Transverse momentum dependence in double parton scattering

Double parton scattering (DPS) is a mechanism in which two hard parton-levelprocesses take place in a single hadron-hadron collision. This can yield importantcontributions to search processes at the LHC, a prominent channel being like-sign leptonpair production via the production of two W bosons of equal charge in a double Drell-Yan process.The factorization theorems allow to write the DPDs cross-section in terms ofperturbatively computable hard scattering part, and non-perturbative objects calleddouble parton distributions (DPDs), which contain a lot of new information abouthadron structure at the quantum level, such as correlations between partons inpolarization, color, and momentum.In this thesis, we describe transverse-momentum dependence in the process ofproduction of two W bosons in proton-proton collision via double parton scattering.This requires so-called transverse momentum-dependent double parton distributions(DTMDs). In the first part of the work, we express DTMDs in the transverse-positionspace, Fourier conjugate to the transverse momenta, and discuss their structure andevolution equations – the renormalization group- and rapidity evolution (Collins-Soper)equation.After that, we identify the regions, where perturbative methods can be used toconnect DTMDs to simpler objects, such as collinear double parton distributions(DPDFs) and single parton distributions (PDFs). These are called the “large-y”, and“short-distance” regions, and are described in the later part of the work. We describethe initial conditions for DPDs in both regions and the corresponding form of theCollins-Soper equation. We analyze the position-space dependence of DTMDs in bothapproximations and their corresponding uncertainties due to the perturbative matchingto either DPDFs or PDFs.Later, we discuss the non-perturbative input required in the computation andpresent a scheme needed to i) extrapolate the perturbatively computed approximation ofDPDs to non-perturbative distances, and ii) interpolate between the two approximationsvalid in different subregions of the phase space. In the final part, we computethe contribution to the differential cross-section of the considered process in eachregion independently, identify the most important contributions, and discuss theiruncertainties due to the modeling of DTMDs and the rapidity evolution kernels. Finally,we combine all of the contributions and discuss the final results for the differential cross-sections.