## Event-by-Event Fluctuations of Charged and Neutral Kaons in Pb-Pb Collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV with ALICE at the LHC

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In ultra-relativistic heavy-ion collisions, the normal hadronic matter undergoes a transition to a deconfined phase of quarks and gluons. The produced partons interact with each other to form a strongly correlated system of QCD matter widely known as quark-gluon plasma (QGP). The primordial state of matter was believed to have existed for a few millionths of second shortly after the Big Bang. The matter which was created at very high energy density and temperature undergoes a collective expansion and eventually hadronizes. As per Lattice QCD, in the limit of zero baryo-chemical potential and high temperature, hadronic matter is expected to show a phase transition to a deconfined state where the effective mass of quark is zero. The chiral symmetry is expected to be restored. However, strong experimental evidence of the restoration of chiral symmetry in heavy-ion collisions is yet to be observed. Further, it is still a matter of speculation if the de-confinement phase transition and the chiral phase transition occur at the same temperature. Several experimental searches have been made in recent years to understand the de-confinement phase transition while the chiral phase transition is still a mystery for high energy physicists. The analysis of the event-by-event fluctuations of charged and neutral kaons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV is presented using the data collected by ALICE detector at the LHC. The analysis is carried out for different centrality classes (namely 0-10%, 10-20%, 20-40%, 40-60%, and 60-80%). The event and track selection cuts are used to obtain quality tracks. The combined information of TPC and TOF detectors are used to identify charged kaons. The $K_s^0$s are reconstructed from the invariant mass analysis of their hadronic decay channel $K_{s}^{0}\rightarrow \pi^{+}+\pi^-$. These are selected after implementing various topological cuts based on decay length, Cosine of pointing angle (Cos(PA)), Armenteros-Podolanski parameter, DCA to primary vertex, etc. The combinatorial background (due to random $\pi^{+}\pi^{-}$ pairs not originating from $K_s^0$ decay vertex) present in the selected mass range of $\pi^{+}\pi^{-}$ invariant mass distribution is accounted for by performing a detailed background correction. The yield of $K^{\pm}$s and $K_s^0$s are corrected for detector efficiency and limited detector acceptance. The statistical uncertainty is estimated using the sub sample method. The systematic uncertainties due to various sources are estimated for each centrality class. The effect of centrality bin width correction has also been studied. The obtained values of $\nu_{dyn}[K_s^0,K^{\pm}]$ are studied as a function of centrality. The measured $\nu_{dyn}[K_s^0,K^{\pm}]$ values monotonically decrease from peripheral to central collisions. The values are also compared to the expectation of HIJING and AMPT (3 modes) MC models. The estimated values from both the models show similar trend as a function of collision centrality and underestimate the measured values. The $\nu_{dyn}[ K^+, K^-]$ is also estimated and compared to the MC expectations as a function of collision centrality. The obtained values are negative and the magnitude decreases from peripheral to central collisions. The MC estimations also show a good agreement with the measured values. The observation is attributed to the charge conservation as charged kaons are predominately produced by pair creation. The scaled values of measured $\nu_{dyn}[ K_s^0, K^{\pm}]$ (scaled with the number of sources approximated as $\langle dN_{ch}/d\eta \rangle$) exhibit a violation of source scaling, however, the violation is not observed in MC models. The scaled $\nu_{dyn}[ K^{+} K^{-}]$ exhibits some collision centrality dependence, and the implied scaling violation is considerably smaller than that observed for $\nu_{dyn}[ K_s^0, K^{\pm}]$. The study indicates that the correlated production of neutral and charged kaons is different from the correlated production of oppositely charged kaons. A simple toy model simulation of the implementation of DCC like events is carried out to study the sensitivity of the $\nu_{dyn}$ observable in the presence of DCC like events at LHC energy. The $\nu_{dyn}[K_s^0,K^{\pm}]$ is estimated as a function of centrality for four different scenarios related to the size and number of DCC domains. For a given centrality class, $\nu_{dyn}[K_s^0,K^{\pm}]$ shows a monotonic increase with the size of the DCC domain and has a large magnitude for the events containing large DCC domains in this study. The values of $\nu_{dyn}[K_s^0,K^{\pm}]$ scaled by the mean of the number of kaons ($\sqrt{\langle N_{K_s^0} \rangle \langle N_{K^{\pm}} \rangle}$) and mean charged-particle multiplicity ($\langle dN_{ch}/d\eta \rangle$) are observed to be independent of the considered collision centrality class for the baseline measurement, where DCC fluctuations are not introduced. However, with the implementation of DCC fluctuations in the MC model, the scaled values are no longer invariant with centrality classes but sharply increase for most central collisions. The scaled values of the MC (containing DCC fluctuations) are consistent with the ALICE measurement for $\nu_{dyn}[K_s^0,K^{\pm}]$. The mechanism of particle production in high energy hadronic and heavy-ion collisions are studied using different phenomenological approaches. The first approach involves a two-component Glauber model, which is used to describe the contribution of hard and soft processes towards particle production in heavy-ion (Au-Au and Pb-Pb) collisions. The model describes the charged particle multiplicity density and the transverse energy density quite well. It is observed that the fractional contribution of hard processes increases with an increase in beam energy. A pairwise ratio of multiplicity densities for two different energies is obtained for similar $\langle N_{part}\rangle$ values. A scaling observed for the pairwise ratio indicates that the observed trend is due to the contribution from the hard scattering component and the energy difference while the same is not observed for transverse energy densities. The second approach involves the study of the normalized moments of multiplicity distribution in pp collisions in the forward rapidity region using the Weibull model. Two different event classes, NSD (non-singly diffractive events) and INEL $>$ 0 (inelastic events having at least one charged particle for $|\eta|<$ 1.0) are considered in this study. The model describes the charged particle multiplicity distributions quite well. The higher order normalized cumulants and factorial moments (upto 5$^{th}$ order) are calculated from the extracted fit parameters in different event classes for various $\eta$ intervals. The normalized cumulants and factorial moments show an increasing trend with the increase in energy for all $\eta$ windows, however, the second order moments exhibit no beam energy dependence. The observed trend of the higher order moments with the beam energy suggests a strong violation of KNO scaling in forward regions, obtained for both NSD and INEL $>$ 0 event classes. The third approach involves the study of enhancement of strange particles in high multiplicity pp collisions using rope hadronization mechanism implemented in PYTHIA8 model. The measured strangeness enhancement in pp collisions at $\sqrt{s}$ = 7 TeV in ALICE is well described by the rope hadronization mechanism within the framework of color reconnection, while the values obtained without the effect of rope hadronization fail to describe the measured data. The values obtained from the rope hadronization without the color reconnection also fail to describe the data, which indicates that the color reconnection framework is needed with the rope hadronization mechanism to describe the enhancement in data. The observed enhancement of strange particle saturates at higher multiplicities and is independent of the collision energies.

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