Event topology dependence of $J/\psi$ production in proton+proton collisions at $\sqrt{s} = 13$ TeV with ALICE at the LHC and Study of elliptic flow in heavy-ion collisions using event shape and machine learning techniques

Studies related to heavy-ion collisions at the most powerful particle accelerators in the world, the Large Hadron Collider (LHC) at CERN, Switzerland, and the Relativistic Heavy Ion Collider (RHIC) at BNL, USA, have primarily focused on the creation and properties of the primordial matter consisting quarks and gluons. This extremely dense and hot state of thermalized partons is also known as quark-gluon plasma (QGP). Due to the shorter lifetime of QGP, experiments rely on several indirect signatures that hint towards the formation of QGP in ultra-relativistic collisions of nuclear matter. While the formation of QGP has been established for a long time in heavy-ion collisions, its presence in small collision systems still needs to be determined. However, recent measurements of heavy-ion-like behavior in high-multiplicity pp collisions at the LHC have drawn the attention of the heavy-ion physics community. The appearance of ridge-like structures and the enhancement of strangeness add to these speculations. Increased production of strange hadrons can only be explained via forming a strongly interacting medium at thermal and chemical equilibrium. To determine whether the underlying physics processes involved in the strangeness production can also be probed with topological event selection instead of the average charged-particle multiplicity, a relatively new event shape classifier has been introduced at the LHC, known as the transverse spherocity ($S_0$). This event-shape observable can decouple the jet-dominated events from the events with spherical soft emission of particles. The first event is called the jetty type, and the latter is called the isotropic type. Jetty events result from enhanced contributions of perturbative QCD processes; however, isotropic events arise due to the interplay of several soft QCD processes, such as the multi-parton interactions and the initial and final state radiations. It is found that the production rates of strange particles are slightly higher for soft isotropic events and highly suppressed in hard jetty events. This supports the hypothesis that in high-multiplicity pp collisions, heavy-ion-like effects such as strangeness enhancement and radial flow are manifested in the isotropic events. Thus, transverse spherocity can separate events based on azimuthal topology and control heavy-ion-like effects in high-multiplicity pp collisions. A similar study of strange hadron production with topological event selection can also be performed for the case of charm hadrons. In the presence of QGP, the yield of charmonium ($c\bar{c}$) is suppressed compared to the yield in the non-QGP scenarios in hadronic collisions. Therefore, studies involving charm hadrons with different topological event selections can help us understand its production mechanism and constrain various phenomenological models. Additionally, it can help us understand the observed heavy-ion-like effects in isotropic events in high-multiplicity pp collisions at the LHC. With these motivations, this analysis measures the $p_{\rm T}$-differential yield of inclusive $J/\psi$ as a function of transverse spherocity in high-multiplicity pp collisions at $\sqrt{s} = 13$~TeV with ALICE. For this analysis, the reconstruction of $J/\psi$ is performed through the electromagnetic decay channel, $J/\psi \rightarrow \mu^{+}\mu^{-}$ , B.R.~=~($5.961 \pm 0.033)\%$ in forward rapidity, $2.5<y<4.0$, using the forward muon spectrometer. For the estimation of transverse spherocity, midrapidity tracklets $(|\eta|<0.8)$ are reconstructed using the Silicon Pixel Detector (SPD), which is the innermost central barrel detector in ALICE. The V0 scintillator detectors with a pseudorapidity coverage of $2.8<\eta<5.1$ (V0A) and $-3.7<\eta<-1.7$ (V0C) have been used for the estimation of event multiplicity. Such event shape-based analysis can also be implemented in heavy-ion collisions for different purposes. The appearance of strong transverse collectivity in non-central heavy-ion collisions is considered to be another signature of QGP. In non-central heavy-ion collisions, the initial spatial anisotropy gets converted into the final state momentum anisotropy during the medium evolution process and is reflected in the azimuthal momentum distribution of the charged particles. This is quantified as the anisotropic flow coefficients. To study the effect of topological event selection on the anisotropic flow coefficients, we implement transverse spherocity-based event shape analysis in heavy-ion collisions. Using transverse spherocity as an event shape tool, this study will complement the current event shape approach based on flow vectors in heavy-ion collisions. We report an extensive study of transverse spherocity dependence of elliptic flow of charged particles in Pb--Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$~TeV using a multiphase transport model (AMPT). The elliptic flow for identified light-flavor hadrons and their number-of-constituent-quark scaling are also investigated in different event classes using transverse spherocity at RHIC and LHC energies. This study implements the two-particle correlation method to extract the transverse momentum differential elliptic flow coefficients. The two-particle correlation method helps in removing substantial nonflow from the calculation using a relative pseudorapidity cut between the particle pairs. Over the years, special attention has been given to the theoretical understanding of elliptic flow by modeling the medium evolution through relativistic hydrodynamics and various transport models. From the experimental side, the standard event plane method or the complex reaction plane identification method, the multi-particle correlation, and the cumulant method are usually followed to estimate elliptic flow. For the first time, we implement a feed-forward deep neural network to estimate the elliptic flow coefficient from the final state particle kinematics in heavy-ion collisions. The flow coefficients are embedded in the final state multi-particle correlations; hence, a deep neural network can be trained on simulated data to learn these correlations and efficiently measure the flow coefficients. The machine learning (ML) model is trained on simulated minimum bias Pb--Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$~TeV using the AMPT string melting model. After successful training, the same ML model is applied across several collision systems at RHIC and LHC energies. Since elliptic flow has several dependencies, such as centrality, transverse momentum, particle species (or mass), and collision energy, it is interesting to explore the prediction capability of the ML model in these sectors. The model predictions for the elliptic flow of light-flavor hadrons and the number-of-constituent-quark scaling depicting the partonic level collectivity are also covered. These results from the ML model are compared to experimental findings, wherever possible.