Hydrodynamic characteristics of the medium produced in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76\;\text{TeV}$ and $5.02\;\text{TeV}$ at the LHC using the ALICE setup

The finding that the medium produced in relativistic heavy-ion collisions, denominated as quark gluon plasma (QGP), behaves almost like an ideal fluid caused a flood of initiatives to try to determine their characteristics. Apart from the equation of state and the phase diagram, the most relevant characteristics of a fluid are its transport coefficients. The transport coefficients drive the evolution of the fluid in its return to equilibrium. The success of hydrodynamic models in reproducing experimentally measured values led to the proliferation of methods that extracted the transport coefficients of QGP from hydrodynamic simulations. Using models to infer transport coefficients incorporates an uncertainty inherent in the model chosen and the initial conditions with which the simulation begins. The objective of this thesis is to extract the transport coefficients of the QGP directly, from experimental measures, using two-particle momentum components correlations. Two-particle correlations have emerged as one of the best tools to characterize particle production and to study the dynamics of heavy-ion collisions. Two-particle correlations that usually appear in the experimental measures are two-particle number correlations. However, when it comes to characterizing the transport properties of QGP, it is the correlations of the components of the momentum that are relevant, although their experimental presence is still scarce. Gavin et al. proposed a two-particle transverse momentum correlator to extract the specific shear viscosity, $\eta/s$, of QGP and, latter, to extract its relaxation time. Dobado et al. proposed a two-particle transverse momentum energy correlator to extract the specific bulk viscosity, $\zeta/s$, of QGP. This thesis focuses on the extraction of the two-particle transverse momentum correlator as a function of the relative angular separation. The measurement of the charge independent correlator in lead--lead, Pb--Pb, collisions is made for the first time at LHC energies. The measure of the charge dependent correlator in Pb--Pb collisions, and of both correlator versions, charge independent and charge dependent, in proton--proton, pp, collisions and in proton-lead, p--Pb, collisions is the first being made. The correlator is parameterized using a bidimensional multi-component model, new for this correlator, to capture its main characteristics. The charge independent correlator behavior is compared with results at RHIC energies and with results from other two-particle correlators measured at LHC energies. Likewise, the evolution with the collision characteristics of both versions of the correlator are compared with predictions from theoretical models implemented in event generators. None of the models reproduce the richness of nuances presented by the correlator, which allows to set constrains on the theoretical models used by these generators. The characteristics of the medium affect the scope of the effects of its fluctuations, i.e. the extent of the transfer of these fluctuations between neighbor fluid cells. The effects of the transfer of the transverse momentum fluctuations are manifested in the shape of the two-particle transverse momentum correlator, and their extent, in its width. Using the evolution with the characteristics of the collision of the two-particle transverse momentum correlation longitudinal width, a value $\eta/s=0.066\pm0.012$ has been extracted. The value is in the scope of those extracted by using model simulations although somewhat lower than the theoretical limit $1/4 \pi$. On the other hand, the analysis of the correlator in small systems, \pp and \pPb, has allowed the extraction of a longitudinal width that does not vary with the characteristics of the collision, which allows the correlator to be qualified as sensitive to the formation of the QGP. The extensive analysis of the two-particle transverse momentum correlator has allowed to verify its sensitivity to the transverse momentum fluctuations transfer processes, differing from that of other two-particle correlators. It has been found how this sensitivity allows to set constrains on how the physics of heavy-ion collisions processes are implemented in event generators. Likewise, the sensitivity of the correlator has allowed to establish differences between heavy-ion systems and small systems, at a time when the minimum size of a drop of QGP is in question. The longitudinal behavior of the correlator has allowed the extraction of a value of $\eta/s$ which, although due to the nature of the method, implies convolution throughout the entire life of the system, it comes, for the first time at LHC energies, directly from measured data. The experimental measure of the transverse momentum correlators is in its dawn and the results of this thesis will contribute to give it a considerable boost.