NNPDF groups, we present an updated combination of global PDF fits: PDF4LHC21. It is based on the Monte Carlo combination of the CT18, MSHT20, and NNPDF3.1 sets followed by either its Hessian reduction or its replica compression. Extensive benchmark studies are carried out in order to disentangle the origin of the differences between the three global PDF sets. In particular, dedicated fits based on almost identical theory settings and input datasets are performed by the three groups, highlighting the role played by the respective fitting methodologies. We compare the new PDF4LHC21 combination with its predecessor, PDF4LHC15, demonstrating their good overall consistency and a modest reduction of PDF uncertainties for key LHC processes such as electroweak gauge boson production and Higgs boson production in gluon fusion. We study the phenomenological implications of PDF4LHC21 for a representative selection of inclusive, fiducial, and differential cross sections at the LHC. The PDF4LHC21 combination is made available via the LHAPDF library and provides a robust, user-friendly, and efficient method to estimate the PDF uncertainties associated to theoretical calculations for the upcoming Run III of the LHC and beyond.

We present an updated determination of nuclear parton distributions (nPDFs) from a global NLO QCD analysis of hard processes in fixed-target lepton-nucleus and proton-nucleus together with collider protonnucleus experiments. In addition to neutral-and charged-current deep-inelastic and Drell-Yan measurements on nuclear targets, we consider the information provided by the production of electroweak gauge bosons, isolated photons, jet pairs, and charmed mesons in proton-lead collisions at the LHC across centre-ofmass energies of 5.02 TeV (Run I) and 8.16 TeV (Run II). For the first time in a global nPDF analysis, the constraints from these various processes are accounted for both in the nuclear PDFs and in the freeproton PDF baseline. The extensive dataset underlying the nNNPDF3.0 determination, combined with its model-independent parametrisation, reveals strong evidence for nuclear-induced modifications of the partonic structure of heavy nuclei, specifically for the small-x shadowing of gluons and sea quarks, as well as the large-x anti-shadowing of gluons. As a representative phenomenological application, we provide predictions for ultra-high-energy neutrino-nucleon cross-sections, relevant for data interpretation at neutrino observatories. Our results provide key input for ongoing and future experimental programs, from that of heavy-ion collisions in controlled collider environments to the study of high-energy astrophysical processes.

We present a compression algorithm for parton densities using synthetic replicas generated from the training of a generative adversarial network (GAN). The generated replicas are used to further enhance the statistics of a given Monte Carlo PDF set prior to compression. This results in a compression methodology that is able to provide a compressed set with smaller number of replicas and a more adequate representation of the original probability distribution. We also address the question of whether the GAN could be used as an alternative mechanism to avoid the fitting of large number of replicas.

We present an updated determination of nuclear parton distributions (nPDFs) from a global NLO QCD analysis of hard processes in fixed-target lepton-nucleus and proton-nucleus together with collider proton-nucleus experiments. In addition to neutral- and charged-current deep-inelastic and Drell–Yan measurements on nuclear targets, we consider the information provided by the production of electroweak gauge bosons, isolated photons, jet pairs, and charmed mesons in proton-lead collisions at the LHC across centre-of-mass energies of 5.02 TeV (Run I) and 8.16 TeV (Run II). For the first time in a global nPDF analysis, the constraints from these various processes are accounted for both in the nuclear PDFs and in the free-proton PDF baseline. The extensive dataset underlying the nNNPDF3.0 determination, combined with its model-independent parametrisation, reveals strong evidence for nuclear-induced modifications of the partonic structure of heavy nuclei, specifically for the small-x shadowing of gluons and sea quarks, as well as the large-x anti-shadowing of gluons. As a representative phenomenological application, we provide predictions for ultra-high-energy neutrino-nucleon cross-sections, relevant for data interpretation at neutrino observatories. Our results provide key input for ongoing and future experimental programs, from that of heavy-ion collisions in controlled collider environments to the study of high-energy astrophysical processes.

We study the phenomenological impact of a recently suggested formalism for the combination of threshold and a so-called threshold-improved transverse momentum resummation, by using it to improve the fixed-order results. This formalism allows for a systematic improvement of the transverse momentum resummation that is valid in the entire range of pT by the inclusion of the threshold contribution. We use the Borel method as a suitable prescription for defining the inverse Mellin and Fourier transforms in the context of combined resummed expression. The study is applied to two QCD processes, namely the Higgs boson produced via gluon fusion and Z boson production via the Drell-Yan mechanism. We compare our results to the standard transverse momentum resummation, as well as to the fixed-order results. We find that the threshold-improved transverse momentum resummation leads to faster perturbative convergence at small pT while the inclusion of threshold resummation improves the agreement with fixed-order calculations at medium and large pT. These effects are more pronounced in the case of Higgs which is known to have slower perturbative convergence.

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We present a more reliable approach to approximate the unknown next-to-next-to-next-to-leading order (N3LO) transverse momentum distribution of colourless final states, namely the Higgs boson produced via gluon fusion and the lepton pair produced via Drell-Yan (DY) mechanism. The approximation we construct relies on the combination of various resummation formalisms -namely threshold, smallpt and high energy resummations -by exploiting the singularity structure of the large logarithms in Mellin space. We show that for the case of Higgs boson production, the approximate N3LO transverse momentum distribution amounts to a correction of a few percent with respect to the NNLO result with a reduction in the scale dependence.