Abstract: Tremendous efforts have been made to understand the Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism, which led to the successful discovery of the Higgs Boson and the clarification of the
orgin of the mass of fundamental particles. However, it is often forgotten that the vast majority of visible matter is given by baryons,
which gain most of their mass dynamically within poorly known non-perturbative Quantum Chromo Dynamics processes. The best laboratory to study the underlying mechanisms of non-perturbative Quantum Chromo Dynamics is still given by the nucleon and the central question of how the macroscopic properties of a nucleon
like its mass, spin and size can be comprehensively decomposed into the microscopic description in terms of quarks, antiquarks and gluons remains still open.

A major part of the COMPASS-II program is dedicated to the investigation of Generalized Parton Distributions (GPDs), which aim for the most complete description of the partonic structure of the nucleon, comprising both, spacial and kinematic distributions. By including transverse degrees of freedom, a three dimensional picture of baryonic matter is created, which will revolutionise our understanding of what comprises 99 percent of the visible matter.

GPDs are experimentally accessible via lepton-induced exclusive reactions, in particular the Deeply Virtual Compton Scattering (DVCS) and Deeply Virtual Meson Production (DVMP). At COMPASS,
those processes are investigated using a high intensity muon beam of 160\,GeV/c together with a 2.5\,m-long liquid hydrogen target and an open field two stage spectrometer, to detect and identify charged and neutral particles. In order to optimize the selection of exclusive reactions at those energies, the target is surrounded by a new barrel-shaped time-of-flight system, which detects the recoiling target
particles.

A pilot run dedicated to the measurement of Generalized Parton distributions performed in 2012 allows for detailed performance studies of the new target time-of-flight system and for the worlds first measurement of the pure DVCS cross section at intermediate $x_{Bj}$. Within the concept of Generalised Parton Distributions the dependence of the DVCS cross section on the square of the four-momentum transfer to the target proton is closely related to the transverse size of the nucleon. The pioneering measurement carried out within this thesis will give a first evaluation of the transverse size of the nucleon as a function of the Bjorken scaling variable $x_{Bj}$ in the uncharted territory of
$10^{−2} < x_{Bj} < 0.2$

Deeply virtual compton scattering at CERN - what is the size of the proton?