This dissertation presents a theoretical study of soft hadron production in relativistic heavy-ion collisions. The aim is to explore the principles governing the hadronization of the expanding quark-gluon plasma (QGP) fireball, and to understand its properties. Strange hadron production and strangeness abundance in the QGP help us to look before the instant of hadronization. Consideration of entropy and charm production further enhances the reach back in time to the first instances of the heavy ion collision. Much of the ongoing effort is to demonstrate the validity of a QGP hadronization model which describes the particle production data accurately and thus allows us to carry out the above research program. We perform a centrality dependent study of multistrange hadrons from Au-Au collisions at √SNN = 62.4 GeV, data obtained at the Relativistic Heavy Ion Collider (RHIC). We show that the statistical hadronization model (SHM) well describes particle production. For all centralities, the particle production conditions are compatible with the earlier proposed critical hadronization pressure suggesting a set of universal hadronization conditions of QGP. Heavy-ion collisions at the Large Hadron Collider (LHC) present a new challenge for SHM in describing particle production at TeV energy scales. The chemical non-equilibrium model gives a good description of the hadron production in Pb-Pb collisions at √SNN = 2.76 TeV consistently as a function of centrality. Moreover, the model parameters, such as chemical freeze-out temperature, assume expected values suggested by results from previous studies at lower energies. The quark-gluon plasma fireball hadronizes at the same universal hadronization conditions, that is a common critical pressure, entropy and energy density. At LHC energies, a significant amount of charm is expected to be produced. It is therefore crucial to incorporate charm into the present description of particle production. We present a new tool, an upgraded SHARE with CHARM program, that quantifies the effect of charm on the yield of lighter hadrons and physical properties of the hadronizing fireball. In addition to light flavors (u,d,s), SHARE with CHARM describes charm hadron production and decays of charm hadrons. According to present experimental results, charm decays mainly affect the yields of multistrange particles. This dissertation begins with an introduction to the particle production in heavy-ion collisions and SHM framework, followed by a summary of results that are either published or submitted to peer-reviewed journals and others which are published as conference proceedings. Reprints of the publications are attached to the dissertation as appendices. Each appendix is prefaced with a short summary of presented results, and my contribution to these works is described.

We study particle production and its density evolution and equilibration in hot dense medium, such as hadronic gas after quark gluon plasma hadronization and relativistic electron positron photon plasma. For this study we use kinetic momentum integrated equations for particles density evolution with Lorentz invariant reaction rates. We extend these equations, used before for two-to-two particles reactions (1 + 2 ↔ 3 + 4), to the case of two-to-one and backward reactions (1 + 2 ↔ 3). One type of hot dense medium, which we study, is hadronic gas produced at quark gluon plasma hadronization in heavy ions collisions in SPS, RHIC and LHC experiments. We study hadron production at quark gluon plasma hadronization and their evolution in thermal hadronic gas phase. We consider non-equilibrium hadronization model, for which the yields of the light quark hadrons are defined by entropy conservation. Yields of hadrons containing heavier (strange, charm, bottom) quarks are mainly controlled by flavor conservation. We predict yields of charm and bottom hadrons within this non-equilibrium statistical hadronization model. Then we use this non-equilibrium hadronization as the initial condition in the study of hadronic kinetic phase. During this time period some hadronic resonances can be produced in lighter hadrons fusion. This reaction is opposite to resonance decay. Production of resonances is dominant over decay if there is non-equilibrium excess of decay products. Within this model we explain apparently contradictory experimental results reported in RHIC experiments: ∑(1385) yield is enhanced while ∧(1520) yield is suppressed compared to the statistical hadronization model expectation obtained without kinetic phase. We also predict Δ(1232) enhancement. The second type of plasma medium we consider is the relativistic electron position photon plasma (EP³) drop. This plasma is expected to be produced in decay of supercritical field created in ultrashort laser pulse. We study at what conditions this plasma drop is opaque for photons and therefore may reach thermal and chemical equilibrium. Further we consider muon and pion production in this plasma also as a diagnostic tool. Such heavy particles can be diagnostic tool to study the properties of EP³ plasma, similar to the role taken by heavy hadrons production in heavy ions collisions. Finally all these theoretical developments can be applied to begin a study of particles evolution in early universe in temperatures domain from QGP hadronization (160 MeV) to nucleosynthesis (0.1 MeV). The first results on pion equilibration are presented here.

In part to search for a possible critical point (CP) in the phase diagram of hot nuclear matter, a beam energy scan was performed at the Relativistic Heavy-Ion Collider at Brookhaven National Laboratory. The Solenoidal Tracker at RHIC (STAR) collected Au+Au data sets at beam energies, √sNN , of 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV. Such a scan produces hot nuclear matter at different locations in the phase diagram. Lattice and phenomenological calculations suggest that the presence of a CP might result in divergences of the thermodynamic susceptibilities and correlation lengths. The statistical moments of the identified-particle multiplicity distributions directly depend on both the thermodynamic susceptibilities and correlation lengths, possibly making the shapes of these multiplicity distributions sensitive tools for the search for the critical point. The statistical moments of the multiplicity distributions of a number of different groups of identified particle species were analyzed. Care was taken to remove a number of experimental artifacts that can modify the shapes of the multiplicity distributions. The observables studied include the lowest four statistical moments (mean, variance, skewness, kurtosis) and some products of these moments. These observables were compared to the predictions from several approaches lacking critical behavior, such as the Hadron Resonance Gas model, mixed events, (negative) binomial, and Poisson statistics. In addition, the data were analyzed after gating on the event-by-event antiproton-to-proton ratio, which is expected to more tightly constrain the event trajectories on the phase diagram.