Phenomenology of Transverse Momentum Distributions in hadronic observables

One of the main aims of hadronic physics is to describe the internal structure of the nucleon in terms of its constituents, quarks and gluons (collectively called partons). A lot of information has been collected over the past forty years concerning the distribution of partons in one dimension, encoded in the well–known collinear Parton Distribution Functions (PDFs). In the last years, we are extending the study to the distribution of partons in full three–dimensional momentum space, encoded in the so–called Transverse Momentum Distributions (TMDs). This thesis describes a suite of computing tools for the extraction of TMDs, entirely developed by our research group over the last three years, and presents a state–of–the–art extraction of these functions from experimental data. The thesis first summarizes the theoretical framework for the extraction of TMDs in two types of scattering processes: the Drell–Yan process (pp → llX), and Semi—Inclusive Deep Inelastic Scattering (lp → lhX). The thesis then presents the numerical framework we implemented to study TMDs. It consists of a suite of tools, which we called NangaParbat. It is written in C++ and is publicly available. NangaParbat can be used to extract TMDs, to produce grids for TMDs and TMD–related observables, and to have easy access to TMD extractions, through interpolation and convolution tools. Therefore, NangaParbat can be a very useful asset for the scientific community working on the phenomenology of hadronic physics. Finally, the thesis presents our most recent extraction of TMDs, which reached the unprecedented accuracy of Next–to–Next–to–Next–to–Leading Logarithm (N3LL). We used Drell–Yan data from various experiments, including those at the LHC, and spanning a wide kinematic range. We obtained a very good description of both the shape and the normalization of the data without introducing normalization coefficients as it was done in the literature before: this result was made possible only through the unsurpassed perturbative accuracy of the fit and the optimized numerical and analytical integration techniques that we used.