Studies on particle production in proton-proton collisions at the LHC energies using ALICE-TOF and MC data

In the ultra-relativistic heavy-ion collisions, a de-confined state of strongly interacting quarks and gluons is expected to form. This state of matter is usually known as the Quark-Gluon Plasma (QGP) and is governed by the theory of Quantum Chromodynamics (QCD). Various experimental facilities at the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) and Large Hadron Collider (LHC) at the European Organisation for Nuclear Research (CERN) are realising and characterising the QGP state by studying different observables of nuclear collisions. Apart from the heavy-ion collisions, at the LHC, protons are also accelerated to the highest energies ever achieved in the laboratory. The increased energy of proton beams has opened up possibilities of producing large numbers of final-state particles (high-multiplicity events). For these events, the charged particle multiplicity becomes similar to those measured in peripheral heavy-ion collisions. Therefore, studies on the properties of the matter formed in these high-multiplicity pp collisions have become significantly important. Moreover, recent results from high-multiplicity events of p-Pb collisions at LHC energies reveal several collective behaviours reminiscent of those observed for the Pb-Pb collisions. Thus, it became important to investigate various observables of nuclear collisions in the high-multiplicity event of the pp collisions to have a deeper insight into the production mechanism of particles as well as the properties and evolution of the matter formed. The excellent particle identification capabilities of ALICE (A Large Ion Collider Experiment) sub-detectors over a wide range of transverse momentum provide scope to study various observables of heavy-ion collisions to have a better insight into the particle production mechanism and the properties of the matter created in such collisions. The time of flight (TOF) detector of ALICE can identify various primary particles, namely, pions, kaons, and protons at the intermediate transverse momentum region. Further, the application of statistical unfolding method on TOF data enables particle identification up to higher $p_{\rm T}$ regions than the usual particle identification technique using TOF. Another advantage of this method is that it is independent of any Monte Carlo information and simulation for what concerns the PID efficiency and contamination from different particles. Therefore, identifications of these particles with the TOF detector as a function of $p_{\rm T}$, applying statistical unfolding technique, are of immense significance. Recent results from high-multiplicity pp collisions at $\sqrt{s}=$~7~TeV and p-Pb collisions at $\sqrt{s_{NN}}=$ 5.02 TeV have shown several collective behaviours similar to that observed in heavy-ion collisions. These include mass-dependent hardening of $p_{\rm T}$ spectra, enhanced production of baryons over mesons at the intermediate $p_{\rm T}$, non-zero elliptic flow coefficients etc. In heavy-ion collisions, these results could be well explained by considering the hydrodynamic evolution of the system. However, for small systems like pp collisions, mechanisms responsible for the modification of the spectral shape of particles with mass, non-vanishing elliptic flow coefficient etc., have not been established yet. Therefore, more detailed studies on pp collisions for different multiplicity classes are crucial at the LHC energy. Moreover, previous studies on light flavour particle production were performed for different colliding systems, each at different collisions energy. In this thesis, pions, kaons and protons are identified with the Time-of-Flight (TOF) detector of ALICE in pp collisions at $\sqrt{s}=$~13~TeV using statistical unfolding technique and are studied as a function of $p_{\rm T}$ for different charged-particle multiplicity classes. This study will offer the unique opportunity to disentangle the effect of centre-of-mass energy from the multiplicity dependent studies. For the complete measurement of the $p_{\rm T}$ spectra, results of the TOF detector are also combined with the measurements performed with other detectors/analysis techniques such as ITS, TPCTOF, rTPC, kinks, etc. The $p_{\rm T}$ spectra of various identified particles, namely pions, kaons and protons, are observed to become harder with increasing multiplicity, and the effect is more pronounced for heavier particles like protons. The average transverse momentum ($\langle p_{\rm T} \rangle$) of the identified particle also shows centrality and mass-dependent hardening behaviour with multiplicity similar to those observed for the $p_{\rm T}$ spectra. Further, the p/$\pi$ ratio shows a depletion at low $p_{\rm T}$, enhancement at intermediate $p_{\rm T}$, and constant behaviour at high $p_{\rm T}$ with increased charged-particle multiplicity. These behaviour are qualitatively similar to those observed for the Pb-Pb collisions at the LHC energy, consistent with the picture of hydrodynamical evolution of the system with a common radial velocity. Moreover, the $p_{\rm T}$-integrated K/$\pi$ ratio increases with increasing multiplicity, whereas the p/$\pi$ ratio shows no significant evolution with increasing multiplicity for the pp collisions. The increasing behaviour of the K/$\pi$ ratio with multiplicity in heavy-ion collisions can be described by the enhanced production of strangeness or a reduced canonical suppression in larger freeze-out volumes. Moreover, the $p_{\rm T}$-integrated yield ratios of $K_s^0$, $\Lambda$, $\Xi$, $\Omega$ to pions increases with increasing multiplicity for pp collisions and the effect is found to be more pronounced for particles having larger strangeness content. However, no significant energy dependent evolution of these ratios could be observed. These particles ratios are found to follow a common trend and scale with the charged-particle multiplicity, rather than colliding systems and collisions energies. Understanding particle production mechanisms is yet another important motivation of nuclear collision studies. Usually, particles produced in such collisions exhibit fluctuations in number density in various phase-spaces, which are believed to occur due to different processes of particle production mechanism. This type of fluctuations is generally known as non-statistical or dynamical fluctuations and is much larger than the statistical one arising due to finiteness in particles' yield. Dynamical fluctuations mainly arise due to correlated emission of particles, which in turn, is related to various particle production mechanisms or/and a possible phase transition that occurs during the evolution of the system. Further, it has been reported that the correlated emission of particles may also occur due to a mechanism called colour reconnection (CR) between the partons. To better understand the collision dynamics, it therefore becomes essential to disentangle and analyse these dynamical fluctuations from the mixture of statistical and dynamical one. Among various available mathematical tools, the Scaled Factorial Moment (SFM) technique is a widely accepted one that can separate the dynamical fluctuations from the mixture of the two. Previous lower energies experimental results on SFM analysis of various systems starting from the e$^{+}$e$^{-}$ to heavy-ion collisions indicate a power-law growth of average scaled factorial moments $\langle F_{q}\rangle$ with decreasing phase-space bin width, or otherwise, with the increasing number of bins in which the phase-space is divided. Such behaviours are found to be a general characteristic of the experimental data. However, previous measurements on intermittent emission of charged particles were carried out mostly with passive detectors such as nuclear emulsion at relatively lower collisions energies for small and heavy-ion systems. No serious attempt has been made to investigate dynamical fluctuation using the scaled factorial moment technique at the LHC energies. In this investigation, an attempt has been made to explore the possibility of analysing dynamical fluctuations at the LHC energies in the light of the SFM technique with MC events generated with the \textsc{Pythia} Monash model. Further, the colour reconnection (CR) mechanism, implemented in \textsc{Pythia}, also found to explain several collective effects in the high-multiplicity pp events. Colour reconnection (CR) is a string fragmentation model, where the final partons are considered to be colour connected in such a way that the total string length becomes as short as possible, which in turn, results in correlated emission of final state particles. It is therefore very important to examine the contribution, if any, of the colour reconnection in the observed correlated emission of particle. In this present investigation, the SFM analysis of \textsc{Pythia} generated data, which incorporates the CR, is also carried out for pp collisions at $\sqrt{s}=$ 2.76, 7 and 13 TeV. An apparent increase in ln$\langle F_{q}\rangle$ with increasing lnM could be observed in one-dimensional pseudorapidity ($\eta$), azimuthal angle ($\phi$) and two-dimensional $\eta-\phi$ spaces of high-multiplicity pp events of $\sqrt{s}=$ 2.76, 7 and 13 TeV, indicating a clear intermittent type of emission of particles. On the other hand, no such intermittent type of emission could be observed in minimum bias pp collisions. The intermittency index ($\alpha_q$) is found to increase with increasing order of the moments q in all studied spaces of high-multiplicity pp events. Moreover, the strength of the intermittency index ($\alpha_q$) is observed to be more in two-dimensional (2D) $\chi(\eta-\phi)$ space and least in one-dimensional $\chi(\eta)$ space. However, intermittency indices are found to independent of collisions energy. Further, studies on anomalous dimensions d$_q$ show that it increases with increasing order of the moment q. This type of increasing behaviour of anomalous dimension with q suggests the multi-fractal nature of emission spectra and indicates the production of particle via cascading mechanism in the high multiplicity pp events. Moreover, studies on the exponent $\lambda_q$ indicate that such events exhibit a non-thermal phase transition like behaviour in 2D $\chi(\eta-\phi)$ space for q=q$_c$=4. This critical value of the order of the moment q$_c$ separates frequently occurring small fluctuations from rarely occurring large fluctuations. Further, studies with the colour reconnection (CR) mechanism in \textsc{Pythia} suggest that intermittency strength varies significantly with the variation of the strength of the CR, i.e. reconnection range (RR). With the increase of RR, a significant increase in the intermittent behaviour could be observed in comparison to default (RR = 1.8) and RR = 0.0 \textsc{Pythia} data. This increasing behaviour of intermittency is due to the fact that the increased strength of the colour reconnection produces more correlated emission of particles in these high-multiplicity pp events. A significant increase in anomalous dimensions ($d_q$) could be observed with the order of the moments q for RR=1.8 and 3.0, but not much variation in $d_q$ could be observed for RR=0.0. Moreover, the position of the $\lambda_q$ minimum is found to decrease to q=q$_c$=3.65 for the higher value of CR strength, i.e., RR=3.0 whereas, no minimum in $\lambda_q$ is evident for RR=0.0 data sets. Therefore, it is evident that the colour reconnection mechanism in \textsc{Pythia} has a significant effect on the observed intermittency and hence on the nonthermal phase-transition like behaviour in the studied high-multiplicity pp events. Nevertheless, the colour reconnection can not solely be attributed as the cause of observed intermittency in the \textsc{Pythia} generated pp data at $\sqrt{s}=$ 2.76, 7 and 13 TeV.