Renormalization Group Analysis of ρ-Meson Properties at Finite Density

We calculate the density dependence of the ρ-meson mass and coupling constant(gρNN ) for ρ-nucleon-nucleon vertex at one loop using the lagrangian where the ρ-meson is included as a dynamical gauge boson of a hidden local symmetry. From the condition that thermodynamic potential should not depend on the arbitrary energy scale, renormalization scale, one can construct a renormalization group equation for the thermodynamic potential and argue that the various renormalization group coefficients are functions of the density or temperature. We calculate the β-function for ρ-nucleon-nucleon coupling constant (gρNN ) and γ-function for ρ-meson mass (γmρ). We found that the ρ-meson mass and the coupling constant for gρNN drop as density increases in the low energy limit.