An event-by-event study of local fluctuations in multiparticle production at ultra-relativistic energies

Chapter 2: Details of the physics observables and methodology to determine these observables, studied in this thesis, for understanding the charged particle production and to characterise the medium formed in Pb−Pb collisions during RunII of the LHC operation are given in this chapter. Before that, a discussion on the QCD phase diagram and related concepts, with perspective to the observables under study is given. An overview of the QCD phase diagram, with a focus on the region of relatively high temperature and low chemical potential, where the QCD phase transition and the critical point are expected is given along with a review of different order parameters used to understand the quark-hadron phase transition. A system undergoing second order phase transition at the critical point exhibits scale invariance, fractal structures and self-similarity, due to long-range correlations. This behaviour can be described through scaling laws characterised by a handful of critical exponents, dictated by the universality class to which the phase transition belongs. An elaborate discussion on this is given followed by details on the intermittency analysis and analysis methodology for two dimensional study. Observables − NFM ($F_{q}$ ($M$)), fractal parameter ($D_{q}$), intermittency indices ($\varphi_{q}$), and scaling exponent ($\nu$) are all defined and the procedure to obtain these is also presented. Results and observations from the intermittency analysis of a few models and experiments (NA61, STAR) are also given.

Chapter 4: This chapter gives a detailed discussion on the analysis performed on the experimental data and event samples from the Monte Carlo event generators. At the outset, description of the datasets, event selection, filterbit cuts on tracks and techniques used to extract the clean data from the raw data is given. The intermittency analysis as described in Chapter 2 is performed on the generated and reconstructed Monte Carlo events from the HIJING and the Monte Carlo closure test so performed is discussed. Analysis results from various steps and cut study are given. M−scaling behaviour of the NFM ($F_{q}$), i.e., $ln (F_{q})$ vs $ln (M^2)$ behaviour, for the charged particles produced in the mid rapidity region in the full azimuth for different soft $p_{T}$ (transverse momentum) intervals is also studied. Scaling exponent ($\nu$), a parameter to quantify fluctuations of charged particle density in the spatial phase space extracted from the scaling of $ ln (F_q)$ with $ln (F_2)$ is studied for its dependence on the $p_T$ bin, $p_T$ bin width and centrality. Observations and results from this study are found to be in agreement with some models and theoretical predictions. Cut studies performed on data for its comparison with results from RunI (Pb−Pb, 2.76 TeV) are discussed in detail. Observations and results obtained from data are compared with that from HIJING event samples and PYTHIA8/Angantyr for Pb−Pb collisions at $\sqrt{s_{NN}}$ = 2.76 and 5.02 TeV.