Renormalization Group Analysis of ρ-Meson Properties at Finite Density

Abstract

We calculate the density dependence of the $\rho$-meson mass and coupling constant($g_{\rho NN}$) for $\rho$-nucleon-nucleon vertex at one loop using the lagrangian where the $\rho$-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 $\beta$-function for $\rho$-nucleon-nucleon coupling constant ($g_{\rho NN}$) and $\gamma$-function for $\rho$-meson mass (${\gamma }_{m_{\rho }}$). We found that the $\rho$-meson mass and the coupling constant for $g_{\rho NN}$ drop as density increases in the low energy limit.

24 pages, 10 figures, revised version

References in corpus (2)

• $Nd\to {}^{3}H\gamma$ with Effective Field Theory
• A Schematic Model for $\rho$-$a_1$ Mixing at Finite Density and In-Medium Effective Lagrangian

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