Event shape and Multiplicity dependence of $\phi$ meson production in Proton+Proton collisions with ALICE at the LHC and Characterization of Heavy-ion collisions using Relativistic Kinetic Theory

From the ancient times, exploration of the unknown has been the intrinsic nature of Mankind, which is also one of the core principles of fundamental research in basic sciences. To explore the nature of the Universe, an engineering marvel, ``Large Hadron Collider (LHC)" was built at CERN, Geneva. One of the main goals of the LHC is to study the matter at high temperature and density where quantum chromodynamics (QCD) predicts the existence of quark-gluon plasma (QGP) in ultra-relativistic heavy-ion collisions. In central heavy-ion collisions, nucleons in the overlap regions (participants) undergo multiple collisions. These central events produce a large number of particles. Even though many of the observed particles are just the result of the fragmentations of pieces of the two nuclei which release some of the bound nucleons, at high incident energies considerable amount of particle creation occurs. While the particles created are mostly pions, the production of relatively heavy particles than pions and heavy flavor (strange and charm) quark matter also takes place. However, historically the pp collisions were considered as a baseline for the formation of QGP in heavy-ion collisions due to their significantly smaller system size compared to heavy-ion collisions. In pp collisions, it was expected that the final state particles are only the result of the fragmentations of pieces of the two protons. Recent multiplicity dependent measurements of identified particle production from the experiments at the LHC have revealed surprising discovery of QGP-like behavior, such as strangeness enhancement, flow-like pattern and double ridge structure in high multiplicity proton+proton (pp) collisions, which raise concerns whether pp collisions can be used as a proper benchmark for comparison with heavy-ion results to understand the formation of a medium with high temperature/energy density. These behaviours have important consequences in understanding the data from heavy-ion collisions at the LHC energies as one should consider the contribution of QGP-like effects in small systems. They open new directions for theoretical and experimental studies of small collision systems. While hydrodynamic calculations describe data qualitatively, other approaches suggest that these can be initial state effects. To understand the recent measurements, it is important to perform double differential studies of pp collisions with event shape observables and charged-particle multiplicity. Event shape observables like transverse spherocity, allow the possibility to separate the high and low number of MPI events to isolate the behavior of particles inside jets (hard processes) and pertaining to the soft processes. This result can help to understand more on the jet production, identified particle ratios (baryon to meson and strange to non-strange), double ridge structure and the steep rise of mean transverse-momenta of charged particles in small systems compared to large systems. A comprehensive differential study using event shapes would reveal interesting features, which could be exploited to improve models as well. Study of resonances containing strange quarks as a function of charged-particle multiplicity, would provide important contribution to the origin of QGP-like effects in pp collisions. Resonances are usually referred as the particles, which have higher mass than the corresponding ground state particle(s) with similar quark content. As hadronic resonances decay strongly, they have very short lifetime, $\tau \sim$ few fm/c. Before decaying, these particles can only travel upto few femto-meters, which is about the diameter of proton. The width ($\Gamma$) and lifetime ($\tau$) of the resonances are related by the Heisenberg's uncertainty relation, i.e. $\Gamma\tau = \hbar$. As the broad resonance states decay very shortly after their production, it can only be measured by reconstruction of their decay daughters in a detector. The typical lifetime of experimentally measured hadronic resonances ranges from 1.1 fm/c to 46 fm/c. Hadronic resonances are produced in the bulk of the expanding medium in heavy-ion collisions and they can decay while still traversing in the medium. The decay daughters may interact with other particles in the medium, which would result in suppression of resonances while their reconstruction, as the invariant mass of the daughters may not match that of the parent particle. This process is known as re-scattering. In other way, resonances can be regenerated as a consequence of pseudo-elastic collisions in the hadronic phase of the medium, which would result in enhancement of resonances. Resonances, with relatively higher life-time, might not go through any of the above mentioned processes. It may also happen that the re-scattering and re-generation processes compensate each other. Thus, the interplay of these processes makes the study of resonances in heavy-ion collisions more fascinating. Also resonances like, K*(892)$^{0}$ and $\phi$(1020) contain strange (or anti-strange) quarks, they can be used for a systematic study of the particle species dependence of the partonic energy loss in the medium. Also, recent results from LHC suggest that $\phi$ behaves like a particle with net strangeness of 1 or 2 in small systems. These observations open new directions for theoretical and experimental studies of pp collisions. So far, none of the models explain the recently discovered behaviors satisfactorily. The major objectives of the thesis are to understand the processes discussed above with the double differential (Event shape and Multiplicity) study of $\phi$ meson production with ALICE at the LHC. Also, we phenomenologically attempt to formulate a model to characterize the heavy-ion collisions using relativistic kinetic theory in the form of Boltzmann Transport equation using relaxation time approximation