Study Of Quark Matter Under A Strong Magnetic Field In NJL Model

In this paper,we use the Nambu–Jona-Lasinio(NJL)model to study the properties of quark matter in the presence of a strong magnetic field.First,the basic knowledge of quantum chromodynamics and the thermodynamic treatment of the NJL model are briefly introduced.The interaction between quarks is introduced by the scalar and pseudoscalar four-fermion coupling.In the chiral limit,both the dynamical quark mass and the quark condensate can play as the order parameter of the chiral symmetry to reflect the QCD chiral phase transition.When the chiral symmetry is broken,the quark condensate is not zero,and quark obtains larger dynamical mass by the gap equation.When the chiral symmetry is restored,the quark condensate tends to zero,and the dynamical mass approaches to the current quark mass.Recently,the QCD running coupling is obtained as a function of the magnetic field.The QCD running coupling constant is given by fitting lattice QCD data.In the mean field approximation and based on the self-consistent solutions of gap equations,the properties and stabilities of the two-flavor and three-flavor quark matter are studied in the NJL model.By numerically solving the gap equations of two-flavor and the three-flavor quark and comparing the fixed coupling and the running coupling cases,we find that the dynamical quark masses as functions of the magnetic field strength are not monotonous in the fully chirally broken phase with a magnetic-field-dependent running coupling.Instead,it decreases as the magnetic field increases in a certain interval.But for smaller values of the magnetic field,the dynamical masses with the two kinds of couplings will be gradually close to each other.Compared with the fixed coupling,the stability of magnetized quark matter with the running coupling is enhanced by lowering the free energy per baryon,which is expected to be more stable than that of the conventional constant coupling case.Therefore,under a magnetic field of a proper magnitude,the quark matter with a magnetic-field-dependent running coupling can be absolutely stable.