A Study Of The Pole Mass And Screening Mass Of The Neutral Pion Meson Under The Magnetic Field In The NJL Model

In high-energy and nuclear physics,the study of hadronic properties has been always one of the hottest topics in the world,and also been one of the most important approaches to deepen the understanding of the strong interactions.Especially,as is well known,ex-tremely high temperatures and strong magnetic fields can be produced in relativistic heavy ion collisions,which will have an significant influence on the hadronic properties.There-fore,it is of great scientific value to investigate the modifications of hadronic properties under these extreme environmental conditions,which will help to reveal the phase tran-sitions and phase structures of the strongly interacting matter.In this thesis,we mainly study the effects of strong magnetic field on the pole mass and screening mass of the neu-tral pion meson at both zero and finite temperature in the framework of the two-flavor Nambu-Jona-Lasinio(NJL)model.Firstly,based on the Lagrangian of NJL model,the constituent quark mass is solved in the Hartree-Fock approximation(or mean field approximation)by using two different but equivalent forms of quark propagators in the magnetic field,i.e.the Landau level representation propagator and the proper time representation propagator.And then,the pole mass and screening mass(including longitudinal and transverse screening mass)of the neutral pion meson at finite temperature and magnetic field are obtained by using the random phase approximation(RPA)method in the NJL model,and both temperature and magnetic filed dependence curves of these three meson masses are computed numerically.On the one hand,the results show that when the temperature reaches the Mott temperature,the pole mass of ?0under the magnetic field will exhibit a suddenly jump,which is due to the infrared divergence by the dimensional reduction of the magnetic filed.In particular,the stronger the magnetic field is,the higher the Mott temperature is.On the other hand,we compare the pole masses and two kinds of screening masses for ?0with each other,since the relationships between them will reflect the space-time anisotropy caused by the temperature and the magnetic field.