Finite Volume And Chiral Chemical Potential Effects On Chiral Phase Transition

As an essential part of the Standard Model of particle physics,quantum chromo-dynamics(QCD)is the fundamental theory of strong interaction between quarks and gluons in the Universe.There are two basic features of QCD at low energy region:col-or confinement and dynamical chiral symmetry breaking.Discussions regarding phase diagram of QCD matters have dominated research over decades.Moreover,the search for the critical end point(CEP)on the phase diagram has been propelled to the forefront in recent years from both theories and experiments.In this analysis,we use the non-pertubative and effective model-Polyakov-loop-extended Nambu-Jona-Lasinio model within finite volume and chiral chemical potential to study the chiral phase transition and locate the CEP.In Chapter 2,we give a detailed introduction of NJL model within the mean-field approximation.Much attention has been paid to the spontaneous chiral symmetry breaking of NJL model,and based on the definition of spontaneous symmetry breaking we gave a very clear and self-consistent interperation.As our interview,the Lagrangian density of NJL model within the mean-field approximation represents the ground state Lagrangian density of the NJL model,which is broken by existence of the vacuum quark condensate.In addition,the existence of vacuum quark condensate depends on the coupling constant of strong interaction.In a word,the coupling constant of strong interaction leads to the chiral symmetry breaking of the ground state Lagrangian densi-ty of the NJL model,but the Lagrangian density of the NJL model remains unchanged under the chiral transformation.So that the chiral symmetry of the NJL model is spon-taneouly broken.In Chapter 3,chiral chemical potential,?₅is introduced to investigate the QCD susceptibilities and chiral phase transition within the Polyakov-loop-extended Nambu-Jona-Lasinio models in the mean-field approximation.We concentrate on the effect of chiral chemical potential on the phase diagram and the QCD susceptibilities.Moreover,it's worth noting that chiral chemical potential has more and more prominent impact on the susceptibilities and the phase diagram with the decrease of the temperature based on our results,which coincides with the prediction that the chiral symmetry is dynamical broken in the first-order phase transition region and gets partly restored in the crossover region.Meanwhile,we explained why there is no CEP₅.In Chapter 4,the finite-volume effect on the QCD phase diagram is investigated via the two-flavor Polyakov-loop-modified Nambu-Jona-Lasinio model in the presence of the chiral chemical potential within the mean-field approximation.Our calculations concentrate on the quark condensate,chiral number density and its derivative,namely QCD susceptibilities.We find the chiral number density decreases as the system size gets smaller.It is also confirmed that the volume of the strongly interacting matter has an influence on the phase diagram,in particular on the crossover region and the location of chiral transition line.Therefore,the critical end point(CEP)also shifts with system size.On this basis it follows that study of the finite-volume effect as well as the chiral chemical potential dedicated to the chiral phase transition and probing the location of CEP.