RESUMMATION AND MACHINE LEARNING TECHNIQUES TOWARDS PRECISION PHENOMENOLOGY AT THE LHC

The present thesis focuses on three distinct yet complementary areas in QCD. The first area concerns the resummation of large logarithmic contributions appearing in transverse momentum distributions. In particular, we focus on the hadroproduction of colour singlet final states such as Higgs boson produced via gluon fusion and the production of a lepton-pair via Drell--Yan mechanism. We present phenomenological studies of a combined resummation formalism in which standard resummation of logarithms of Q/pT is supplemented with the resummation of logarithmic contributions at large x. In such a formalism, small-pT and threshold logarithms are resummed up to NNLL and NNLL* respectively. The second area concerns the construction of an approximate NNLO expression for the transverse momentum spectra of the Higgs boson production by exploiting the analytical structure of various resummed formulae in Mellin space. The approximation we construct relies on the combination of two types of resummations, namely threshold and high-energy (or small-x). Detailed phenomenological studies, both at the partonic and hadronic level, are presented. And finally, the third area concerns the a posteriori treatment of Parton Distribution Functions (PDFs), specifically the compression of Monte Carlo PDF replicas using techniques from deep generative models such as generative adversarial models (or GANs in short). We show that such a GAN-based methodology 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. The possibility of using this methodology to address the problem of finite size effects in PDF determination is also investigated.