Mapping the Phase Diagram of Quantum Chromodynamics via Fluctuations

An intriguing question about the phase diagram of QCD is the existence and the location of the critical point on the boundary between the two phases – the hadron gas and the quark-gluon plasma. Heavy-ion collisions provide a unique opportunity to look for signatures of this critical point via the event-by-event fluctuations of particle multiplicities. In order to make conclusive inferences from the experimental data, we need a theoretical framework to connect QCD thermodynamics to the particle spectra and correlations observed by the detectors. In this thesis, I use quantum-field-theoretic techniques to develop necessary ingredients to describe the thermodynamics, dynamics, and freeze-out of fluctuations in such a framework. In the first part of the thesis, we use universality of critical phenomenon and the lightness of physical quark masses to deduce certain non-trivial scaling features of the QCD equation of state (EoS). In the second part of the thesis, we demonstrate how slowing down near the critical point affects the growth of hydrodynamic fluctuations relative to the equilibrium expectations obtained using the EoS. In the final part, we propose a generalization to the half-a-century old Cooper-Frye freeze-out procedure to convert the fluctuations of hydrodynamic densities into particle correlations based on the universal maximum entropy principle. Applying the procedure, we derive relations to obtain important phenomenological constants that determine the magnitude of observed particle multiplicity fluctuations directly in terms of the QCD EoS.