Chiral Phase Transition Of PNJL Model With Chiral Chemical Potential Under Magnetic Field

Quantum chromodynamics(QCD)is a fundamental theory in describing strong interactions,and investigating the phase structure of QCD is of importance for a thorough understanding of the properties of strongly interacting matter in the medium.Experimentally,the deconfinement phase transition and chiral phase transition at high temperature and high density can be explored through heavy ion collision.Moreover,the strong electromagnetic field generated in the process of non-central heavy ion collision provides an important motive for the theoretical study of the influence of the electromagnetic field on the phase transitions.Theoretically,QCD lattice simulation may confront a sign problem,which limits its application.However,some low-energy effective theories of QCD have been widely used in describing the hadronic spectrum and phase transition.The PNJL model adopted in this thesis is a generalization of the NJL model,which describes both spontaneous breaking of chiral symmetry and confinement simultaneously,and better describes the QCD thermodynamics near the phase transition point on the basis of the NJL model.In heavy ion collisions,there may be local chiral imbalance with non-zero topological charge,namely the difference of left-handed and right-handed fermion number,and the effects of chiral imbalance can be conveniently investigated by introducing chemical potential which will not lead to the sign problem in the lattice QCD simulation.In this thesis,we use a PNJL model with two flavors to study the chiral phase transition in the background of a uniform magnetic field,especially the influence of magnetic field on the critical chiral chemical potential.It is shown that the magnetic field catalyzes the spontaneous breaking of the chiral symmetry,where the critical chiral chemical potential increases with the magnetic field.The constituent mass of quark increases with the magnetic field,but its change with the chiral chemical potential is not necessarily monotonic.Near the critical chiral chemical potential,the constituent mass decreases monotonically until the chiral phase transition occurs.We also discuss the effect of volume on the critical chiral chemical potential and find that the reduction of the system scale leads to a distinct increase of the critical chiral chemical potential under our simplified treatment.