Study Of QCD Matter Under A Strong Magnetic Field In Nambu-Jona-Lasinio Model

It is well known that a strong magnetic field could exist in the dense stellar matter and the relativistic heavy ion experiments.The strong magnetic field must have important effects on the properties of the strong interacting matter.Recently,the magnetic-field-or the magnetic-field-and temperature-dependent running coupling constant G'(eB)/G'(eB,T)have been put forward to investigate the inverse magnetic catalysis found by LQCD in NJL model.Consequently,it is of great significance to study the effect of running coupling constant on strong interacting matter under a strong magnetic field.The main contents of this paper include four aspects:magnetic effect and thermal effect on quark matter,the influence of the magnetic-field-and temperature-dependent running coupling on QCD matter,the isospin asymmetric QCD matter realized by scalar and instanton-induced interactions,and the correction to the Coulomb potential of pointlike charge due to the vacuum polarization in a strong magnetic field.In the NJL model,we investigate the stability of quark matter at zero temperature and finite temperature with a magnetic-field-dependent running coupling constant.We mainly disscuss the competition between magnetic effect and thermal effect,that is,the strong magnetic field will make quarks lie in the lowest Landau level,while higher temperature will excite the quarks to higher Landau level,and eventually make the magnetic effect less and less important.But it is found that the magnetized quark matter under the running coupling is more stable than that of the fixed coupling constant at zero temperature.In order to obtain a complete QCD phase diagram,the phase structure becomes particularly important under a strong magnetic field.Firstly,we study the thermodynamic quantities of matter with the fixed coupling and running coupling under zero magnetic field,and find that the dynamical quark mass is lower in the running coupling case.Secondly,we investigate the effect of the magnetic-field-and temperature-dependent running coupling constant on the pseudocritical temperature in the QCD crossover transition region.It is pointed out that the two criteria dM/dT,d?/dT are no longer equivalent when the coupling constant changes with the temperature.Moreover,they satisfy an analytic relation.The difference of pseudocritical temperature obtained by the two criteria becomes apparent as the magnetic field increases.The isospin asymmetric is usual in nature.We study the isospin asymmetric matter realized by scalar and instanton-induced interactions under a strong magnetic field.The different charges of u and d quarks lead to different degenerate factors |q_iB|,which leads to unequal quark number densities.Therefore,the equivalence of dynamical masses of u,d quarks is approximately considered as isospin symmetry under a strong magnetic field.The isospin symmetry can be changed by adjusting the parameter a of the instanton-induced interactions.We find that the dynamical mass of u quark decreases as the increasing a,while the dynamical mass of d quark increases.However,in the case of non-zero chemical potential and non-zero isospin chemical potential,the maximum asymmetric parameter a=0 still satisfies the isospin mass symmetry at a certain critical temperature(T_s).Moreover,as the magnetic field becomes stronger,the T_s will move towards the high temperature zone(chiral restoration phase).The dynamical characteristics under extreme conditions is currently a hot topic in quantum field theory.We mainly discuss the anisotropy of interaction potential under a strong magnetic field,and study the correction of vacuum polarization to the Coulomb potential by calculating the potential function in the coordinate space.