Periodic Reporting for period 1 - ParDHonS_FFs.TMDs (Parton Dynamics in QCD Hadron Structure: collinear FFs and unpolarized TMDs) Reporting period: 2018-09-01 to 2020-08-31 Summary of the context and overall objectives of the project Nucleons, protons and neutrons, are the building blocks of all nuclei, and hence of most of the visible matter in the Universe. Understanding their fundamental structure and dynamics in terms of their partonic constituents – quarks and gluons – is currently one of the main challenges in hadronic physics. Such an understanding is encapsulated in the Standard Model (SM), in which Quantum Chromodynamics (QCD) is the field theory that describes the strong interaction of quarks and gluons. Because energy grows with separation between colour charges (a fundamental characteristic of quarks and gluons), they cannot exist in isolation, but only in neutral colour combinations called hadrons, among which are nucleons.Nucleons are probed in scattering experiments whereby they are bombarded with high energy beams made of other particles (leptons or protons). The analysis of the remnants of these collisions allow scientists to derive information on the distribution of quarks and gluons in protons. This information is encapsulated in Parton Distribution Functions (PDFs) and in Fragmentation Functions (FFs). They encode the probability that a given quark or gluon carrying a given fraction of the parent nucleon’s momentum is struck from the incoming or outgoing nucleon, respectively.This Action aimed at achieving ultimate precision of PDFs and FFs, possibly to match the requirements for discovery at current colliders. One of such colliders, the Large Hadron Collider, is the most powerful particle accelerator ever built by mankind. The determination of PDFs and FFs cannot be reliably achieved from first principles. Instead, they are modelled by means of some parametrisation, which is then optimised by comparing the PDF-dependent prediction of a variety of hadronic cross sections to their actual measurements, a procedure that is called (global) QCD analysis (or fit). In this sense, PDF/FF determinations can be labelled generally as a nonlinear regression problem, whereby one has to learn a set of functions from data. This goal was achieved by developing and utilising innovative artificial intelligence and machine learning techniques, an essential part of the research plan. These techniques allow one to achieve a statistically sound and faithful representation of PDF/FF uncertainties, a feature which is crucial for a characterisation of the SM and for discoveries beyond it. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far The objectives identified in the Action were two: 1) improving the understanding of the hadronisation of partons, by means of an accurate determination of FFs; 2) improving the determination of PDFs, by means of refining the theoretical framework to include higher-order QCD and electroweak corrections, of characterising theoretical uncertainties, and of extending the input data set. Both these objectives have been successfully achieved.Concerning objective 1), three complementary pieces of software were developed to realise the fast computation of the hadronic observables used to extract FFs: APFEL (https://apfel.hepforge.org/ download.html) APFEL++ (https://github.com/vbertone/apfelxx) and NangaParbat (https:// github.com/vbertone/NangaParbat). A global determination of collinear FFs of charged pions and kaons from all available data will be released by the end of 2020. Concerning objective 2) the ER developed PineAPPL, a library that produces fast-interpolation grids of physical cross sections, computed with a general-purpose Monte Carlo generator, accurate to fixed order in the strong, electroweak, and combined strong–electroweak couplings. The PineAPPL library is publicly available from the following link: https://zenodo.org/record/3992765. Furthermore, the ER devised a method to characterise theory uncertainties in PDF fits, and applied it to nuclear uncertainties and to missing higher-order uncertainties. Finally, the ER studied the impact of single-top t-channel, single- and di-jet production and charm-tagged neutrino DIS on PDFs. This work led to three publications. PDF sets incorporating these data sets are publicly available from the NNPDF web page (http://nnpdf.mi.infn.it).All the available results produced as part of this Action are available in terms of publicly available scientific publications and pieces of software, as outlined above. Results have been disseminated through eleven talks delivered at international conferences and workshop. Due to the Covid pandemic, however, these had to be drastically limited in 2020. Outreach and public engagement activities have also been pursued as complementary activities to the dissemination of results. In particular, the ER has joined the 2019 Nikhef Open Day, a one-day event that proposes scientific popularisation for children and young adults, and to the 2019 Nikhef final-year Jamboree, a two-day event that showcase, in an accessible and informal way, the various research lines currently pursued at Nikhef. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) This Action encompassed state-of-the-art research topics in hadron and particle physics, combined with cutting-edge statistical tools. All the results produced are original and the degree of accuracy and sophistication achieved are settling a new standard in the field. Some of the results obtained are unique. For instance, PineAPPL is the only available tool to compute fast-interpolation grids for hadronic observables accurate to next-to-leading order in the strong and electroweak couplings; the methodology to assess theoretical uncertainties in PDF fits, although still in its infancy, is pioneering (no other PDF fits that encompass such uncertainties have been determined so far); and the study of the impact of LHC data has included, for the first time, some processes which had never been investigated before. The scientific outcome of this Action is therefore world-class, it opens new avenues, and is expected to bring in further developments in particle physics phenomenolgy in the coming years.Because this Action focused on fundamental research, it has no tangible and immediate impact on economy and society. However, because of the high inter-disciplinarity of the advanced statistical and computational techniques developed in this Action, some indirect returns are foreseeable in the future. In particular, the relationship between the way in which the problem tackled in this Action was addressed is intertwined with data science, one of the big changers in the current socio-economic framework.