Properties Of Neutral Pions Under Magnetic Field In The NJL Model

The study of QCD matter is one of the hottest topics in modern high-energy physics and nuclear physics research,and it is one of the most important approaches for people to un-derstand the nature of strong interactions.In relativistic heavy ion collision experiments,not only can very high temperatures be produced,but also very strong magnetic fields can be generated.These extreme external conditions will have a very important influence on the properties of hadrons.Therefore,the research on this subject has great theoretical and practical significance.This paper will mainly study the effect of strong magnetic field on the properties of neutral?~0meson in vacuum and at finite temperature.In this paper,the behaviors of both constituent quark and?~0meson masses with increasing temperature in the magnetic field are studied in the framework of two-flavor Nambu–Jona-Lasinio(NJL)model,and the corresponding mechanism behind is briefly discussed.Firstly,based on the Lagrangian density of the NJL model under magnetic fields,the thermodynamic potential of the QCD system at the mean field approximation is derived,and accordingly,the analytical expression of the energy gap equation in the magnetic field is obtained.In this way,the dependences of the constituent quark masses on different magnitudes of the magnetic field are computed numerically,which verifies the magnetic catalysis effect.And then,we use the Random Phase Approximation(RPA)method to obtain the polarization function of the?~0meson,and obtain the curves of the?~0meson mass vs.temperature in the magnetic field.It is found that that the mass of the?~0meson in the magnetic field will be abrupt at a certain temperature(Mott transition temperature),which is caused by the dimension reduction of the fermion systems under strong magnetic fields.Moreover,the Mott temperature increases as the magnetic field increases.In addition,due to the non-reformability of the NJL model,we also explored in detail the effects of different regularization schemes on numerical results.