Event-by-event net-$\Lambda$ fluctuations in Pb-Pb collisions at $\sqrt{s_{NN}} =$ 5.02 TeV with the ALICE detector at the LHC

This dissertation documents the calculation of the cumulants of the net-$\Lambda$ multiplicity distribution in Pb-Pb collisions at $\sqrt{s_{NN}} =$ 5.02 TeV with the ALICE detector at the LHC so as measure, on an event-by-event basis, the effects of quantum number conservation during the phase transition of strongly interacting matter. The Quantum Chromodynamics (QCD) phase diagram depicts a phase transition from a deconfined quark-gluon plasma phase into confined hadronic matter. The quark-gluon plasma is created in ultra-relativistic heavy-ion collisions such as the heavy-ion collisions measured in ALICE, which stands for A Large Ion Collider Experiment. ALICE is a general-purpose, heavy-ion detector at the CERN Large Hadron Collider which focuses on QCD, the strong-interaction sector of the Standard Model. Called the QGP for short, the quark-gluon plasma only exists for a short time (10$^{-23}$ seconds), and at LHC energies, it is only slightly bigger than the size of a proton, making direct observation impossible. Despite this, the temperature and baryon chemical potential of the QGP formation can be indirectly characterized by linking theory (thermodynamic susceptibilities calculated in lattice QCD) and phenomenological models with observables created in the collision such as event-by-event net-particle multiplicity fluctuation measurements. In heavy-ion collisions, fluctuations can be as a result of inhomogeneities in the energy and baryon number deposition in the initial state or due to thermal fluctuations in the subsequent evolution of the system. The latter represents the fluctuations under investigation, particularly in the vicinity of a phase transition. Trivial fluctuations induced by the experimental measurement process such as volume fluctuation effects and baryon number conservation also exist and they are addressed in this analysis. The observables studied and documented in this dissertation are the first two cumulants of the net-$\Lambda$ distribution. In particular, the mean and variance of the net-$\Lambda$ distribution and their ratios were calculated and compared to statistical baselines to search for deviation, if any, from Poisson behavior. The pseudorapidity dependence of the ratio of the second cumulant of the net-$\Lambda$ distribution to the sum of the mean of the $\Lambda$ and $\bar\Lambda$ distributions was also calculated to explore global conservation laws. The deviation from Poisson behavior found in the second cumulant is attributed to global baryon number conservation.