CERN Accelerating science

The main goal of the Large Hadron Collider (LHC) is to understand nature at the fundamental level. Through LHC, one can also study the behaviour of matter at extremely high temperatures and densities. This can be achieved by the collision of ultra-relativistic heavy-ions where quantum chromodynamics (QCD) predicts the formation of a new state of matter called the quark-gluon plasma (QGP). QGP is a thermalized soup of quarks and gluons which is expected to be prevalent in the early stage of the Universe, after a few microseconds of the Big Bang. Historically, the proton+proton (pp) collisions were taken as baseline measurements for QGP production in heavy-ion collisions, as their system size is significantly smaller than that of the heavy-ion collisions. However, recent measurements of strangeness enhancement and ridge-like structure formation in high multiplicity pp events have opened Pandora's box, which raises the question about the viability of using pp collisions as a baseline for the QGP study. Studying the formation of a QGP-like medium in hadronic collisions will help us better understand the experimental data. Thus, it is crucial to approach this problem in a two-fold manner. Firstly, one needs to study the possibility of QGP droplet formation in ultra-relativistic high multiplicity pp collisions through various theoretical and phenomenological models. Secondly, we should look into the experimental data and study the necessary observables that can point us in a conclusive direction in this context. The study of thermodynamic and transport properties is of utmost importance in understanding the matter formed in ultra-relativistic collisions. Knowledge about the initial energy density ($\epsilon$) can tell us whether the system can be possibly deconfined or not. Similarly, the squared speed of sound ($c_{s}^{2}$) helps us to characterize the system. The mean free path ($\lambda$) on the other hand gives us information about the possible thermalization in a medium. The isothermal compressibility ($\kappa_{\rm T}$) can tell us about the system's deviation from a perfect fluid. Moreover, transport properties like shear viscosity to entropy density ratio ($\eta/s$) and bulk viscosity to entropy density ratio ($\zeta/s$) can tell us about the fluidity of the system. All these observables together can help us characterize the systems formed in an ultra-relativistic collision and can suggest whether there is a change in dynamics after a certain temperature. Additionally, one can study the jet transport parameter, which is related to jet quenching in the medium. Experimentally, jet quenching has not been observed in pp collisions. Thus, the study of jet transport parameter through various phenomenological approaches can bring essential insights. In this thesis, we take the well-established QCD-inspired color string percolation model (CSPM) and study various thermodynamic and transport properties, which help us to understand the system produced in hadronic and heavy-ion collisions. In addition, one can also explore the hadronic phase lifetime of the systems from low multiplicity pp collisions to most central heavy-ion collisions. Resonances can be used to study various phases of the hadronic and heavy-ion collision evolution. In this thesis, we estimate the hadronic phase lifetime using a nuclear decay-inspired toy model by using the resonance $K^{*}^{0}$ as a probe. We also use another resonance, $\phi$, to locate the QGP phase boundary. We fit the Boltzmann-Gibbs Blastwave function to the soft part of the transverse momentum spectra of $\phi$ and extract the thermal temperature and the average velocity. We finally estimate the effective temperature, which helps us understand how the system is formed in ultra-relativistic collisions. For the experimental part of this thesis, we have studied $\psi$(2S) polarization in pp collisions at $\sqrt{s}$ = 13 TeV with ALICE at the LHC. The study of polarization in hadronic collisions can help us to understand the production processes involved. There are various conflicting theoretical estimations for charmonia polarization, whereas the experiments show no polarization in pp collisions at $\sqrt{s}$ = 7 and 8 TeV. Thus, one must study charmonia polarization at a higher center of mass energy with better statistics to reach a formal conclusion. Moreover, polarization in pp collisions can be used as a benchmark for polarization studies in heavy-ion collisions where the effects of external magnetic field, initial angular momentum and the impact of QGP can be expected. We study the $\psi$(2S) through the dimuon decay channel with the help of the ALICE muon spectrometer. The polarization parameters can be extracted from the angular distribution of the dimuons. For our analysis, we chose two different frames of reference to remove the frame-dependent biases. Finally, we report our estimation and compare our results with various theoretical models. The primary objective of this thesis is to study and understand polarization of charmonia, specifically $\psi$(2S) meson, in pp collisions at $\sqrt{s}$ = 13 TeV with ALICE at the LHC. In addition, we take the phenomenological CSPM approach to study the matter formed in ultra-relativistic collisions. We also estimate the hadronic phase lifetime and locate the QGP phase boundary using resonances. This thesis is divided into five chapters. The organization of the thesis is as follows: \begin{itemize} \item {\bf Chapter 1} briefly introduces Quantum Chromodynamics, Quark-Gluon plasma and the physics of heavy-ion collisions. Moreover, the motivation for the thesis is also presented here. \item {\bf Chapter 2} discusses the color string percolation model. It gives the formulation of CSPM and then proceeds to estimate various thermodynamic and transport properties within the CSPM approach. In this chapter, we study the change in dynamics of the medium from hadronic to heavy-ion collisions, which can give us hints about the possible formation of QGP droplets in high multiplicity pp collisions. \item {\bf Chapter 3} is dedicated to studying the hadronic phase lifetime and how it can be estimated. It discusses how resonances can be used to probe different phases of heavy-ion collisions. Then, a detailed description of the Boltzmann-Gibbs blastwave function is given, which is used to fit the $\phi$ transverse momentum spectra to estimate the effective temperature, which gives information about the QGP phase boundary. \item {\bf Chapter 4} discusses the study of $\psi$(2S) polarization in pp collisions at $\sqrt{s}$ = 13 TeV with the ALICE experiment. We briefly introduce the ALICE experiment at LHC, mainly the muon spectrometer, which is used for our analysis. We then give a brief theoretical formulation of charmonia polarization. Then, we discuss our experimental methods to extract the polarization parameters. Finally, we report our results and compare with existing theoretical estimations. \item {\bf Chapter 5} summarizes our studies that have been done in this thesis with an outlook. \end{itemize}