Relativistic Hydrodynamic Modeling And Applications In High Energy Heavy-ion Collisions

Quark-gluon plasma（QGP）is a novel state of matter composed of deconfined quarks and gluons that can be created at extremely high temperatures and densities,such as high-energy heavy ion collisions performed at the Large Hadron Collider（LHC）and the Relativistic Heavy Ion Collider（RHIC）.Exploring the nature of such high-temperature and high-density QCD nuclear matter is one of the most important tasks of current high-energy nuclear physics.Lattice QCD simulations has found a rapid smooth transition from QGP to hadron gas at zero baryon chemical potential and high temper-ature.However,at low collision energies,the overlap region of the collisions has finite net baryon density due to baryon stopping effects.Due to the well-known sign problem,the equation of state of QCD matter at finite net baryon chemical potential cannot be di-rectly calculated from lattice QCD.However,many phenomenological models predict the existence of the first-order phase transition line in the region of large baryon chem-ical potentials.This suggests that there must be a QCD critical point between the rapid smooth transition and the first-order phase transition in the QCD phase diagram.One of the most important tasks of RHIC beam-energy-scan program（BES）experiments to locate the QCD critical point and explore the QCD phase diagram.In fact,many im-portant evidences of QGP formation have been observed experimentally,one of which is the strong anisotropic collective flow.This phenomenon leads to azimuthal asym-metry in the momentum distribution of the final-state hadrons.Relativistic hydrody-namics model has been extremely successful in explaining the experimentally observed anisotropic collective flow and describing the space-time evolution of the QGP.Due to the strong interaction among QGP constituents,hydrodynamics transforms the spatial geometric anisotropy of the initial QGP fireball into momentum anisotropy of the final-state hadrons.It is also found that the QGP created in relativistic heavy ion experiments performed at RHIC and LHC behaves like a nearly perfect ideal fluid with an extremely low ratio of shear viscosity to entropy density.The relativistic hydrodynamics framework provides a powerful tool to study the bulk properties of QGP nuclear matter in heavy ion collisions.For example,by study-ing higher-order anisotropic flows,flow fluctuations,and flow correlations,one can con-strain constrain the initial three-dimensional structure and transport coefficients of QGP.Even the collective flow of mini-QGPs in small collision systems can be studied by hy-drodynamics framework.These studies mostly focus on at the LHC energies and RHIC top energies where the net baryon number density is almost zero.However,in the heavy ion collisions at the RHIC-BES energies,the assumption of zero baryon chemical po-tential is no longer valid.In this thesis,in order to investigate the bulk properties of QGP in a finite baryon chemical potential environment produced by heavy ion collisions at RHIC-BES energies,I have extended the（3+1）-dimensional CLVisc viscous hydro-dynamics framework to include not only the energy-momentum conservation equation and the equation of motion for shear tensor,but also the net baryon conservation,the Isreal-Stewart-like diffusion equation for baryon current and bulk pressure.In addition,the NEOS-BQS equation of state with baryon number density degrees of freedom,the fluctuating AMPT initial condition,the fluctuating SMASH initial condition,the fluc-tuating MC-Glauber initial condition,and the SMASH afterburner are also included.The numerical accuracy of the extended CLVisc framework is verified by comparing with the hydrodynamic analytical solution and other numerical hydrodynamic models developed independently.Using the above integrated framework which consists of the MC-GLauber initial conditions,the CLVisc hydrodynamic evolution,the NEOS-BQS equation of state,and the SMASH afterburner,I have investigated the transverse momentum spectra,mean transverse momentum for identified particles and anisotropic flow for charged hadrons at different collisional centrality and over a wide range of RHIC-BES collision ener-gies（7.7-62.4 Ge V）.The integrated framework describes well the experimental data of the abovementioned observations.It also found that the mean transverse momentum of the identified particles and anisotropic flow show a moderate increase with increasing collision energy due to the larger radial flow.We also calculate the multi-particle cu-mulant ratio（v₂{4}）/（v₂{2}）for elliptic flows across RHIC-BES energies and find that the relative fluctuations of elliptic flows is insensitive to the collision energy.This prediction is also consistent with recent experimental data from RHIC-STAR.In addition,we inves-tigate the effects of baryon diffusion and the afterburner on the particle spectrum and anisotropic flow.It is found that the contribution of baryon diffusion to the momentum spectrum and elliptic flow of mesons is almost negligible,and has a significant effect on the momentum spectrum of protons and antiprotons due to the gradient of the ratio of initial chemical potential to temperature.The afterburner would increase the mag-nitude of elliptical flow for the identified particles and lead to stronger blue-shift effect of protons and antiprotons.The extended integrated model provides a benchmark for understanding experimental data on soft particles at RHIC-BES energies and studying the critical properties and phase structure of hot and dense QCD matter.Another important application of the relativistic hydrodynamic framework is that it can provide information on the vorticity during the QGP evolution for the study of the spin polarization ofΛand?Λhyperons.Therefore,the global and local spin polariza-tion ofΛand?Λhyperons in relativistic heavy-ion collisions at RHIC-BES energies are systematically studied using the（3+1）-dimensional CLVisc hydrodynamic framework with the AMPT and SMASH initial conditions.Following the quantum kinetic theory,the polarization vector can be decomposed into components caused by thermal vorticity,shear tensor and the spin Hall effect（SHE）.Firstly,we calculate the global polarization forΛand?Λhyperons,and the numerical results are in agreement with the experimental data from the RHIC-STAR Collaboration.It is also found that the global polarization of?Λhyperons is not always larger than that ofΛdue to various competing effects.For the local spin polarization,it is found that both the SHE induced local spin polarization and the total local spin polarization strongly depend on the initial conditions.For exam-ple,at 7.7 Ge V,the SHE effect gives a considerable contribution in the AMPT initial conditions.It even changes the sign of the total local longitudinal polarization,but the same phenomenon is not observed in the SMASH initial conditions.Also,it is found that the local transverse polarization induced by SHE does not always increase with the decrease of the collision energy in the AMPT initial conditions.Finally,we also find that the local longitudinal polarization is sensitive to the baryon dissipation coefficient,but the local transverse polarization is not.Our findings are helpful for understand-ing the polarization phenomenon and the detailed structure of quark-gluon plasma in relativistic heavy-ion collisions.Previous studies have mainly focused on the phenomenon of anisotropic collective flow in nucleus-nucleus（AA）collisions.Recently,similar strong anisotropic collective flow phenomena have been observed in proton-nucleus（p A）collisions.Based on the（3+1）-dimensional CLVisc hydrodynamic framework with the full fluctuating AMPT initial conditions,we first study the asymmetric longitudinal decorrelations effects of elliptic,triangular,and quadrangular in p A collisions in proton-nucleus collisions at the LHC and RHIC energies.To measure the longitudinal flow decorrelations for asymmet-ric collision systems,we propose a new set of rapidity-asymmetric flow decorrelation functions.Our hydrodynamic numerical results show that the flow decorrelations in proton-going direction are larger than those in nucleus-going direction..We also find a similar collision energy dependence of the decorrelation effect in AA collisions,where the decorrelation effect is stronger in p A collisions at RHIC than at the LHC.In addi-tion,the origin of the anisotropic flow in p A collision systems is still in debate.The main explanations include the final-state effects due to hydrodynamics evolution and the initial state effects due to Color Glass Condensation.Therefore,we also discuss the relative contributions of the initial and final state effects in the longitudinal flow corre-lation in small system.It is found that the collective flow in small system is dominated by the final-state effects,while the relative contribution of the initial effect is around10%in the 0-90%centrality class.Our study helps to reveal the longitudinal structure of mini-QGP in small systems and the origin of flows in relativistic heavy ion collisions.