Renormalization Group Analysis of \rho-Meson Properties at Finite Density

TL;DR

This paper uses renormalization group techniques within a hidden local symmetry framework to analyze how the rho-meson mass and its coupling to nucleons change with increasing density, revealing a decrease at low energies.

Contribution

It introduces a density-dependent renormalization group analysis of rho-meson properties using a hidden local symmetry approach, which is a novel application in this context.

Findings

Rho-meson mass decreases with increasing density.

Rho-nucleon coupling constant drops as density increases.

Renormalization group coefficients depend on density or temperature.

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.