The Masses Of ? And ? At Finite Temperature And Chemical Potential

Investigating the properties of strongly interacting matter at finite temperatures and chemical potentials is one of the important topics in particle physics.From theoretical aspect,chiral phase transition,deconfinement phase transition and color superconduct are expected in QCD phase diagram.Heavy ion collision experiments,for example,experiments at the RHIC and LHC,at sufficiently large beam energies are performed to search the signals of the quark gluon plasma(QGP).In other regions of the QCD phase diagram possible phase transitions with larger chemical potentials are probed at lower beam energies.QCD is the fundamental quantum field theory for the description of strongly interacting matter.It has a great success in dealing with topics at high energy because of the small coupling constant there.However great difficulty arises in dealing with the low energy region with large coupling constant where perturbative approaches are not accessible.There is strong evidence for the existence of two phase transitions for strongly interacting matter.One of them is the chiral phase transition from a state with spontaneously broken chiral symmetry to a chirally symmetric restoration phase.At vanishing chemical potentials,lattice QCD simulations is applicable which suggest a smooth cross-over transition at about T = 160MeV.At non-zero chemical potentials,lattice QCD simulations are confronting so-called fermion sign problem.The fundamental phase structure of strongly interacting matter is still unknown.Besides lattice QCD simulations,a broad range of effective field theoretical models exist for describing properties of the phase diagram and thermodynamic characteristics of strongly interacting matter.These models include mainly Nambu-Jona-Lasinio(NJL)models,quark-meson(QM)models,the chiral perturbative theory and other low-energy chiral models.By construction the NJL model is based on quark degrees of freedom,its Lagrangian incorporates a transparent mechanism for the spontaneous breaking of chiral symmetry and shares with QCD its global symmetries.NJL model is widely used model in investigating low energy QCD both at zero and finite temperature and chemical potential.By using the optimized perturbation theory(OPT)method,a two-flavor NJL model beyond mean field approximation is used to investigate the masses of ? and ? at finite temperature and chemical potential.The results show that in the chiral breaking phase the mass of ? decreases with rising temperature and in the chiral restoration phase it increases with temperature,while the mass of ? always increases with temperature,their masses become degenerated in the chiral restoration phase.The chemical potentials accelerate the chiral restoration and lower the critical temperature.The OPT method change their masses quantitatively,but not qualitatively.