PDF4LHC recommendations for LHC Run II

We provide an updated recommendation for the usage of sets of partondistribution functions (PDFs) and the assessment of PDF and PDF+$\alpha_s$uncertainties suitable for applications at the LHC Run II. We reviewdevelopments since the previous PDF4LHC recommendation, and discuss and comparethe new generation of PDFs, which include substantial information fromexperimental data from the Run I of the LHC. We then propose a new prescriptionfor the combination of a suitable subset of the available PDF sets, which ispresented in terms of a single combined PDF set. We finally discuss tools whichallow for the delivery of this combined set in terms of optimized sets ofHessian eigenvectors or Monte Carlo replicas, and their usage, and provide someexamples of their application to LHC phenomenology

The PDF4LHC21 combination of global PDF fits for the LHC Run III

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.Comment: 87 pages, 44 figures, 11 table

Introduction to deep inelastic scattering: Past and present

At a moment when many of the people attending the conference have not been involved in the early DIS experiments it could be interesting to review how the field of DIS has started and evolved since 45 years. I shall start to remind the heroic years at SLAC, followed by the eraof high precisions fixed target experiments before entering the new kinematic domain and its many surprises at HERA. I shall end by commenting where we are at present five years after the end of data taking at HERA