CERN Accelerating science

The ALICE (A Large Ion Collider Experiment) detector at the Large Hadron Collider (LHC) experiment at CERN has been developed to study the hot-dense deconfined state of quarks and gluons, named Quark Gluon Plasma (QGP), which is expected to be created due to the collisions of heavy ions in the ultra-relativistic energies. It has not yet been possible to probe the QGP directly due to its extremely short life time and microscopic volume. However, a technique, called \enquote{Femtoscopy}, has been developed to measure the space--time dimensions of the hot-dense medium using the momentum correlations of two identical or non-identical particles. The femtoscopic analysis of the correlation functions of charged pion-kaon pairs in 0$-$5\% to 70$-$80\% central Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV in ALICE experiment at the LHC is presented in this thesis. The spherical harmonics representations of the correlation functions ($C^0_0$ and $Re C^1_1$) were studied in different centrality bins. The obtained correlation functions were analysed after taking into account a precise treatment of the non-femtoscopic background. The size of particle-emitting source ($R_{\rm out}$) and the emission asymmetry ($\mu_{\rm out}$) between pions and kaons were extracted from the background-minimised correlation functions. The $R_{\rm out}$ and $\mu_{\rm out}$ were observed to increase from peripheral to central events as the number of participants increased. The $\mu_{\rm out}$ was observed to be negative in all multiplicity classes, which indicates that pions are emitted closer to the center of the particle-emitting source than kaons, and this result is associated with the hydrodynamic evolution of the source. The results were compared with the predictions from THERMINATOR 2 model calculations where a set of additional delay in kaon-emission time were introduced to mimic the rescattering phase in the system. The values of $\mu_{\rm out}$ were observed to lie between the predictions for 0 and 1 fm$/c$ delay in kaon-emission time, indicating the presence of hadronic rescattering phase in the system along with the collective flow. However, in case of $R_{\rm out}$, the predictions underestimated the results in high-multiplicity events. Moreover, no beam-energy dependence of the femtoscopic parameters was found upon comparing the results with previously performed pion-kaon femtoscopic analysis in Pb--Pb events at $\sqrt{s_{\rm {NN}}}=2.76$ TeV. The femtoscopic parameters were also studied as the function of pair-transverse momentum ($k_{\rm T}$) and pair-transverse mass ($m_{\rm T}$) in different centrality classes. The $R_{\rm out}$ was observed to decrease with increasing $k_{\rm T}$ and $m_{\rm T}$ of the pair, indicating the presence of strong collectivity in the system. This thesis also includes the first ever measurement of $R_{\rm out}$ and $\mu_{\rm out}$ for the charged pion-kaon pairs as a function of pair-transverse velocity ($\beta_{\rm T}$). The $R_{\rm out}$ decreased with increasing $\beta_{\rm T}$ of the pair due to the collective effects. The magnitude of $\mu_{\rm out}$ was observed to decrease with increasing $\beta_{\rm T}$ in the high-multiplicity events due to the possible dominance of collectivity over the thermal velocities of the particles, however, it did not follow the similar trend in low-multiplicity events. The predictions from THERMINATOR model underestimated the measured values of $\mu_{\rm out}$ in the lower $\beta_{\rm T}$ region, opening up the possibility to check for the resonance contribution in the lower $\beta_{\rm T}$ region. The values of $\mu_{\rm out}$ were observed to be more closer to the predictions with no additional delay in kaon emission, compared to an additional delay of 1 fm/$c$. This thesis also reports the analysis of two-dimensional $\Delta\eta-\Delta\phi$ correlation functions of the charged-particle pairs in p--p collisions at $\sqrt{s}=7$ TeV and 13 TeV using PYTHIA 8.2 Monte Carlo event generator using color reconnection and rope hadronisation mechanisms. A ridge-like structure has earlier been observed in the long-range near-side region of the $\Delta\eta-\Delta\phi$ correlation functions for charged-particle pairs in heavy-ion collisions which is attributed to the presence of collective effects in the system. However, similar ridge-like structures have also been observed in the long-range near-side of $\Delta\eta-\Delta\phi$ correlation functions for charged-hadron pairs in high multiplicity p--p collisions as reported by the CMS and ATLAS experiments, where no QGP-like medium is expected to be formed. It is shown in this thesis that the color reconnection along with the rope hadronisation mechanism can mimic the features of collectivity and may produce the observed ridge-like structure in the long-range near-side region of $\Delta\eta-\Delta\phi$ correlation functions in high multiplicity p--p collisions without forming a hot-dense medium.