Quantum ChromoDynamics (QCD) is a corner stone of the Standard Model. In the non-perturbative regime first principle calculation is very difficult but phenomenology is rich. The many-body dynamics of quarks interacting in a deconfined state, Quark Gluon Plasma (QGP), produces emergent phenomena which are not manifest in the theory's Lagrangian. QGP can be created in relativistic heavy ion collisions which provide an opportunity to experimentally probe this exotic QCD matter. Of particular interest is the structure of the QCD phase diagram. While the transition from QGP to hadron gas is a cross-over at high collision energies, RHIC's beam energy scan program covers the high baryon density region of the phase diagram to search for signs of a first-order transition and its accompanying critical point.

Bubbling is a general characteristic of first-order phase transitions and may lead to clusters of quarks which coalesce into final state protons in heavy ion collisions. We construct a new observable, $\Delta \sigma^2$, to search for excess clustering in the azimuthal distributions of identified proton tracks. We show that the effects of detector inefficiency and elliptic flow can be corrected and that the observable behaves as expected in various models and simulations. $\Delta \sigma^2$ is measured in STAR's Beam Energy Scan I data set and a strong repulsive interaction among protons is observed. The repulsion is found to depend heavily on the event multiplicity, increasing dramatically in magnitude as the event multiplicity decreases. Energy dependence, absent in model calculations, is observed in STAR data, suggesting a possible scenario of an energy dependent attractive correlation beneath a repulsive background.

In relativistic heavy-ion collisions, experimental evidence indicates that a new form of matter with de-confined quarks and gluons named the Quark-Gluon Plasma(QGP) has been created. The Relativistic Heavy Ion Collider (RHIC) provides a unique opportunity to study the QGP matter.

Strange hadron production is believed to be sensitive to parton dynamics in heavy-ion collisions. In particular, the strange quark production rate and its subsequent evolution in the dense partonic medium depend on the beam energy and the net baryon density. The productions of K_S⁰, &Lambda, &Xi, &Omega at mid-rapidity from Au+Au collisions at the beam energies of 7.7, 11.5, 19.6, 27, and 39GeV from the RHIC Beam Energy Scan Program are measured. We investigate the strangeness enhancement and ratios of anti-baryon to baryon yields as a function of beam energy at RHIC. Nuclear modification factors and ratios of baryon to meson yields are also studied. Implications on collision dynamics due to the increase in the baryon chemical potential at low beam energy and constraints on chemical freeze-out parameters will also be discussed in this thesis.

Parity-odd domains are theorized to form inside the QGP and to cause electric charge separation with respect to the reaction plane in the relativistic heavy-ion collisions via the Chiral Magnetic Effect (CME). Such charge separation has been studied at RHIC and LHC via the difference in two particle correlation between the opposite charge and same charge hadrons. The &Lambda and K_S⁰ particles are charge-neutral, and are supposed to bear no charge separation effects due to CME. We study the correlation between the neutral particle and charged hadron to investigate background for charged hadron correlation. In addition, the large angular momentum in heavy-ion collisions is predicted to lead to the Chiral Vortical Effect (CVE) which induces a baryon number separation, in analogy with the electric

charge separation caused by CME. We carried out a study of &Lambda-p correlations to search for the CVE. We present measurements of correlations for &Lambda-h^±,

K_S⁰-h^±, K_S⁰-p, and &Lambda-p in Au+Au collisions at 39GeV and 200GeV, to study the electric charge and baryon number separations across the reaction plane.

The main goal of high-energy heavy-ion collisions has been to understand Quantum Chromo Dynamics (QCD) under extreme temperature and baryon densities. At ordinary temperatures, the quarks and gluons are confined within hadrons, but at very high temperatures and densities, we have a deconfined phase of quarks and gluons, the Quark Gluon Plasma (QGP). Over the past years, evidence for the distinct phases of QGP and hadron gas has been established experimentally.

Fluctuations and correlations have been considered as sensitive observables to explore the phases of the strongly interacting QCD matter, namely the QGP phase and the Hadron Gas phase, as they can provide essential information about the effective degrees of freedom. The main goal of this thesis is exploring the critical phenomenon in QCD phase diagram. In this thesis, we have studied two main aspects of the QCD phase diagram, namely, the crossover at small baryon chemical potential and signatures of local parton density fluctuation near the critical point within the framework of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC).

Phase transitions and/or critical phenomena are known to lead to local density fluctuations. In the coalescence mechanism of particle production, the baryon formation probability can be influenced by these local parton density fluctuations, thereby leading to clusters and voids in the phase-space distribution of hadrons. In order to probe the density fluctuation in heavy-ion collisions, we studied the distribution of the ratio of particles in a given angular region to the total number of particles produced. We expect the shape of this distribution to be sensitive to clustering in phase space. For the first part, we measured the cumulants of this self-normalized distribution using the data from Au+Au collisions from the STAR Beam Energy Scan program to probe baryon density fluctuations.

Lattice QCD is a well-established non-perturbative approach to solve the theory of quarks and gluons exactly from first principles. However, these calculations are exact only at zero baryon chemical potential ($\mu_B$). In order to explore the phenomenon at finite $\mu_B$, these calculations are extended using Taylor expansion about $\mu_B = 0$. A constraint on the equation of state from Lattice QCD can be achieved by using the ratio of the sixth-order to the second-order baryon susceptibilities. In addition, Lattice QCD also predicts that the ratio of the sixth-order to second-order cumulants of baryon number remains negative at the chiral transition temperature. For the second part, we measured of the sixth-order cumulant for the net-proton (proxy for net-baryon) multiplicity distribution for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV (which corresponds to $\mu_B \sim 20$ MeV) for the high statistics run in the year 2014.

Unfortunately, the higher-order cumulants are very sensitive to experimental artifacts that one has to deal with in the analysis of heavy-ion collision data. The factorial moment method, which is used to account for the effect of detector efficiency, assumes the underlying detector response function to be a Binomial distribution. In order to account for non-Binomial detector responses and multiplicity-dependent efficiency, we developed an unfolding approach to measure efficiency-corrected higher-order cumulants of event-by-event distribution of physical variables.

A new form of matter with de-confined quarks and gluons, named the "Quark Gluon Plasma" (QGP), is predicted by Lattice Qutantum Chromodynamics to exist at high temperatures and/or high baryon density regions in the QCD phase diagram. Experimental evidence indicates that the QCD matter created in high energy Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC) in Brookhaven National Lab is a strongly-coupled Quark-Gluon Plasma. One of the central goals of heavy ion physics is to understand the QGP through quantitative comparisons between theoretical calculations and experimental measurements. Heavy flavor quarks are believed to be a unique probe for this task, because they are dominantly produced in the initial hard scatterings, where the production rate can be well calculated by perturbative-QCD(pQCD). When heavy favor quarks traverse the QGP medium, they bear the imprints of the medium via their interactions with the medium. Dynamical models have been developed to calculate the interactions between heavy quarks and the QGP medium to quantitatively extract the medium properties.

This dissertation presents a series of experimental studies with the electrons produced in the semi-leptonic decays of heavy flavor quarks in Au+Au and p+p collisions, which serve as the proxies for heavy flavor quarks. These electrons are referred to as non-photonic electrons (NPE), to be differentiated from the main background of photonic electrons. The production of NPE at high pT is found to be highly suppressed in central and semi-central Au+Au collisions, compared to binary-collision scaled production in p+p collisions. The azimuthal anisotropy of NPE is found to be finite at high pT, and the azimuthal correlation between high pT NPE and low pT hadrons exhibits a broadening in the away-side, both of which strengthen the evidence for a strong coupling between heavy flavor quarks and the QGP medium. In addition, the bottom quark production cross-section in p+p collisions is obtained based on the measured spectrum of NPE and the ratio of bottom/charm decay electrons.

In high-energy heavy-ion collisions, the Chiral Magnetic Effect (CME) offers a unique window to probe several fundamental properties in quantum chromodynamics (QCD): topological vacuum transitions, chiral symmetry restoration at high temperature, and the properties of a new QCD phase, Quark Gluon Plasma. Furthermore, it simultaneously probes the strong magnetic field (B) created by spectator protons in the colliding nuclei at almost the speed of light. The CME describes an electric charge separation of nearly massless quarks, which are at local chirality imbalance, along the B direction, manifestly violating local P and CP symmetries. This charge separation effect is quantified by the Δγ112 correlator between pairs of final-state charged hadrons and the reaction planes of the collision. However, due to the complex dynamics of the expanding fireball, the major background in CME search comes from the elliptic flow coupling with physics such as resonance decay, local charge conservation, and local momentum conservation. In order to mitigate the flow background in CME measurement, a novel event shape selection (ESS) approach is developed that manages to classify events based on their emission pattern shapes and determines Δγ112_ESS at the zero-flow limit. Furthermore, the spectator protons collected by STAR EPD detector are used to reconstruct the reaction plane correlated with B direction, while minimizing nonflow backgrounds. The search for the CME in the RHIC Beam Energy Scan phase II (BES-II) carries great scientific impact. It promises a thorough systematic investigation by the newly developed methods to mitigate all known backgrounds and by utilizing the stronger magnetic field provided by larger collision systems of Au+Au. With significantly higher data quality compared to BES-I and the successful development of a new ESS methodology, we observed a positive charge separation of 3-sigma significance in the 20-50% centrality range of Au+Au collisions at each of the three center-of-mass energies, 11.5, 14.6, and 19.6 GeV. The findings and physics implications will be discussed.

The Cryogenic Underground Observatory for Rare Events (CUORE) experiment at Gran Sasso National Laboratory in Italy searches for neutrinoless double-beta (0νββ) decay of Te-130. The experimental sensitivity relies heavily on the background rate in the 0νββ decay region of interest (ROI). In CUORE, the dominant source of background in the ROI are degraded alpha particles originating from contaminated surfaces facing the detector.This dissertation focuses on the work toward developing a detailed background model of the CUORE physics data in the ∼3 MeV – 7 MeV energy region, in order to identify and constrain the alpha background contribution to the ROI. A subset of the CUORE physics data collected between March 2019 and November 2020, corresponding to 433.3 kg/yr exposure TeO2, was used to identify the background sources contributing to the alpha energy region. Multiplicity information, based on the number of CUORE crystals that detect energy depositions within a given space-time window, was used to distinguish bulk and surface contaminations. Monte Carlo simulations of the energy spectra of the identified background sources were used to constrain the characteristic depths of the surface contaminations used in the background model. This detailed study of the background alpha spectrum shape complements to previous background source investigations that used very coarse spectrum binning and allowed us to examine features of the detector energy response that depend on the depth of the surface contaminations.

A prominent goal within the field of modern heavy-ion collisions is to uncover the phase diagram of QCD. Studies of the properties of systems created in heavy-ion collisions strongly suggest that a new state of matter described by quark and gluon degrees of freedom, the quark-gluon plasma, is created when nuclei are collided at very high-energies. Consequently, the QCD phase diagram may contain a rich structure in regions currently accessible to heavy-ion experiments, including a possible critical point where the transformation between hadronic and partonic matter changes from a smooth crossover to a first-order phase transition. Whether this is the case will have to be born out through a combination of experimental analyses and state-of-the-art simulations of heavy-ion collisions.

We present a mean-field model of the dense nuclear matter equation of state designed for use in computationally demanding hadronic transport simulations. Our approach, based on the relativistic Landau Fermi-liquid theory, allows us to construct a family of equations of state spanning a wide range of possible bulk properties of dense QCD matter. For the application to simulations of heavy-ion collisions at intermediate beam energies, and in particular having in mind studies centered on probing the regions of the QCD phase diagram most relevant to the search for the QCD critical point, we further present and discuss parametrizations of the developed equation of state describing dense nuclear matter with two phase transitions: the known nuclear-liquid gas phase transition in ordinary nuclear matter, with its experimentally observed properties, and a postulated phase transition at high temperatures and high baryon number densities, meant to model the QCD phase transition from hadronic to quark and gluon degrees of freedom.

We implement the developed model in the hadronic transport code SMASH, and show that the resulting dynamic behavior reproduces theoretical expectations for the thermodynamic properties of the system based on the underlying equation of state. In particular, we discuss simulations of systems initialized in regions of the phase diagram affected by the conjectured QCD critical point, and we demonstrate that they reproduce effects due to critical behavior. Specifically, we show that pair distribution functions calculated from hadronic transport simulation data are consistent with theoretical expectations based on the second-order cumulant ratio, and can be used as a signature of crossing the phase diagram in the vicinity of a critical point. Through this, we validate the use of hadronic transport codes as a tool to study signals of a phase transition in dense nuclear matter.

We additionally present a novel method that may enable a measurement of the speed of sound and its derivative with respect to the baryon number density in heavy-ion collisions. The devised approach is based on a connection between the speed of sound and the cumulants of the net baryon number, which in the context of the search for the QCD critical point are given considerable attention due to their potential to signal critical fluctuations. We confirm the applicability of the proposed method in two models of dense nuclear matter, including the parametrization of the equation of state developed in this work. Application of our approach to available experimental data implies that the derivative of the speed of sound is non-monotonic in systems created in collisions at intermediate to low energies, which in turn may be connected to non-trivial features in the underlying equation of state.

The Quark Gluon Plasma (QGP), a state of matter in which deconfinement and chiral symmetry restoration occur, can be produced by ultra-relativistic heavy-ion collisions. This state of matter is of great interest because in QGP, the colored quarks and gluons, fundamental entities in matter whose interactions are governed by the Quantum ChromoDynamics (QCD), can exist as a fluid over an extended volume much larger than the size of nuclei. The Chiral Vortical Effect (CVE) is a QCD phenomenon related to the quark chirality arising from the topological sector of the QCD and the large vorticity of the QGP created. The search for quark chirality effects has been a major scientific objective at RHIC. \The Solenoid Tracker at RHIC (STAR) detector, located at the Relativistic Heavy-Ion Collider (RHIC) in the Brookhaven National Laboratory (BNL), provides the experimental capability needed to probe the QGP, with the particle tracking and identification abilities built into the different parts of the detector. This thesis focuses on the search for the CVE with STAR data from Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 27 GeV and 19.6 GeV, from Run 2018 and 2019, repsectively. \ In order to search for the CVE, measurements of the correlations of the azimuthal angles between baryons, $\Lambda$ and protons, were made, in the form of observables $\gamma_{112} \equiv \langle \cos(\phi_{\alpha} + \phi_{\beta} - 2\Psi_{RP}) \rangle$ and $\gamma_{132} \equiv \langle \cos(\phi_{\alpha} - 3\phi_{\beta} + 2\Psi_{RP}) \rangle$, in which mathematically the CVE effects would be made manifest. $\alpha$ and $\beta$ represent the charge of the correlated particles, and to reduce the background, we take $\Delta\gamma \equiv \gamma_{OS} - \gamma_{SS}$, where we subtract the measurement of the correlation of pairs of same charge particles (SS) from that of opposite charge particles (OS). The KFParticle package was used for the reconstruction of the $\Lambda$ particles. To have a better interpretation of the results, the observables $\kappa_{112} \equiv \Delta\gamma_{112} / (v_{2}\cdot\Delta\delta)$ and $\kappa_{132} \equiv \Delta\gamma_{132} / (v_{2}\cdot\Delta\delta)$ were computed that allows for comparison across different systems. Specifically, these observables were compared with data generated from the A Multi-Phase Transport Model (AMPT) simulations. \ In addition, the flow-related background was also something that needed to be dealt with to get a clearer signal from the $\Delta\gamma_{112}$ and $\Delta\gamma_{132}$ observables. The Event Shape Selection method was applied in order to project the events to zero flow, attempting to reduce the flow-related background as much as possible. The Event Plane Detector (EPD) event plane was used as well to reduce the non-flow backgrounds. \ Our search yielded no definitive observation of the proposed CVE signal. We obtained an upper limit on the CVE signal from Au+Au collisions at 19.6 GeV and 27 GeV energies. Because of large statistical errors due to limited number of $\Lambda$ per event, the obtained upper limit is not very stringent. We will also discuss a possible effect due to the presence of baryon annihilations and the future direction of CVE searches. Large statistical data sets will be critical for those efforts.