Study Of The Effective Meson Mass At High Density

Recently ,the physical property of the nuclear matter underextreme conditions of high temperature and density ,especially theeffective masses of meson and nucleon, have attracted wideinterest .In 1991 the Brown and Rho argued that the masses of σ,ρandω mesons and nucleons satisfy)mm *NN ≈ mmρρ* ≈mmωω*≈mmσσ*≈[1 ?(TTc)2]n(1?2λρρ0where the masses with asterisks stand for the finite-temperature andfinite-density values , the Tc is the transition temperature,0ρ is asaturated density(0ρ =0.17 fm ?3) ,and n,λare constants . A lot ofresearches showed that the relation cited above is right.If we wantto get the effective mass by the method of computing the mesonself-energy , we need to consider the change of the effective massof the nucleon along with the increasing density of the nuclearmatter,namely considering the fluctuation of the vaccum.Whentaking no account of the change of the effective mass of nucleonwith the increasing density of nuclear matter ,the effective mass ofthe ρ-meson, ω-meson increases generally.Only when the effectivemass of nucleon which changes with the increasing density isconsidered, the effective masses of the ρ-meson, ω meson decreasein general.This text uses two kinds of methods to study the mass of mesonwhich changes with the increasing density.One method employsthe meson self-energy,another method employs the renormalizationgroupThe interaction Lagrangian between the nucleon and theπ-meson has two forms,one form named pseudo-scalarcoupling,another form named pseudo-vector coupling.Thepseudo-vector coupling Lagrangian between the nucleon and theπ-meson is non-renormalization ,in other words the theoreticalinfinitude can not be subtracted by adding finite counterparts to theLagrangian. Firstly,we employ the dimension regulation to the πmeson self-energy of pseudo-vector coupling,then subtract theinfinitude from it directly.By this way we can get the finiteterms .When we consider the effective mass of the nucleon,we alsoemployed two methods,one called the Mean-Field method andanother called nucleon self-energy method.After we gained theeffective mass of the nucleon ,we set them into the formula of theπ-meson self-energy respectively.Through the calculation, we findthe conclusion that the effective mass of the π meson decreasesunder the lower density,and increases under the higherdensity.Furthermore,the two different definitions of the effectivemass of the nucleon have the similar influence on the change trendof the effective mass of the π-meson.The only difference is theextent.We apply the renormalization group to the chiral σ ? ωmodel .Using the chiral σ ? ω model,we find the conclusionthat the running masses of the π-meson and the σ-meson descreasewith the increasing density of the nuclear matter,at the same timewe gain the running coupling constant which also decreases withthe increasing density.