Study Light Meson Mass Evolution With Temperature

The properties of Quantum Chromodynamics in finite temperature is one of the hot topics in particle physics. In nature, when the universe begins, the whole world is a world of quarks and gluons. In small heavenly bodies, such as neutron stars, the QCD matter can be realized in low temperature and high density. Therefore exploring the nature of quark gluon plasma is important in understanding QCD deeply and investigating the evolving of the universe. In this field, whether the phase transition from low temperature(low density) to high temperature (high density) happens or not, if happens, what is the order of the phase transition, is what one concerns.The two important phase transition is deconfinement phase transition and chirally restoring phase transition. One of the important properties of the nonabelian QCD theory is asymptotic freedom. It means that with the increasing energy scale, the coupling constant becomes smaller. So one expects that in high temperature and (or) high density QCD will go through a hadron state to a new matter state with onshell quarks and gluons---quark gluon plasma. In the meantime, the spontaneous breaking of chiral symmetry presents in low energy QCD due to the condensation of scalar quark pairs.So, one expects that in high temperature, the quark condensation will be dissolved due to thermal fluctuation, and chiral symmetry will restore. Thus, another phase transition---chiral phase transition is an important topic in hot QCD.The linear a model is one of the important models dealing with the low energy and hot properties of QCD. It is not QCD, but the investigation of this model is helpful and instructive for investigating hot QCD and low energy QCD which is difficult to be dealt with. The simplest model is the O(N) model in d+1spacetime which is the basic or prototype of many physics system one interests in. The fundamental degree of freedom is a bosonic field with N components. When the Lagrangian shows the spontaneous breaking of chiral symmetry, it becomes the linear a model. In this thesis, the U(2)×U(2) linear a model we used is a generalization of original SU (2) linear a model.In this thesis, we investigate the temperature evolving of the masses of the light mesons σ、π、a and η by the finite temperature field theory in the frame of the U(2)xU(2) linear σ model. Our calculation suggests that the masses ofπ、a and η i U(2)xU(2)ncrease monotonically with increasing temperature, while the mass of σ decrease monotonically. No evidence of chiral symmetry restoration happens in the mass spectrum.