Measurement of the J/$\psi$ elliptic flow in $\mathrm{Pb\mbox{-}Pb}$ collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV with the muon spectrometer of ALICE at the LHC

Extreme temperatures and energy densities produced in ultra-relativistic heavy-ion collisions at the Large Hadron Collider provide a unique opportunity to study the properties of matter. A phase transition of the hadronic matter to a deconfined medium of quarks and gluons, the Quark-Gluon Plasma (QGP), is predicted by QuantumChromodynamics and considerable theoretical and experimental efforts have been invested to study its properties. Among the prominent probes of the QGP, heavy quarks play a crucial role since they are created in primary hard-scattering processes, before the QGP formation, and their number is conserved throughout the partonic and hadronic phases of the collision. Bound states of heavy quarks – quarkonium (charmonium for ${\mathrm c}\bar{{\mathrm c}}$ and bottomonium ${\mathrm b}\bar{{\mathrm b}}$) provide remarkable probes of the medium. At LHC energies, experimental observations of quarkonium in A-A collisions are reproduced through two antagonist mechanisms: a sequential suppression of the quarkonium states, early suggested as a signature of the QGP, and quarkonium (re)generation by (re)combination of deconfined quarks. However, theoretical predictions carry large uncertainties and many unknows remain. The momentum space azimuthal anisotropy of charmonium production (referred as elliptic flow $v_2$) should help to clarify the picture and to constrain the model parameters. If charm quarks (re)combine in the medium into ${\mathrm c}\bar{{\mathrm c}}$ pairs, the J/$\psi$ originating from (re)combination should inherit their flow. Previous studies have shown first hints of a positive J/$\psi$ $v_2$ in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76 $TeV. This thesis focuses on the measurement of J/$\psi$ azimuthal anisotropy in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$TeV where a slightly stronger (re)generation component is predicted with respect to lower collision energies, and a factor of 3 more data were collected. The study of J/$\psi$ $v_2$ provides important information on the magnitude and dynamics of charmonium suppression and (re)generation mechanisms. In addition, it offers a unique insight on charm quark evolution and interactions in the expanding medium.