Measurement of electroweak-boson production in p$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 8.16 TeV with ALICE

The matter that surrounds us is made of quarks, forming bound states through the exchange of gluons. These interactions are described by the quantum chromodynamics (QCD) theory. Similarly to regular matter, this quark matter can be found in various states that one can depict by means of a phase diagram. The exploration of this diagram, a necessary step for the understanding of QCD and quark matter, is done in the laboratory by means of heavy-ion collisions (HIC). In these studies, it is of utmost importance to have a precise knowledge on the initial state of the collision, as to disentangle the initial state effects from the effects occurring at later stages. This thesis aims at providing information on the initial state through the measurement of the electroweak-boson production in proton-lead (p$-$Pb) collisions. Indeed, the production of these hard processes is directly dependent on the internal structure of the colliding ions, represented by the nuclear parton distribution functions (nPDF). The bosons are detected via their muonic decay channel, such that the whole process is independent from the strong force, and the information on the initial state reach the detector without being affected by the surrounding medium, if any. This document presents the measurements of the Z$^0$- and W$^\pm$-boson production in p$-$Pb collisions at a centre-of-mass energy $\sqrt{s_{\rm NN}}$ = 8.16 TeV with ALICE. The results are reported and discussed within the scope of their comparison with similar measurements from other LHC Collaborations, at different energies, or with theoretical calculations from different recent nPDF models.