Study of the $\rm{J}/\psi$ production in pp collisions at $\sqrt{s}$ = 5.02 TeV and of the $\rm{J}/\psi$ production multiplicity dependence in p-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 8.16 TeV with ALICE at the LHC

The ALICE experiment at CERN probes the state of hot and dense QCD matter created in ultrarelativistic heavy ion collisions - the Quark Gluon Plasma (QGP). Due to its short lifetime, the QGP can be studied only via its signatures. The suppression of $\rm{J}/\psi$ was proposed as a proof of formation of the deconfined medium. Nevertheless, it became clear that the real picture is far more complex as there are other competing mechanisms affecting the $\rm{J}/\psi$ production. To understand which effects acting on the $\rm{J}/\psi$ production in nucleus-nucleus collisions truly stem from the presence of the QGP, ALICE also studies the production of $\rm{J}/\psi$ in pp and p-Pb collisions. The QGP is expected not to form in these systems. Furthermore, measurements of the $\rm{J}/\psi$ production in p-Pb collisions can unveil information on the effects originating from the binding of the nucleons in the nucleus, referred to as the cold nuclear matter effects (CNM). The objective of this thesis is to study the production of $\rm{J}/\psi$ at forward rapidity with the ALICE Muon Spectrometer. The inclusive $\rm{J}/\psi$ production cross section in pp collisions at $\sqrt{s}$ = 5.02 TeV, and its dependence on $\pt$ and rapidity, were examined and compared with theoretical calculations as well as measurement at other LHC energies. The data are well described by a sum of pQCD calculations for prompt and FONLL calculations for non-prompt contribution. The multiplicity differential $\rm{J}/\psi$ production was studied in p-Pb and Pb-p collisions at $\sqrt{s_{\rm{NN}}}$ = 8.16 TeV, as well as its mean transverse momentum. The measurement shows a rapidity dependent behaviour of relative $\rm{J}/\psi$ yields. The $\rm{J}/\psi$ mean transverse momentum on the other hand is identical in the two measured rapidity intervals. The new analysis increased the precision and extended the measurement to higher multiplicities compared to previous measurement at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV. We find that both relative yields and relative $\ave{\pt}$ are independent of centre-of-mass energy