Study On Chiral Phase Transition And Phase Diagram Of QCD

Physics is a science which mainly studies the properties of matter.High energy nuclear physics is one field of physics on a really small scale like 1 fm.Two nuclei are accelerated with extremely high energy and a new matter state with really high temperature,density,etc.can be created.We called this new matter phase as Quark Gluon Plasma(QGP).Around 2000,Relativistic Heavy Ion Collider(RHIC),which is located in Brookhaven National Laboratory(BNL)at US,did lots of experiments to search for the signals of QGP and finally found the evidences of existence of QGP.Large Hadron Collider(LHC)at European Organization for Nuclear Research(CERN)and Facility for Antiproton and Ion Research(FAIR)which is under construction located in GSI Helmholtz Centre for Heavy Ion Research also study or will study properties of QGP.However,it is very tough to carry out such studies.On the one hand,theoretical physicists propose many possible properties of QGP.On the other hand,experimental physicists propose some corresponding probes to detect them.Since it is difficult to obtain the coordinate information of particles in relativistic heavy-ion collision exper-iments,we usually use the momenta information of particles,such as the isotropic flow.In the QGP phase with the chiral symmetry restored,due to the really high magnetic field generated by spectators and unequal numbers of left-handed and right-handed particles,an electric current along the direction of magnetic field is created,which is called the Chiral Magnetic Effect(CME).The CME has a dual effect named the Chiral Separation Effect(CSE).Interplay between the CME and the CSE can induce a collective excitation named the Chiral Magnetic Wave(CMW).Normally,people think that the magnetic field has its maximum value in the direction vertical to the reaction plane,so the electric current induced by the CME also has its maximum value in this direction.Based on this point,several probes are proposed.Both the STAR collaboration at RHIC and the ALICE collaboration at LHC found the possible signals of charge separation at Au+Au@200 Ge V and Pb+Pb@2.76 Te V.But there are many background contributions that can also lead to same results like charge separation,such as the Transpose Momentum Conservation(TMC),resonance decays and the Local Charge Conservation(LCC),and the CMS collaboration at LHC observed similar charge separation results in small system+Pb.The experimental methods are still under debate.There could be two ways to distinguish the real CME signal and the background contribution.One of them is to propose some better probes and the other one is to propose some new experiments like U+U and isobaric nuclei(same nucleon numbers,but different proton numbers)collision experiments.The other interesting project is to find the Critical End Point(CEP)of the hadron-quark phase transition.Lattice QCD calculation told us that there is a smooth crossover between hadron gas and QGP at low chemical potentials,but many model calculations show that such phase transition becomes a first-order one at large chemical potentials.In-between the crossover and the first-order phase transition along the phase boundary is the critical end point.One expects that some non-monotonic behaviors with respect to the collision energy can be found.Some probes are also proposed,like high moments of conserved net-charge numbers,such as the net-electric charge number,net-baryon number and net-strangeness number,which have one-to-one correspondence to the susceptibilities that can be calculated by theories.STAR proposed the Beam Energy Scan(BES)experiment to find the signals of CEP.In theoretical calculations,due to the complexities of the many-body problem and the Fermi-sign problem in lattice QCD calculations,the QCD effective models together with the mean-field approximation method become useful tools.On the other hand,since relativistic heavy-ion collisions contain complicated dynamical processes,many transport and hydrodynamics models are developed.This thesis mainly studies two following aspects,one of them is to study the CME and some related phenomenon in a box system and the other is to study QCD phase transition based on the extended-AMPT model with the partonic phase described by the Poyakov-looped Nambu-Jona-Lasinio(pNJL)model.Part One:We do a semi-classical derivation and obtain two types of equation of motions(EOM),i.e.the Spin EOM(SEOM)and the Chiral EOM(CEOM).We study the CMW with a simple initial state and solve the density distribution numerically from the CMW equation.We build a box system with the periodic boundary condition,and the four momenta and particle number are conserved.First,we study the dynamics from two types of EOMs.It was shown that the CEOM is unphysical for particles with too small momenta and some artificial cut off should be applied.We found that currents induced by the CME from both EOMs are lower than the theoretical limit,and the current from the SEOM is lower than that in the CEOM with the same constant magnetic field.With a damping magnetic field,the current from the CEOM has a rapidly response,while the current from the SEOM may has a relaxation process.Further more,we study the behaviours of the CMW in a box system.We start from a sine-like initial density distribution,and obtain the phase velocity and diffusion constant of the CMW from fitting the density distribution by solving the CMW equation.It is found that the phase velocities from the SEOM and CEOM are both smaller than theoretical limit.For systems simulated based on both EOMs,the phase velocity has a weak dependence on the specific shear viscosity,while the diffusion coefficient is more sensitive to the specific shear viscosity.The diffusion coefficient increases with the increasing specific shear viscosity,while both the phase velocity and the diffusion coefficient decrease with the increasing temperature of the system.The phase velocity is larger from the CEOM compared to that from the SEOM,while the dependence of the diffusion coefficient on the strength magnetic field is different in the two EOMs.The above are studies on the parton transport with chiral symmetry restored.Part two:We have employed the pNJL model to describe the partonic phase in the AMPT model,and give a finite vector coupling parameter which may lead to the elliptic flow splitting between quarks and anti-quarks.On the other hand,we can do some thermodynamic calculations to obtain the information of phase diagrams,such as the critical end point.In order to change gradually the momentum distributions of partons to those in the(p)NJL model,we employ special treatments similar to Pauli blockings,and introduce the stochastic method to reproduce more accurately the collision rate.Besides,the mean-field potentials have also been incorporated in the hadronic phase,and an improved quark coalescence algorithm to combine partons close in phase space has also been employed in the extended AMPT model.We have studied the density evolution in the central region of both the parton phase and the hadronic phase,and obtained the corresponding trajectories in the phase diagram in collisions at different energies.We find that the extended AMPT model describes reasonably well the experimental data of particle spectra,e.g.,?~±,K~±and(anti-)protons at RHIC-BES energies.In the NJL model the partons with momenta smaller than a cutoff value are not affected by the mean-field potential,while in the pNJL model there is no such cut-off.Due to the presence of the Polyakov-loop contribution to the energy density,the pNJL model has a slightly longer life time of the partonic phase,compared with the case of the NJL model.Combining the above two aspects,these is a larger elliptic flow splitting between quarks and and anti-quarks in the pNJL model than in the NJL model,especially between s and(?)quarks.Such elliptic splittings between baryons and anti-baryons are expected to be preserved after hadronization and after the hadronic evolution with different hadronic mean-field potentials.To fit the experimental data better,one needs a stronger vector coupling at lower collision energies but a weaker vector coupling at higher collision energies.The above are studies on the effective QCD phase diagrams.