Precision QCD at the LHC: from the structure of the proton to all-order resummations

Experiments at the LHC are collecting a wealth of data with an unprecedented level of precision. As a consequence, the theoretical error is now starting to lag behind the experimental one, and a ceaseless effort is required to reduce the theory uncertainty to match the precision of the data. At hadron colliders, QCD predictions are obtained by convoluting perturbative parton-level results with non-perturbative PDFs, whose precise determination is crucial to reach percent-accurate theoretical predictions. At the parton level, cross sections are obtained through a perturbative expansion in the strong coupling. In some cases, large terms appear at all orders and spoil the convergence of the series. The perturbative description is rescued by resumming the series to all orders, thereby making theory calculations accurate in regions where a fixed-order treatment is not sufficient. In this thesis I first present two global PDF sets where fixed-order calculations are supplemented by threshold and high-energy resummation, respectively. In the first case, it is found that including resummation into PDFs can compensate for the enhancement in the partonic cross sections, with implications for high-mass resonance searches. In the second case, resummation quantitatively improves the description of the HERA structure functions, thus providing evidence of the onset of a new dynamical regime of QCD in the HERA data. I then focus on Higgs production in gluon fusion. The effect of threshold resummation on the total cross section is found to significantly improve the convergence of the perturbative series and to provide a robust method for estimating missing higher order uncertainty. Finally, I present predictions for the Higgs transverse-momentum spectrum both in the inclusive case and within fiducial cuts, exploiting a novel approach where transverse-momentum resummation is performed in direct space.