Inclusive J/ψ production in pp and Pb-Pb collisions at forward rapidity at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV in ALICE at the LHC

High-energy hadron-hadron collisions are considered as a useful tool which helps us to understand particle production mechanisms with the help of the Quantum Chromodynamics (QCD) theory. At extremely high temperature and/or high density, ordinary matter undergoes a phase transition, predicted by QCD, and reaches a new phase of matter in which quarks and gluons are deconfined. This new phase of QCD matter is called quark-gluon plasma (QGP). In laboratory, ultra-relativistic heavy-ion collisions are used to satisfy the temperature and density condition in order to recreate the QGP. To probe and characterize the QGP properties, many observables have been proposed. In particular, charmonium, made of a pair of charm and anticharm quarks, is one of the proposed probes because the $c\bar{c}$ are produced at the initial stage of the heavy-ion collision and can cross and interact with the hot and dense formed medium. Besides, charmonium production involves hard and soft energy scales and therefore provides an opportunity to study both perturbative and non-perturbative aspects of the QCD. In this manuscript, we report on inclusive J/$\psi$ production at forward rapidity in pp and Pb-Pb collisions measured at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV in A Large Ion Collider Experiment (ALICE) at the LHC. The measurements are performed in the J/$\psi$ dimuon decay channel with the muon spectrometer. The high-statistic pp data sample and the full Pb-Pb data sample of the LHC Run 2 period are analyzed and those datasets permit to obtain more precise results than the earlier published results. The J/$\psi$ production cross section in pp collisions that serves as a reference for the measurements in Pb-Pb collisions is presented as a function of the transverse momentum ($p_\mathrm{T}$) and of the rapidity ($y$). The J/$\psi$ nuclear modification factor, defined as the ratio of the yield in Pb-Pb collisions to the cross section in pp collisions scaled by the nuclear overlap function, is shown as a function of $p_{\mathrm{T}}$. The measurements are extended in $p_{\mathrm{T}}$, with respect to previous results, up to 20 GeV/$c$. The J/$\psi$ production cross section measured in pp collisions is compared to different theoretical calculations based on non-relativistic QCD (NRQCD) model and on colour evaporation model (CEM). In Pb-Pb collisions, a comparison between the measured J/$\psi$ nuclear modification factor and the theoretical calculations based on transport and on statistical model is presented.