Determination of TMD parton densities from HERA data and application to pp processes

The topic of this thesis is a new approach to solve the DGLAP evolution equation to obtain not only the collinear Parton Distribution Functions (PDFs) but also the Transverse Momentum Dependent (TMD) PDFs (TMDs). The DGLAP equation is solved with the Parton Branching (PB) method, which allows a determination of kinematic variables at every branching and a construction of the TMDs in a large range in longitudinal momentum fraction $x$ and evolution scale $\mu^2$. The new method is validated against the semi-analytical solutions for the usual integrated parton distribution functions. Moreover, the PB method enables to study details of the parton evolution in a way which is not possible in standard methods. The PB method is applied to perform a fit to HERA H1 and ZEUS combined $F_2$ data using the xFitter package. The newly obtained TMDs are used for predictions of the $Z$ boson $p_{\bot}$ spectrum and a comparison with a measurement from LHC is performed. This thesis is a part of a broader approach to obtain predictions for many QCD observables where the hard process and higher order corrections follow the same TMDs. The method to solve evolution equations is a first step towards a consistent treatment of parton densities and the simulation of higher order corrections used in the predictions for high energy collisions of particles