CERN Accelerating science

Quark-Gluon Plasma (QGP) is the deconfined state of strongly interacting mater, predicted by Quantum Cromodynamics (QCD), which is expected to exist in the early stages of evolution of the Universe, just after the Big-Bang. To access information about QGP; such as formation, evolution, composition etc., it is impossible to go back to the early stages of the Universe. A similar environment can be created in the laboratory by ultrarelativistic heavy-ion collisions, where a deconfined state of matter is expected to be formed at high temperature and/or energy density. Quarkonia, the bound state of heavy- quarks ($charm$ or $bottom$ quark) and its corresponding anti-quark, constitute one of the most interesting probes of the QGP because of its early formation in the collisions and therefore experience the whole QGP evolution. Besides this motivation, the study of quarkonium production is very interesting since it can contribute to our understanding of QCD, the theory of strong interaction. The study of production of $charmonia$ ($c$$\bar{c}$) and $bottomonia$ ($b$$\bar{b}$) in hadronic collisions is an important testing ground for QCD. From the discovery of J/$\psi$($c$$\bar{c}$) meson in November 1974, till now, the understanding of its production mechanism is still an open problem to the scientific society. Although there are many theoretical models developed over the years, they are still not able to consistently reproduce the different physical observables such as the quarkonium production cross section, the transverse momentum distributions, and polarization within the same calculation framework. At the Large Hadron Collider (LHC), the study of event multiplicity dependent production of charmonium is a topic of high interest which is believed to give insight into the processes on the partonic level. In particular, it gives an opportunity to study the interplay between hard and soft mechanisms in particle production. Therefore, J/$\psi$ production versus multiplicity measurement at the LHC energies is extremely interesting and represents a crucial step forward in understanding the physics involved in quarkonium production processes, and provides the necessary understanding for the measurements in search of QGP in heavy-ion collisions. No doubt, J/$\psi$ is an unique candidate to probe the system formed in heavy-ion as well as pp collisions. But at the same time, one needs to understand the nature of phase transition in heavy-ion collisions to have a complete picture of QCD. Solenoidal Tracker (STAR) at Relativistic heavy-ion Collider (RHIC) experiment has measured net-proton fluctuation in beam energy scan (BES) energies and a first order phase transition has been predicted with critical point around $\sqrt{sNN}$ = 19.6 GeV. As STAR operates at finite temperature and baryon chemical potential (µ$_{B}$), we expect a finite amount of baryon stopping at these energies. In that case, it is necessary to understand the signature of critical point explicitly by disentangling produced and stopped baryons. Lastly, to understand the system formed is heavy-ion (or pp) collisions, a proper under- standing of the freeze out stages (hadronic phase) is highly needed. In such high multiplicity environments in heavy-ion and pp collisions, statistical model can be applied to study hadronic yield measurements and hence to draw the information about the freeze-out stages. It is believed that with local temperature fluctuations and long-range correlation, the system formed in heavy-ion and pp collisions may not acquire a thermal equilibrium. Therefore, a statistical model which describes the system away from thermal equilibrium, the Tsallis non-extensive stastistics, is a suitable choice to infer the properties of freeze-out in such systems. In this thesis, firstly, we study inclusive J/$\psi$ production as a function of charged-particle multiplicity density in pp collisions at center-of-mass energies of $\sqrt{s}$ = 13 TeV, obtained with the ALICE experiment at the LHC. This kind of study is complementary to that performed as a function of the collision centrality in heavy-ion collisions. Furthermore, the observation of long range, near-side angular correlations (ridge) in high-multiplicity pp collisions is an indication that pp collisions also exhibit collective (like) behavior as seen in heavy-ion collisions. The measurements of particle production as a function of the charged particle multiplicity in small systems provide a way to detect the possible presence of collective final state effects. The present analysis allows to search for these effects in events with a very high charged particle multiplicity. The study of J/$\psi$ production with multiplicity is highly important to shed light in this context. For the current study, J/$\psi$ mesons are measured at forward rapidity (2.5 < $y$ < 4), via their decay into muon pairs (µ$^{+}$µ$^{-}$), which are detected by the ALICE Muon Spectrometer. Whereas, charged-particle density has been estimated using Silicon Pixel Detector (SPD) at the mid rapidity ($\mid$$\eta$$\mid$ < 1.0). In the second part of the thesis, we have discussed a technique to disentangle produced and stopped protons to have a clear understanding of the net-proton fluctuation result of STAR experiment. Finally, the freeze-out properties have been studied using Tsallis non-extensive statistics.