The Thermal Masses Of ??? Mesons Under Magnetic Fields

Taking into account the influence of an external magnetic field on hot QCD matter has attracted great attention in recent years.Many remarkable effects,such as the chiral magnetic effect,magnetic catalysis or inverse magnetic catalysis effect are predicted.Strong magnetic fields may be produced in the evolution of early universe,neutron stars(magnetars),and especially the non-central heavy-ion collision(the magnetic field strength of the order eB?15m?2 can be achieved at LHC).Though in heavy-ion collisions,magnetic fields exist only for a very short interval of time,they are good enough to substantially affect the fire-ball.The applicability of QCD in low energy becomes difficult due to its non-perturbative features and the complication of dealing with the perturbative expansion.Moreover,when the chemical potential is taken into account,the lattice QCD,which is from the first principle,confronts serious sign problem.Before QCD was established,some phenomenological models have been established to describe the stong interaction.They were not totally replaced even QCD was established,instead they have developed forward and become low energy effective models for the strong interaction.They include the chiral perturbative theory,quark-meson models and NJL models.The NJL models whose fundamental degrees of freedom are quarks,not only are applied to investigate the strong interaction at zero temperature,but also are applied to topics at finite temperature and chemical potential.Especially in order to deal with deconfinement phase transition,PNJL models are developed.Therefore,NJL models have become important models at finite temperature.On the other hand,the perturbative calculation is more complicated at finite temperature,one usually use resummation techniques to obtain reliable results.The OPT method which is used in this thesis is one of the resummation techniques.In this thesis,we investigate the masses of sigma and neutral pion mesons in hot matter under a constant magnetic field using a two-flavor NJL model beyond the mean field approximation.By using OPT method,we expand the effective potential and meson polarization functions perturbatively to the first order.The results show that:(l)the mass of the ? meson increases with magnetic field and the mass of the neutral pion almost keeps a constant with the increasing of the magnetic field;(2)the chemical potential affect the mass of the mesons very slightly.