Study Of The Effective Pion Mass At High Density

The study on nuclear force is very important in understanding the physical nature of nuclear system. In the one boson exchange theory, nuclear force is formed by the imaginary mesons between nucleons.the long-range part of a nuclear force is mainly contributed by the exchanges ofÏ€mesons; the middle-range part of a nuclear force is mainly formed by the changes ofσmesons or the exchanges of doubleÏ€mesons; while the short-range part of a nuclear force depends mainly on the exchanges ofρmesons andωmesons.Therefore, theσ,ω,Ï€,ρmesons are of vital importance in those nuclear problems. In recent years, the nature of those mesons and nucleons under high temperature and high density conditions, especially the changes of their mass in nuclear matter have always been the center of people's interests.In theory, the deduction of the hadron mass in nuclear matter can be taken as the proof of both the partial restoration of chiral symmetry and QCD Scaling Invariance. Brown and Rho ever raised [1]a relation:Here in this relation, T, refers to the transition temperature,ρ₀refers to saturated density andρ₀=0.17fm^-3, and n,λare constants. In the above relation we can see that the effective mass of nucleons,σmesons,ωmesons, ρmesons decreases as the density of a nuclear matter increases. Many researches have shown that such vector mesons asρandωfit this relation, while such scalar mesons asÏ€andσdon't[2,3].This paper will discuss the rules of the change of the effective mass ofÏ€mesons. as for the effective mass ofÏ€mesons becoming too big, caused by the interaction effect of pseudo-scalar couplingÏ€mesons and nucleons, as is mentioned in document[14,15], the document [14] directly introduces the interaction effect of pseudo-vector couplingÏ€mesons and nucleons without considering the non-renormalization of that effect. This paper first discusses the interaction effect of pseudo-scalar couplingÏ€mesons and nucleons, then introduces the pseudo-vector couplingÏ€mesons and nucleons caused by the change of Non linear field developed by Weiberg [16-18]and Schwinger [19]. This is different from introducing the pseudo-vector couplingÏ€mesons and nucleons directly, because by doing so, only limited counter terms are needed, and thus it can be renormalized.