Non-perturbative Study Of QCD Chiral Phase Transition In A Finite Volume

As far as we know,the most fundamental particles that make up this world are quarks.Undoubtedly,an in-depth study of quarks helps us understand the origin of mass and the evolution of the universe.Quantum chromodynamics(QCD)has been widely accepted as the basic theory for studying strongly-interacting matter.We hope to get the complete information about the world of strongly-interacting matter from the basic interactions between quarks and gluons that described by QCD.However,due to the remarkable feature of QCD,that is,asymptotic freedom.In the low momentum transfer region,the coupling constant between quark and gluon becomes so large that we can no longer use the perturbation expansion method to calculate step by step.So a variety of effective models have been proposed.Such as,Dyson-Schwinger Equation-s(DSEs),Chiral effective theory,Polyakov-Nambu-Jona-Lasinio(PNJL)model and so on.In this paper,we use the QCD effective models to study strongly-interacting matter from two aspects.On the one hand,we use the NJL model to study the zero-temperature and finite-quark chemical potential chiral phase transition and the equation of state.On the other hand,we use the PNJL model and ESEs to study the finite-size effects on chiral phase transition.In chapter 2,we first make a detailed derivation of the mathematical form of the NJL model,and then determine the required parameters by fitting the pseudoscalar mesons masses and decay constants under the proper-time normalization.Then we study the chiral phase transition at zero-temperature and finite-chemical potential and find that under the proper-time normalization,the chiral phase transition is a Crossover.Next,we consider the chemical potential equilibrium and the electrical neutral con-dition to obtain the equation of state that can be used to study the relationship between mass and radius of neutron stars.Finally,we compared the stability of the two flavors and 2+1 flavors of QCD matter and find that the 2+1 flavors is more stable.In chapter 3,within the framework of Polyakov-Nambu-Jona-Lasinio model and by means of Multiple Reflection Expansion,we study the finite volume effects on chiral phase transition,especially its influence on the location of the possible critical end point(CEP).Compared to other methods,MRE describes the sphere instead of cubic,which is closer to the fireball produced by the relativistic heavy ion collisions.Therefore,the surface and curvature effects of the sphere are properly considered.Our results show that,if the radius of spherical volume is larger than 10 fm,finite volume effects are negligible.In the radius 2 fm?10fm,we find that the CEP shifts rapidly toward smaller temperatures but almost stay constant quark chemical potential,?(?)312MeV,when the radius decreases.This is an encouraging fact for the CEP search in heavy-ion collision experiments.In addition,we also study the finite volume effects on masses of mesons,we find for ? and K,their masses increase with decreasing volumes.But for?,? and ?' the situation is just the opposite.Especially,the masses of chiral partners ?and ? get closer as the volume decreases,indicating that the dynamical chiral symmetry breaking effect reduces with decreasing volume.In addition,in order to compare the influences of finite volume effects on chiral phase transition under different models,we also studied the finite volume chiral phase transition within the framework of DSEs.