| It is generally believed that QCD is the most effective theory for strong interaction. There are rich phase structures in QCD at finite temperature and baryon chemical density, for instance, from hadron gas to quark-gluon plasma, chiral symmetry breaking phase and its restoration phase, the color superconductivity at low temperature and baryon chemical density. Recently, the study on the QCD phase structure is extended to finite isospin density. The physical motivation of it is related to the investigation of compact stars, isospin asymmetric nuclear matter and heavy ion collision at intermediate energy.For pion(π0,π+andπ-which are triplet of isospin), the study shows the three masses of them are equal when the isospin symmetry of system is preserved. But they will split into three lines if the symmetry is broken. At lower isospin chemical potential, i.e.μI < mπ, there exists only explicit breaking, in this area, the masses ofπ+andπ- split, and change linearly with respect toμI,Mπ+ =mπ-μI,Mπ- =mπ+μI.However, these relations are not true for high isospin chemical potential.Nucleon-proton, neutron are the duplicate states of isospin. Ignoring the electromagnetism interaction, they have the same value of mass when the isospin symmetry of system is preserved. After its breaking, their masses should split. By analogy with pion, we guess , in the normal phase, the splitting masses change linearly with respect toμI too.NJL model is the effective model for QCD, especially at low or intermediate energy. We used this model to construct nucleon in the paper. Nucleon is regarded as the composite particle of quark and diquark under NJL. We first constructed diquark in NJL by Random Phase Approximation(RPA) on the analogy of pion. We used the three-body Faddeev equation to get its nucleon solution. By the use of static approximation , Faddeev equation reduced to a effective two-body BS equation, then the RPA was used again to attain the construct of nucleon. We utilized the dispersion relation to get the corresponding mass. We found that in normal phase at zero temperature, the masses of proton and neutron splitted linearly, with respect to the increase ofμI, the mass of proton went down, but the neutron gave the opposite. Different from pion, the nucleon mass also depended on baryon chemical potentialμB. They all went down by the increase ofμB. Then we went into finite temperature, we investigated the mass splitting in normal phase and the change of nucleon mass with respect to temperature. We found that the mass splitting of nucleon changed linearly with respect toμI too, besides their mass change by the temperature, when T was under about 50Mev, they didn't change, but when T went up , the mass of nucleon increased faster. |
