Measurement of $R_{2}(\Delta\eta,\Delta\varphi)$ and $P_{2}(\Delta\eta,\Delta\varphi)$ correlation functions in pp collisions at $\sqrt{\textit{s}}$ = 13 TeV with ALICE at the LHC

ALICE (A Large Ion Collider Experiment) is a multi-purpose detector at LHC (Large Hadron Collider) designed to explore a hot and dense QCD matter known as quark-gluon plasma (QGP), which was believed to be formed after a few microseconds of the Big Bang. Correlation functions are used to study this new state of matter by analyzing the particles produced in ultra-relativistic high-energy collisions. In this thesis, the two-particle differential-number correlation function ($R_{2}(\Delta\eta,\Delta\varphi)$) and transverse momentum ($\textit{p}_{\rm T}$) correlation function ($P_{2}(\Delta\eta,\Delta\varphi)$) are used instead of other correlation functions because they do not rely on the detection efficiencies and mixed event background subtraction technique used in previous studies. The particle production mechanism, flow, diffusivity, jets, charge and momentum conservation, resonance decays, Bose-Einstein correlations, and other aspects of high-energy collisions were better understood using charge-independent and charge-dependent combinations of $R_{2}(\Delta\eta,\Delta\varphi)$ and $P_{2}(\Delta\eta,\Delta\varphi)$. Simulation studies of charge-independent and charge-dependent combinations of $R_{2}(\Delta\eta,\Delta\varphi)$ and $P_{2}(\Delta\eta,\Delta\varphi)$ correlation functions were performed using PYTHIA and HERWIG models in pp collisions at $\sqrt{\textit{s}}$ = 2.76 TeV. Unidentified ($h^{\pm}$) and identified ($\pi$$^{\pm}$, K$^{\pm}$ and p($\bar{p}))$ charged hadrons were selected in three different $\textit{p}_{\rm T}$ ranges ( 0.2 - 2.0 $\rm{GeV}/\textit{c}$, 2.0 - 5.0 $\rm{GeV}/\textit{c}$ and 5.0 - 30.0 $\rm{GeV}/\textit{c}$ ) to understand the soft and hard QCD processes. The shapes and strengths of $R_{2}$ and $P_{2}$ were compared to get a better understanding and modeling of the angular ordering of particles created by hadronization in jets, as well as a better description of the jet fragmentation functions of identified species at low momentum fraction ($z$). $R_{2}$ and $P_{2}$ were measured in pp collisions at $\sqrt{\textit{s}}$ = 13 TeV for unidentified charged hadrons ($h^{\pm}$) in the $\textit{p}_{\rm T}$ interval of 0.2 - 2.0 $\rm{GeV}/\textit{c}$. This work complements the recent ALICE measurements to gain a better understanding of the jet contribution and nature of collectivity in small systems. Both $R_{2}$ and $P_{2}$ have near-side and away-side correlation structures that are qualitatively similar but quantitatively different. In addition, for both charge-independent and charge-dependent combinations, like in the simulation work and the published ALICE results for p-Pb and Pb-Pb collisions, $P_{2}$ has a substantially narrower near-side peak than $R_{2}$. This work served as a baseline for p-Pb and Pb-Pb results, as they are sensitive to the interplay between the underlying event and mini-jets in pp collisions.